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LIGHT.
J.ONDON : PJlINTIin BV
SPOTTISWOODU AND CO., NKW-STHKKT SQVABIi
AND PARLIAMENT STBUET
NOTES
OF A COUESE OF NINE LECTURES ON
LIGHT
DELIVERED AT
THE ROYAL INSTITUTION OF GREAT BRITAIN
APRIL 8— JUNE 3, 1869
BY
JOHN TYNDALL, LL.D. F.B.S.
LONDON :
LONGMANS, OKEEN, AND CO.
1870.
[TJie right of translation is reserved.]
UP.
PREFACE.
THESE NOTES were prepared for the use of those who attended
my Lectures on Light last year, and were not intended for
further publication. Enquiries and requests regarding them
from teachers and students who have read them, cause me
now to think that the Notes may be useful beyond their
contemplated limits. The Messrs. Longman have therefore
undertaken their publication in a very cheap form.
To my friend Professor Goodeve, who has been kind
enough to look over the proofs, my best thanks are due
and tendered.
ROYAL INSTITUTION: May, 1870.
237353
CONTENTS.
General Considerations. Rectilinear Propagation of Light V .1
Formation of Images through small Apertures . . i . 2
Shadows ......... f»
Enfeeblement of Light by Distance ; Law of Inverse Square! r .3
Photometry, or the Measurement of Light . .- ,' '- « . 4
Brightness . *"'••' *•' . . . .6
Light requires Time to pass through Space f' . . .6
Aberration of Light . . » .-'....* . .7
Reflexion of Light (Catoptrics) — Plane Mirrors . . . .8
Verification of the Law of Reflexion ,. '^' . . . „
Reflexion from Curved Surfaces : Concave Mirrors . . .11
Caustics by Reflexion (Catacaustics) '. . ' '.""' ' '. l .13
Convex Mirrors ..... •<''.*>-v '" '* . 14
Refraction of Light (Dioptrics) . . .' * ' T' '" ' . ' ' .15
Opacity of Transparent Mixtures . «- .' . • .19
Total Reflexion . . . -:^ •. - '^v >' . 20
Lenses . .• . , . . « . .22
Converging Lenses . i . . •' * « '•' '• > * .'' • >»
Diverging Lenses . . < • .*' •- . . . , „
Vision and the Eye .-' ,^<; . . l^j . . . 23
Adjustment of the Eye : tTse of Spectacles . . . . .24
The Punctum Coecum . . . . . . .26
Persistence of Impressions , , . . . . .26
Bodies seen within the Eye . . . . . .27
The Stereoscope . . . . . . . . 2S
Nature of Light ; Physical theory of Reflexion and Refraction . . 29
viii Contents.
PAOH
Theory of Emission V . . . . . .30
Theory of Undulation . . . . . . .31
Prisms . » ,. ,» . . . . .34
Prismatic Analysis of Light : Dispersion . . . . „
Invisible Eays : Calorescence and Fluorescence . . . .35
Doctrine of Visual Periods . . . . . .36
Doctrine of Colours . . . . . . .37
Chromatic Aberration. Achromatism . . . . .38
Subjective Colours . . . . . . .39
Spectrum Analysis . . . . . . .40
Further Definition of Radiation and Absorption . . . .41
The pure Spectrum : Fraunhofer's Lines . . ; . .42
Reciprocity of Radiation and Absorption . . . . .43
Solar Chemistry . . . . . . . .44
Planetary Chemistry . . . . . . .45
Stellar Chemistry .........
Nebular Chemistry . . . . . . .46
The Red Prominences and Envelope of the Sun . . . - . „
The Rainbow . . . . . . .
Interference of Light .......
Diffraction, or the Inflexion of Light .....
Measurement of the Waves of Light . . . .
Colours of Thin Plates . . . . . »
Double Refraction . . . . .
Phenomena presented by Iceland Spar . . ,;4 . : <
Polarization of Light ..... ? I
Polarization of Light by Reflexion . . .J ;v
Polarization of Light by Refraction . . .
Polarization of Light by Double Refraction
Examination of Light transmitted through Iceland Spar .
Colours of Double-refracting Crystals in Polarized Light .
Rings surrounding the Axes of Crystals in Polarized Light
Elliptic and Circular Polarization .
Rotatory Polarization . . . . • , if > .
CONCLUSION * . . % * • .§
NOTES
ON
LIGHT
General Considerations. Rectilinear Propagation of Light.
1. The ancients supposed light to be produced and vision excited
by something emitted from the eye. The moderns hold vision to
be excited by something that strikes the eye from without. What
that something is we shall consider more closely subsequently.
2. Luminous bodies are independent sources of light. They
generate it and emit it, and do not receive their light from other
bodies. The sun, a star, a candle-flame, are examples.
3. Illuminated bodies are such as receive the light by which they
are seen from luminous bodies. A house, a tree, a man, are examples.
Such bodies scatter in all directions the light which they receive ;
this light reaches the eye, and through its action the illuminated
bodies are rendered visible.
4. All illuminated bodies scatter or reflect light, and they are dis-
tinguished from each other by the excess or defect of light which they
send to the eye. A white cloud in a dark-blue firmament is distin-
guished by its excess of light; a dark pine-tree projected against the
same cloud is distinguished through its defect of light.
5. Look at any point of a visible object. The light comes from
that point in straight lines to the eye. The lines of light, or rays as
they are called, that reach the pupil form a cone, with the pupil for a
base, and with the point for an apex. The point is always seen at
the place where the rays which form the surface of this cone inter-
sect each other, or, as we shall learn immediately, where they seem to
intersect each other.
6. Light, it has just been said, moves in straight lines; you see a
luminous object by means of the rays which it sends to the eye, but
you cannot see round a corner. A small obstacle that intercepts the
view of a visible point is always in the straight line between the eye
H
2 : Votes on Light.
und tlie point. , In ii darlVropm let a small hole be made in a window-
shutter, and let the sun "shine through the hole. A narrow luminous
beam will mark its course on the dust of the room, and the track of
the beam will be perfectly straight.
7. Imagine the aperture to diminish in size until the beam passing
through it and marking itself upon the dust of the room shall dwindle
to a mere line in thickness. In this condition the beam is what we
call a ray of light.
Formation of Images through small Apertures.
8. Instead of permitting the direct sunlight to enter the room by
the small aperture, let the light from some body illuminated by the
sun — a tree, a house, a man, for example — be permitted to enter. Let
this light be received upon a white screen placed in the dark room.
Every visible point of the object sends a straight ray of light through
the aperture. The ray carries with it the colour of the point from
which it issues, and imprints that colour upon the screen. The sum
total of the rays falling thus upon the screen produces an inverted
image of the object. The image is inverted because the rays cross
each other at the aperture.
9. Experimental Illustration. — Place a lighted candle in a small
camera with a small orifice in one of its sides, or a large one covered
by tinfoil. Prick the tinfoil with a needle; the inverted image of the
flame will immediately appear upon a screen placed to receive it. By
approaching the camera to the screen, or the screen to the camera,
the size of the image is diminished ; by augmenting the distance
between them, the size of the image is increased.
10. The boundary of the image is formed by drawing from every
point of the outline of the object straight lines through the aperture,
and producing these lines until they cut the screen. This could not
be the case if the straight lines and the light rays were not coincident.
11. Some bodies have the power of permitting light to pass freely
through them ; they are transparent bodies. Others have the power
of rapidly quenching the light that enters them ; they are opaque
bodies. There is no such thing as perfect transparency or perfect
opacity. The purest glass and crystal quench some rays ; the most
opaque metal, if thin enough, permits some rays to pass through it.
The redness of the London sun in smoky weather is due to the partial
transparency of soot for the red light. Pure water at great depths is
blue; it quenches more or less the red rays. Ice when seen in large
masses in the glaciers of the Alps is blue also.
Shadows.
12. As a consequence of the rectilinear motion of light, opaque
bodies cast shadows. If the source of light be a point, the shadow is
sharply defined ; if the source be a luminous surface, the perfect
shadow is fringed by an imperfect shadow called a penumbra.
Shadows. 3
13. When light emanates from a point, the shadow of a sphere
placed in the light is a divergent cone sharply defined.
14. When light emanates from a luminous globe, the perfect
shadow of a sphere equal to the globe in size will be a cylinder • it
will be bordered by a penumbra.
15. If the luminous sphere be the larger of the two, the perfect
shadow will be a convergent cone ; it will be surrounded by a penum-
bra. This is the character of the shadows cast by the earth and moon
in space ; for the sun is a sphere larger than either the earth or the
moon.
16. To an eye placed in the true conical shadow of the moon, the
sun is totally eclipsed ; to an eye in the penumbra, the sun appears
horned ; while to an eye placed beyond the apex of the conical shadow
and within the space enclosed by the surface of the cone produced,
the eclipse is annular. All these eclipses are actually seen from time
to time from the earth's surface.
17. The influence of magnitude maybe experimentally illustrated
by means of a batswing or fishtail flame ; or by a flat oil or paraffin
flame. Holding an opaque rod between the flame and a white screen,
the shadow is sharp when the edge of the flame is turned towards the
rod. When the broad surface of the flame is pointed to the rod, the
real shadow is fringed by a penumbra.
18. As the distance from the screen increases, the penumbra
encroaches more and more upon the perfect shadow, and finally
obliterates it.
19. It is the angular magnitude of the sun that destroys the
sharpness of solar shadows. In sunlight, for example, the shadow of
a hair is sensibly washed away at a few inches distance from the
surface on which it falls. The electric light, on the contrary,
emanating as it does from small carbon points, casts a defined
shadow of a hair upon a screen many feet distant.
Enfeeblement of Light by Distance; Law of Inverse Squares.
20. Light diminishes in intensity as we recede from the source of
light. If the luminous source be a point, the intensity diminishes as
the square of the distance increases. Calling the quantity of light
falling upon a given surface at the distance of a foot or a yard —
1, the quantity falling on it at a distance of 2 feet or 2 yards is ^,
at a distance of 3 feet or 3 yards it is -^, at a distance of 10 feet or
10 yards it would be T-^-, and so on. This is the meaning of the law
of inverse squares as applied to light.
21. Experimental Ilhtstrations.— Pl&ce your source of light,
which may be a candle-flame — though the law is in strictness truo
only for points — at a distance say of 9 feet from a white screen.
Hold a square of pasteboard, or some other suitable material, at a
4 Notes on Light.
distance of 2^ feet from the flame, or ^th of the distance of \ the
screen. The sqtfare casts a shadow upon the screen.
22. Assure yourself that the area of this shadow is sixteen times
that of the square which casts it; a student of Euclid will see in a
moment that this must be the case, and those who are not geometers
can readily satisfy themselves by actual measurement. Dividing, for
example, each side of a square sheet of paper into four equal parts,
and folding the sheet at the opposite points of division, a small square
is obtained y^gth of the area of the large one. Let this small square,
or one equal to it, be your shadow- casting body. Held at 2^ feet
from the flame, its shadow upon the screen 9 feet distant will be
exactly covered by the entire sheet of paper. When therefore the
small square is removed, the light that fell upon it is diffused over
sixteen times the area on the screen ; it is therefore diluted to T^th
of its former intensity. That is to say, by augmenting the distance
four-fold we diminish the light sixteen-fold.
23. Make the same experiment by placing a square at a distance
of 3 feet from the source of light and 6 from the screen. The
shadow now cast by the square will have nine times the area of the
square itself; hence the light falling on the square is diffused over
nine times the surface upon the screen. It is therefore reduced to
•|th of its intensity. That is to say, by trebling the distance from
the source of light we diminish the light nine-fold.
24. Make the same experiment at a distance of 4^- feet from the
source. The shadow here will be four times the area of the shadow-
casting square, and the light diffused over the greater square will be
reduced to ^th of its former intensity. Thus, by doubling the dis-
tance from the source of light we reduce the intensity of the light
four-fold.
25. Instead of beginning with a distance of 2J feet from the
source, we might have begun with a distance of 1 foot. The area of
the shadow in this case would be eighty-one times that of the square
which casts it ; proving that at 9 feet distance the intensity of the
light is -j^y of what it is at 1 foot distance.
26. Thus when the distances are
1, 2, 3, 4, 5, 6, 7, 8, 9, &c,
the relative intensities are
1> ?> 4> TB") ^5> ^V? TIT? ~tti "gT> &C>
This is the numerical expression of the law of inverse squares.
Photometry, or the Measurement of Light.
27. The law just established enables us to compare one light with
another, and to express by numbers their relative illuminating
powers.
28. The more intense a light, the darker is the shadow which it
Photometry, or the Measurement of Light. 5
casts; in other words, the greater is the contrast between the
illuminated and unilluminated surface.
29. Place an upright rod in front of a white screen and a candle-
flame at some distance behind the rod, the rod casts a shadow upon
the screen.
30. Place a second flame by the side of the first, a second shadow
is cast, and it is easy to arrange matters so that the shadows shall be
close to each other, thus offering themselves for easy comparison to
the eye. If when the lights are at the same distance from the screen
the two shadows are equally dark, then the two lights have the same
illuminating power.
31. But if one of the shadows be darker than the other, it is
because its corresponding light is brighter than the other. Remove
the brighter light farther from the screen, the shadows gradually
approximate in depth, and at length the eye can perceive no dif-
ference between them. The shadow corresponding to each light is
now illuminated by the other light, and if the shadows are equal it
is because the quantities of light cast by both upon the screen are
equal.
32. Measure the distances of the two lights from the screen, and
square these distances. The two squares will express the relative
illuminating powers of the two lights. Supposing one distance to
be 3 feet and the other 5, the relative illuminating powers are as 9
to 25.
Brightness.
33. But if light diminishes so rapidly with the distance — if, for
example, the light of a candle at the distance of a yard is 100 times
more intense than at the distance of 10 yards — how is it that on
looking at lights in churches or theatres, or in large rooms, or at
our street lamps, a light 10 yards off appears almost, if not quite, as
bright as one close at hand ?
34. To answer this question I must anticipate matters so far as to
say that at the back of the eye is a screen, woven of nerve-filaments,
named the retina ; and that when we see a light distinctly, its image
is formed upon this screen. This point will be fully developed
when we come to treat of the eye. Now the sense of external brightness
depends upon the brightness of this internal retinal image, and not
upon its size. As we retreat from a light, its image upon the retina
becomes smaller, and it is easy to prove that the diminution follows
the law of inverse squares. That at a double distance the area of the
retinal image is reduced to one-fourth, at a treble distance to one-
ninth, and so on. The concentration of light accompanying this
decrease of magnitude exactly atones for the diminution due to dis-
tance ; hence, if the air be clear, the light, within wide variations
of distance, appears equally bright to the observer.
35. If an eye could be placed behind the retina, the augmentation
6 Notes on Light.
or diminution of the image, with the decrease or increase of dis-
tance, might be actually observed. An exceedingly simple apparatus
enables us to illustrate this point. Take a pasteboard or tin tube,
three or four inches wide and three or four inches long, and cover one
end of it with a sheet of tinfoil, and the other end with tracing-paper,
or ordinary letter paper wetted with oil or turpentine. Prick the
tinfoil with a needle, and turn the aperture towards a candle-name.
An inverted image of the flame will be seen on the translucent paper
screen by the eye behind it. As you approach the flame the image
becomes larger, as you recede from the flame the image becomes
smaller ; but the brightness remains throughout the same. It is so with
the image upon the retina.
36. If a sunbeam be permitted to enter a room through a small
aperture, the spot of light formed on a distant screen will be round,
whatever be the shape of the aperture ; this curious effect is due to
the angular magnitude of the sun. Were the sun a, point, the light
spot would be accurately of the same shape as the aperture. Supposing
then the aperture to be square, every point of light round the sun's
periphery sends a small square to the screen. These small squares are
ranged round a circle corresponding to the periphery of the sun ;
through their blending and overlapping they produce a rounded out-
line. The spots of light which fall through the apertures of a tree's
foliage on the ground are rounded for the same reason.
Light requires Time to pass through Space.
37. This was proved in 1675 and 1676 by an eminent Dane, named
Olaf Rcemer, who was then engaged with Cassini in Paris in observing
the eclipses of Jupiter's moons. The planet, whose distance from the
sun is 475,693,000 miles, has four satellites. We are now only con-
cerned with the one nearest to the planet. Roemer watched this
moon, saw it move round in front of the planet, pass to the other
side of it, and then plunge into Jupiter's shadow, behaving like a
lamp suddenly extinguished : at the other edge of the shadow he
saw it reappear like a lamp suddenly lighted. The moon thus acted
the part of a signal light to the astronomer, which enabled him to
tell exactly its time of revolution. The period between two suc-
cessive lightings up of the lunar lamp gave this time. It was found
to be 42 hours, 28 minutes, and 35 seconds.
38. This observation was so accurate, that having determined the
moment when the moon emerged from the shadow, the moment of its
hundredth appearance could also be determined. In fact it would be
100 times 42 hours, 28 minutes, 35 seconds, from the first observation.
39. Roemer's first observation was made when the earth was in the
part of its orbit nearest Jupiter. About six months afterwards, when
the little moon ought to make its appearance for the hundredth time,
it was found unpunctual, being fully 15 minutes behind its calculated
Light requires Time to pass through Space. 7
time. Its appearance, moreover, had been growing gradually later, as
the earth retreated towards the part of its orbit most distant from
Jupiter.
40. Rcemer reasoned thus : — ' Had I been able to remain at the
other side of the earth's orbit, the moon might have appeared always
at the proper instant ; an observer placed there would probably have
seen the moon 15 minutes ago, the retardation in my case being due
to the fact that the light requires 15 minutes to travel from the place
where my first observation was made to my present position.'
41. This Hash of genius was immediately succeeded by another.
' If this surmise be correct,' Rcemer reasoned, ' then as I approach
Jupiter along the other side oi the earth's orbit, the retardation ought
to become gradually less, and when I reach the place of my first obser-
vation there ought to be no retardation at all.' He found this to be
the case, and thus proved not only that light required time to pass
through space, but also determined its rate of propagation.
42. The velocity of light as determined by Rcemer is 192,500 miles
in a second.
The Aberration of Light.
The astounding velocity assigned to light by the observations of
Roemer received the most striking confirmation from the English
astronomer Bradley in the year 1723. In Kew Gardens to the present
hour there is a sundial to mark the spot where Bradley discovered
the aberration of light.
43. If we move quickly through a rain-shower which falls vertically
downwards, the drops will no longer seem to fall vertically, but will
appear to meet us. A similar deflection of the stellar rays by the
motion of the earth in its orbit is called the aberration of light.
44. Knowing the speed at which we move through a vertical rain-
shower, and knowing the angle at which the rain-drops appear to
descend, we can readily calculate the velocity of the falling drops of
rain. So likewise, knowing the velocity of the earth in its orbit, and
the deflection of the rays of light produced by the earth's motion, we
can immediately calculate the velocity of light.
45. The velocity of light, as determined by Bradley, is 191,515
miles per second — a most striking agreement with the result of
Rcemer.
46. This velocity has also been determined by experiments over
terrestrial distances. M. Fizeau found it thus to be 194,677 miles a
second, while the later experiments of M. Foucault made it 185,177
miles a second.
47. 'A cannon-ball,' says Sir John Herschel, 'would require
seventeen years to reach the sun, yet light travels over the same space
in eight minutes. The swiftest bird, at its utmost speed, would re-
quire nearly three weeks to make the tour of the earth. Light
performs the same distance in much less time than is necessary for a
8 Notes on Light.
single stroke of its wing ; yet its rapidity is but commensurate with the
distance it has to travel. It is demonstrable that light cannot reach our
system from the nearest of the fixed stars in less than five years, and
telescopes disclose to us objects probably many times more remote.'
The Reflexion of Light (Catoptrics) — Plane Mirrors.
48. When light passes from one optical medium to another, a
portion of it is always turned back or reflected.
49. Light is regularly reflected by a polished surface ; but if the
surface be not polished the light is irregularly reflected or scattered.
50. Thus a piece of ordinary drawing-paper will scatter a beam of
light that falls upon it so as to illuminate a room. A plane mirror
receiving the sunbeam will reflect it in a definite direction, and
illuminate intensely a small portion of the room.
51. If the polish of the mirror were perfect it would be invisible,
we should simply see in it the images of other objects; if the room
were without dust particles, the beam passing through the air would
also be invisible. It is the light scattered by the mirror and by the
particles suspended in the air which renders them visible.
52. A ray of light striking as a perpendicular against a reflecting
surface is reflected back along the perpendicular ; it simply retraces
its own course. If it strike the surface obliquely, it is reflected
obliquely.
53. Draw a perpendicular to the surface at the point where the
ray strikes it ; the angle enclosed between the direct ray and this per-
pendicular is called the angle of incidence. The angle enclosed by
the reflected ray and the perpendicular is called the angle of reflexion.
54. It is a fundamental law of optics that the angle of incidence is
equal to the angle of reflexion.
Verification of the Law of Reflexion.
55. Fill a basin with water to the brim, the water being blackened
by a little ink. Let a small plummet — a small lead bullet, for example
— suspended by a thread, hang into the water. The water is to be our
horizontal mirror, and the plumb-line our perpendicular. Let the
plummet hang from the centre of a horizontal scale, with inches
marked upon it right and left from the point of suspension, which is
to be the zero of the scale. A lighted candle is to be placed on one
side of the plumb-line, the observer's eye being at the other.
56. The question to be solved is this : — How is the ray which
strikes the liquid surface at the foot of the plumb-line reflected ?
Moving the candle along the scale, so that the tip of its flame shall
stand opposite different numbers, it is found that, to see the reflected
tip of the flame in the direction of the foot of the plumb-line, the line
of vision must cut the scale as far on the one side of that line as the
Verification of the Law of Reflexion. 9
candle is on the other. In other words, the ray reflected from the
foot of the perpendicular cuts the scale accurately at the candle's dis-
tance on the other side of the perpendicular. From this it immediately
follows that the angle of incidence is equal to the angle of reflexion.
57. With. an artificial horizon of this kind, and employing a
theodolite to take the necessary angles, the law has been established
with the most rigid accuracy. The angle of elevation to a star being
taken by the instrument, the telescope is then pointed downwards
to the image of the star reflected from the artificial horizon. It is
always found that the direct and reflected rays enclose equal angles
with the horizontal axis of the telescope, the reflected ray being as far
below the horizontal axis as the direct ray is above it. On account
of the star's distance the ray which strikes the reflecting surface is
parallel with the ray which reaches the telescope directly, and from this
follows, by a brief but rigid demonstration, the law above enunciated.
58. The path described by the direct and reflected rays is the
shortest possible.
59. When the reflecting surface is roughened, rays from different
points, more or less distant from each other, reach the eye. Thus, a
breeze crisping the surface of the Thames or Serpentine sends to the
eye, instead of single images of the lamps upon their margin, pillars
of light. Blowing upon our basin of water, we also convert the
reflected light of our candle into a luminous column.
60. Light is reflected with different energy by different substances.
At a perpendicular incidence, only 18 rays out of every 1000 are
reflected by water, 25 rays per 1000 by glass, while 666 per 1000
are reflected by mercury.
61. When the rays strike obliquely, a greater amount of light than
that stated in 60 is reflected by water and glass. Thus, at an inci-
dence of 40°, water reflects 22 rays ; at 60°, 65 rays ; at 80°, 333
rays; and at 89^-° (almost grazing the surface), it reflects 721 rays
out of every 1000. This is as much as mercury reflects at the same
incidence.
62. The augmentation of the light reflected as the obliquity
of incidence is increased may be illustrated by our basin of water.
Hold the candle so that its rays enclose a large angle with the liquid
surface, and notice the brightness of its image. Lower both the
candle and the eye until the direct and reflected rays as nearly as
possible graze the liquid surface ; the image of the flame is now
much brighter than before.
Reflexion from Looking-glasses. — Various instructive experiments
with a looking-glass may here be performed and understood.
63. Note first when a candle is placed between the glass and the
eye, so that a line from the eye through the candle is perpendicular
to the glass, that one well-defined image of the candle only is seen.
64. Let the eye now be moved so as to receive an oblique reflexion;
••^9 image is no longer single, a series of images at first partially
10 Notes on Light.
overlapping each other being seen. By rendering the incidence
sufficiently oblique these images, if the glass be sufficiently thick,
may be completely separated from each other.
65. The first image of the series arises from the reflexion of the
light from the anterior surface of the glass.
66. The second image, which is usually much the brightest, arises
from reflexion at the silvered surface of the glass. At large in-
cidences, as we have just learned, metallic reflexion far transcends
that from glass.
67. The other images of the series are produced by the reverbera-
tion of the light from surface to surface of the glass. At every return
from the silvered surface a portion of the light quits the glass and
reaches the eye, forming an image ; a portion is also sent back to the
silvered surface, where it is again reflected. Part of this reflected
beam also reaches the eye and yields another image. This process
continues : the quantity of light reaching the eye growing gradually
less, and, as a consequence, the successive images growing dimmer,
until finally they become too dim to be visible.
68. A very instructive experiment illustrative of the augmentation
of the reflexion from glass, through augmented obliquity, may here be
made. Causing the candle and the eye to approach the looking-glass,
the first image becomes gradually brighter ; and you end by rendering
the image reflected from the glass brighter, more luminous, than that
reflected from the metal. Irregularities in. the reflexion from looking-
glasses often show themselves ; but with a good glass — and there are
lew glasses so defective as not to possess, at all events, some good
portions — the succession of images is that here indicated.
69. Position and Character of Images in Plane Mirrors.— The
image in a plane mirror appears as far behind the mirror as the object
is in front of it. This follows immediately from the law which
announces the equality of the angles of incidence and reflexion.
Draw a line representing the section of a plane mirror; place a
point in front of it. Rays issue from that point, are reflected from the
mirror, and strike the pupil of the eye. The pupil is the base of
a cone of such rays. Produce the rays backward ; they will intersect
behind the mirror, and the point will be seen as if it existed at the
place of intersection. The place of intersection is easily proved to be
as far behind the mirror as the point is in front of it.
70. Exercises in determining the positions of images in a plane
mirror, the positions of the objects being given, are here desirable.
The image is always found by simply letting fall a perpendicular
from each point of the object, and producing it behind the mirror, so
as to make the part behind equal to the part in front. We thus learn
that the image is of the same size and shape as the object, agreeing
with it in all respects save one — the image is a lateral inversion of
the object.
71. This inversion enables us, by means of a mirror, to read
Verification of the Law of Reflexion. 11
writing written backward, as if it were written in the usual way.
Compositors arrange their type in this backward fashion, the type
being reversed by the process of printing. A looking-glass enables
us to read the type as the printed page.
72. Lateral inversion comes into play when we look at our own
faces in a glass. The right cheek of the object, for example, is the
left cheek of the image ; the right hand of the object the left hand of
the image, &c. The hair parted on the left in the object is seen
parted to the right of the image, &c.
73. A plane mirror half the height of an object gives an image
which embraces the whole height. This is readily deduced from
what has gone before.
74. If a plane mirror be caused to move parallel with itself, the
motion of an image in the mirror moves with twice its rapidity.
75. The same is true of a rotating mirror: when a plane mirror is
caused to rotate, the angle described by the image is twice that
described by the mirror.
76. In a mirror inclined at an angle of 45 degrees to the horizon,
the image of an erect object appears horizontal, while the image of a
horizontal object appears erect.
77. An object placed between two mirrors enclosing an angle
yields a number of images depending upon the angle enclosed by the
mirrors. The smaller the angle, the greater is the number of images.
To find the number of images, divide 360° by the number of degrees
in the angle enclosed by the two mirrors, the quotient, if a whole
number, will be the number of images, plus one, or it will include the
images and the object. The construction of the kaleidoscope depends
on this.
78. When the angle becomes 0, — in other words, when the mirrors
are parallel, — the number of images is infinite. Practically, however,
we see between parallel mirrors a long succession of images, which
become gradually feebler, and finally cease to be sensible to the eye.
Reflexion from Curved Surfaces : Concave Mirrors.
79. It has been already stated and illustrated that light moves in
straight lines, which receive the name of rays. Such rays may be
either divergent, parallel, or convergent.
80. Rays issuing from terrestrial points are necessarily divergent.
Rays from the sun or stars are, in consequence of the immense dis-
tances of these objects, sensibly parallel.
81. By suitably reflecting them, we can render the rays from
terrestrial sources either parallel or convergent. This is done by
means of concave mirrors.
82. In its reflexion from such mirrors, light obeys the law already
enunciated for plane mirrors. The angle of incidence is equal to the
angle of reflexion.
83. Let M N be a very small portion of the circumference of a circle
12
Notes on Light.
with its centre at O. Let the line a x, passing through the centre, cut
the arc M N into two equal parts at a. Then imagine the curve M N
twirled round a a? as a fixed axis ; the curve would describe part of a
spherical surface. Suppose the surface turned towards x to be
silvered over, we should then have a concave spherical reflector ; and
we have now to understand the action of this reflector upon light.
FIG. 1.
84. The line a x is the principal axis of the mirror.
85. All rays from a point placed at the centre O strike the surface
of the mirror as perpendiculars, and after reflexion return to O.
86. A luminous point placed on the axis beyond O, say at #, throws
a divergent cone of rays upon the mirror. These rays are rendered
convergent on reflexion, and they intersect each other at some point
on the axis between the centre O and the mirror. In every case the
direct and the reflected rays (x m and m x' for example) enclose equal
angles with the radius (O m) drawn to the point of incidence.
87. Supposing x to be exceedingly distant, say as far away as the
sun from the small mirror, — or, more correctly, supposing it to be
infinitely distant, — then the rays falling upon the mirror will be
parallel. After reflexion such rays intersect each other, at a point
midway between the mirror and its centre.
88. This point, which is marked F in the figure, is the principal
focus of the mirror ; that is to say, the principal focus is the focus of
parallel rays.
89. The distance between the surface of the mirror and its prin-
cipal focus is called the focal distance.
90. In optics, the position of an object and of its image are always
exchangeable. If a luminous point be placed in the principal focus,
the rays from it will, after reflexion, be parallel. If the point be
placed anywhere between the principal focus and the centre O, the
rays after reflexion will cut the axis at some point beyond the centre.
91. If the point be placed between the principal focus F and the
Reflexion from Curved Surfaces. 13
mirror, the rays after reflexion will be divergent — they will not inter-
sect at all — there will be no real focus.
92. But if these divergent rays be produced backwards, they will
intersect behind the mirror, and form there what is called a virtual, or
imaginary focus.
Before proceeding further, it is necessary that these simple details
should be thoroughly mastered. Given the position of a point in
the axis of a concave mirror, no difficulty must be experienced in
finding the position of the image of that point, nor in determining
whether the focus is virtual or real.
93. It will thus become evident that while a point moves from
an infinite distance to the centre of a spherical mirror, the image of
that point moves only over the distance between the principal focus
and the centre. Conversely, it will be seen that during the passage
of a luminous point from the centre to the principal focus, the image
of the point moves from the centre to an infinite distance.
94. The point and its image occupy what are, called conjugate foci.
If the last note be understood, it will be seen that the conjugate foci
move in opposite directions, and that they coincide at the centre of
the mirror.
95. If instead of a point an object of sensible dimensions be placed
beyond the centre of the mirror, an inverted image of the object
diminished in size will be formed between the centre and the principal
focus.
96. If the object be placed between the centre and the principal
focus, an inverted and magnified image of the object will be formed
beyond the centre. The positions of the image and its object are, it
will be remembered, convertible.
97. In the two cases mentioned in 95 and 96 the image is formed in
the air in front of the mirror. It is a real image. But if the obj ect be
placed between the principal focus and the mirror, an erect and mag-
nified image of the object is seen behind the mirror. The image is
here virtual. The rays enter the eye as z/they came from an object
behind the mirror.
98. It is plain that the images seen in a common looking-glass are
all virtual images.
99. It is now to be noted that what has been here stated regarding
the gathering of rays to a single focus by a spherical mirror is only
true when the mirror forms a small fraction of the spherical surface.
Even then it is only practically, not strictly and theoretically, true.
Caustics by Reflexion (Catacaustics).
100. When a large fraction of the spherical surface is employed as
a mirror, the rays are not all collected to a point ; their intersections,
14 Notes on Light.
on the contrary, form a luminous surface, which in optics is called a
caustic (German, Brennflache).
101. The interior surface of a common drinking-glass is a curved
reflector. Let the glass be nearly filled with milk, and a lighted
candle placed beside it ; a caustic curve will be drawn upon the
surface of the milk. A carefully bent hoop, silvered within, also
shows the caustic very beautifully. The focus of a spherical mirror
is the cusp of its caustic.
102. Aberration. — The deviation of any ray from this cusp is
called the aberration of the ray. The inability of a spherical mirror
to collect all the rays falling upon it to a single point is called the
spherical aberration of the mirror.
103. Real images, as already stated, are formed in the air in front
of a concave mirror, and they may be seen in the air by an eye placed
among the divergent rays beyond the image. If an opaque screen,
say of thick paper, intersect the image, it is projected on the screen
and is seen in all positions by an eye placed in front of the screen.
If the screen be semi-transparent, say of ground glass or tracing-
paper, the image is seen by an eye placed either in front of the screen
or behind it. The images in phantasmagoria are thus formed.
Concave spherical surfaces are usually employed as burning-
mirrors. By condensing the sunbeams with a mirror 3 feet in
diameter and of 2 feet focal distance, very powerful effects may be
obtained. At the focus, water is rapidly boiled, and combustible
bodies are immediately set on fire. Thick paper bursts into flame
with explosive violence, and a plank is pierced as with a hot iron.
Convex Mirrors.
104. In the case of a convex spherical mirror the positions of its
foci and of its images are found as in the case of a concave mirror.
But all the foci and all the images of a convex mirror are virtual.
105. Thus to find the principal focus you draw parallel rays which,
on reflection, enclose angles with the radii equal to those enclosed by
the direct rays. The reflected rays are here divergent ; but on being
produced backwards, they intersect at the principal focus behind the
mirror.
106. The drawing of two lines suffices to fix the position of the
image of any point of an object either in concave or convex spherical
mirrors. A ray drawn from the point through the centre of the
mirror will be reflected through the centre ; a ray drawn parallel to
the axis of the mirror will, after reflection, pass, or its production
will pass, through the principal focus. The intersection of these two
reflected rays determines the position of the image of the point.
Applying this construction to objects of sensible magnitude, it follows
that the image of an object in a convex mirror is always erect and
diminished.
107. If the mirror be parabolic instead of spherical, all parallel
Refraction of Liyht.
15
rays falling upon the mirror are collected to a point at its focus ;
conversely, a luminous point placed at the focus sends forth parallel
rays : there is no aberration. If the mirror be elliptical, all rays emitted
from one of the foci of the ellipsoid are collected together at the
other. Parabolic reflectors are employed in lighthouses, where it is
an object to send a powerful beam, consisting of rays as nearly as pos-
sible parallel, far out to sea. In this case the centre of the flame is
placed in the focus of the mirror; but, inasmuch as the flame is of
sensible magnitude, and not a mere point, the rays of the reflected
beam are not accurately parallel.
The Refraction of Light (Dioptrics).
108. We have hitherto confined our attention to the portion of a
beam of light which rebounds from the reflecting surface. But in
general, a portion of the beam also enters the reflecting substance,
being rapidly quenched when the substance is opaque (see note 11),
and freely transmitted when the substance is transparent.
109. Thus in the case of water, mentioned in note 60, when the
incidence is perpendicular all the rays are transmitted, save the 18
referred to as being reflected. That is to say, 982 out of every 1000
rays enter the water and pass through it.
110. So likewise in the case of mercury, mentioned in the same
note ; 334 out of every 1 000 rays falling on the mercury at a perpen -
dicular incidence, enter the metal and are quenched at a minute depth
beneath its surface.
We have now to consider that portion of the luminous beam which
enters the reflecting substance ; taking, as an illustrative case, the
passage from air into water.
111. If the beam fall upon the water as a perpendicular, it pur-
sues a straight course through the water : if the incidence be oblique,
the direction of the beam is changed
at the point where it enters the water.
112. This bending of the beam is
called refraction. Its amount is dif-
ferent in different substances.
113. The refraction of light obeys
a perfectly rigid law which must be
clearly understood. Let A B C D,
fig. 2, be the section of a cylindrical
vessel which is half filled with water,
its surface being AC. E is the centre
of the circular section of the cylinder,
and B D is a perpendicular to the
surface at E. Let the cylindrical en-
velope of the vessel be opaque, say of
brass or tin, and let an aperture be imagined in it at B, through
16 Notes on Light.
which a narrow light-beam passes to the point E. The beam will
pursue a straight course to D without turning to the right or to the
left,
114. Let the aperture be imagined at m, the beam striking the
surface of the water at E obliquely. Its course on entering the liquid
will be changed ; it will pursue the track E n.
115. Draw the line m o perpendicular to B D, and also the line
n p perpendicular to the same B D. It is always found that m o
divided by n p is a constant quantity, no matter what may be the
angle at which the ray enters the water.
116. The angle marked x above the surface is called the angle
of incidence ; the angle at y below the surface is called the angle of
refraction ; and if we regard the radius of the circle A B C D as
unity or 1, the line m o will be the sine of the angle of incidence;
while the line n p will be the sine of the angle of refraction.
117. Hence the all-important optical law — The sine of the angle of
incidence divided by the sine of the angle of refraction is a constant
quantity. However these angles may vary in size, this bond of rela-
tionship is never severed. If one of them be lessened or augmented,
the other must diminish or increase so as to obey this law. Thus if
the incidence be along the dotted line m' E, the refraction will be along
the line E n'j but the ratio of mf o' to n' p' will be precisely the same
as that of m o to n p,
118. The constant quantity here referred to is called the index of
refraction.
119. One word more is necessary to the full comprehension of the
term sine, and of the experimental demonstration of the law of
refraction. When one number is divided by another the quotient
is called the ratio of the one number to the other. Thus 1 divided
by 2 is J-, and this is the ratio of 1 to 2. Thus also 2 divided by 1
is 2, and this is the ratio of 2 to 1. In like manner 12 divided by
3 is 4, and this is the ratio of 12 to 3. Conversely, 3 divided by 12
is ^, and this is the ratio of 3 to 12.
120. In aright-angled triangle the ratio of any side to the hypo-
thenuse is found by dividing that side by the hypothenuse. This
ratio is the sine of the angle opposite to the side, however large or
small the triangle may be. Thus in fig. 2 the sine of the angle x in
the right-angled triangle E o m is really the ratio of the line o m to
the hypothenuse E w; it would be expressed in a fractional form
thus, — . In like manner the sine of y is the ratio of the line n p
to the hypothenuse E n, and would be expressed in a fractional form
thus, JJT-. These fractions are the sines of the respective angles,
whatever be the length of the line E m or E n. In the particular
case above referred to, where these lines are considered as units, the
The Refraction of Light.
17
77?, 0
np
fractions — p and -y- , or in other words m o and n p, become, as stated,
the sines of the respective angles. We are now prepared to under-
stand a simple but rigid demonstration of the law of refraction.
FIG. 3.
....
121. MLJKisa cell with parallel glass sides and one opaque
end M L. The light of a candle placed at A falls into the vessel,
the end M L casting a shadow which reaches to the point E. Fill the
vessel with water, — the shadow retreats to H through the refraction
of the light at the point where it enters the water.
122. The angle enclosed between M E and M L is equal to the
angle of incidence rr, and in accordance with the definition given
L E L H
in 120
is its sine; while Trrr is the sine of the angle of re-
fraction y. All these lines can be either measured or calculated.
If they be thus determined, and if the division be actually made, it
L E L H
will always be found that the two quotients TTF~P and AFT? stand in
a constant ratio to each other, whatever the angle may be at which
the light from A strikes the surface of the liquid. This ratio in the
4
case of water is -q, or, expressed in decimals, 1*333.*
123. When the light passes from air into water, the refracted ray
is bent towards the perpendicular. This is generally, but not always,
the case when the light passes from a rarer to a denser medium.
124. The principle of reversibility which runs through the whole
of optics finds illustration here. When the ray passes from water to
air it is bent from the perpendicular: it accurately reverses its course.
125. If instead of water we employed vinegar the ratio would be
1-344; with brandy it would be 1*360; with rectified spirit of wine
1-372; with oil of almonds or with olive oil T470; with spirit of
* More accurately, 1-336.
C
18 Notes on Light.
turpentine 1/605; with oil of aniseed 1*538; with oil of bitter
almonds 1*471; with bisulphide of carbon T678; with phosphorus
2-24.
126. These numbers express the indices of refraction of the
various substances mentioned ; all of them refract the light more
powerfully than water, and it is worthy of remark that all of them,
except vinegar, are combustible substances.
127. It was the observation on the part of Newton, that, having
regard to their density, 'unctuous substances' as a general rule re-
fracted light powerfully, coupled with the fact, that the index of
refraction of the diamond reached, according to his measurements,
so high a figure as 2'439, that caused him to foresee the possible
combustible nature of the diamond. The bold prophecy of Newton*
has been fulfilled, the combustion of a diamond being one of the
commonest experiments of modern chemistry.
128. It is here worth noting that the refraction by spirit of tur-
pentine is greater than that by water, though the density of the
spirit is to that of the water as 874 is to 1000. A ray passing obliquely
from the spirit of turpentine into water is bent from the perpendicular,
though it passes from a rarer to a denser medium ; while a ray
passing from water into the spirit of turpentine is bent towards the
perpendicular, though it passes from a denser to a rarer medium.
Hence the necessity for the words ' not always' employed in 123.
129. If a ray of light pass through a refracting plate with parallel
surfaces, or through any number of plates with parallel surfaces, on
regaining the medium from which it started, its original direction is
restored. This follows from the principle of reversibility already
referred to.
130. In passing through a refracting body, or through any number
of refracting bodies, the light accomplishes its transit in the minimum
of time. That is to say, given the velocity of light in the various
media, the path chosen by the ray, or, in other words, the path
which its refraction imposes upon the ray, enables it to perform
its journey in the most rapid manner possible.
131. Eefraction always causes water to appear shallower, or a
transparent plate of any kind thinner, than it really is. The lifting
up of the lower surface of a glass cube, through this cause, is very
remarkable.
132. To understand why the water appears shallower, fix your
attention on a point at its bottom, and suppose the line of vision from
that point to the eye to be perpendicular to the surface of the water.
Of all rays issuing from the point, the perpendicular one alone
reaches the eye without refraction. Those close to the perpendi-
cular, on emerging from the water, have their divergence augmented
* ' Car ce grand homrae, qui mettait la plus grande severite dans ses expe-
riences, et la plus grande reserve dans ses conjectures, n'hesitait jamaisa suivre
les consequences d'une verite aussi loin qu'elle pouvait le conduire.' — BIOT.
The Re/r action of Light. 1 9
by refraction. Producing these divergent rays backwards, they in-
tersect at a point above the real bottom, and at this point the bottom
will be seen.
133. The apparent shallowness is augmented by looking obliquely
into the water.
134. In consequence of this apparent rise of the bottom, a straight
stick thrust into water is bent at the. surface from the perpendicular.
Note the difference between the deportment of the stick and of a
luminous beam. The beam on entering the water is bent towards
the perpendicular.
135. This apparent lifting of the bottom when water is poured into
a basin brings into sight an object at the bottom of the basin which is
unseen when the basin is empty.
Opacity of Transparent Mixtures.
136. Reflexion always accompanies refraction ; and if one of these
disappear, the other will disappear also. A solid body immersed in
a liquid having the same refractive index as the solid, vanishes ; it
is no more seen than a portion of the liquid itself of the same size
would be seen.
137. But in the passage from one medium to another of a different
refractive index, light is always reflected ; and this reflexion may be
so often repeated as to render the mixture of two transparent substances
practically impervious to light. It is the frequency of the reflexions
at the limiting surfaces of air and water that renders foam opaque.
The blackest clouds owe their gloom to this repeated reflexion, which
diminishes their transmitted light. Hence also their whiteness by
reflected light. To a similar cause is due the whiteness and imper-
viousness of common salt, and of transparent bodies generally when
crushed to powder. The individual particles transmit light freely ;
but the reflexions at their surfaces are so numerous that the light is
wasted in echoes before it can reach to any depth in the powder.
138. The whiteness and opacity of writing-paper are due mainly to
the same cause. It is a web of transparent fibres, not in optical con-
tact, which intercept the light by repeatedly reflecting it.
139. But if the interstices of the fibres be filled by a body of the
same refractive index as the fibres themselves, the reflexion at their
limiting surfaces is destroyed, and the paper is rendered transparent.
This is the philosophy of the tracing-paper used by engineers. It is
saturated with some kind of oil, the lines of maps and drawings being
easily copied through it afterwards. Water augments the transparency
of paper, as it darkens a white towel ; but its refractive index is too
low to confer on either any high degree of transparency. It however
renders certain minerals, which are opaque when dry, translucent.
140. The higher the refractive index the more copious is the
reflexion. The refractive index of water, for example, is 1*336; that
c2
20 Notes on Light.
of glass is 1-5. Hence the different quantities of light reflected by
water and glass at a perpendicular incidence, as mentioned in note GO.
It is its enormous refractive strength that confers such brilliancy
upon the diamond.
Total Reflexion.
Bead notes 123 and 124; then continue here.
141. When the angle of incidence from air into water is nearly 90°,
that is to say, when the ray before entering the water just grazes its
surface, the angle of refraction is 48-1°. Conversely, when a ray passing
from water into air strikes the surface at an angle of 48^-° it will, on
its emergence, just graze the surface of the water.
142. If the angle which the ray in water encloses with the per-
pendicular to the surface be greater than 48^°, the ray will not quit
the water at all: it will be totally reflected at the surface.
143. The angle which marks the limit where total reflexion begins
is called the limiting angle of the medium. For water this angle is
48° 27', for flint glass it is 38° 41', while for diamond it is 23° 42'.
144. Realise clearly that a bundle of light rays filling an angular
space of 90° before they enter the water, are squeezed into an angular
space of 48° 27' within the water, and that in the case of diamond the
condensation is from 90° to 23° 42'.
145. To an eye in still water its margin must appear lifted up.
A fish, for example, sees objects, as it were, through a circular aperture
of about 97° (twice 47° 27') in diameter overhead. All objects down
to the horizon will be visible in this space, and those near the horizon
will be much distorted and contracted in dimensions, especially in
height. Beyond the limits of this circle will be seen the bottom of
the water totally reflected, and therefore depicted as vividly as if seen
by direct vision.*
146. A similar effect, exerted by the atmosphere (when no clouds
cross the orbs), gives the sun and moon at rising and setting a slightly
flattened appearance.
147. Experimental Illustrations. — Place a shilling in a drinking-
glass ; cover it with water to about the depth of an inch, and tilt the
glass so as to obtain the necessary obliquity of incidence at the surface.
Looking upwards towards the surface, the image of the shilling will
be seen shining there, and as the reflexion is total, the image will be
as bright as the shilling itself. A spoon suitably dipped into the
glass also yields an image due to total reflexion.
148. Thrust the closed end of an empty test-tube into a glass of
water. Incline the tube, until the horizontal light falling upon it shall
be totally reflected upwards. When looked down upon, the tube
appears shining like burnished silver. Pour a little water into the
* Sir John Herschel.
Total Reflexion. 21
tube : as the liquid rises, it abolishes total reflexion, and with it
the lustre, leaving a gradually diminishing lustrous zone, which dis-
appears wholly when the level of the water within rises to, or above,
that of the water without. A tube of any kind stopped watertight will
answer for this experiment, which is both beautiful and instructive.
149. If a ray of light fall as a perpendicular on the side of a right-
angled isosceles glass prism, it will enter the glass and strike the
hypothenuse at an angle of 45°. This exceeds the limiting angle of
glass ; the ray will therefore be totally reflected ; and, in accordance
with the law mentioned in note 54, the direct and reflected rays will
be at right angles to each other. When such a change of direction
is required in optical instruments, a right-angled isosceles prism is
usually employed.
150. When the ray enters the prism parallel to the hypothenuse,
it will be refracted, and will strike the hypothenuse at an angle
greater than the limiting angle. It will therefore be totally reflected.
If the object, instead of being a point, be of sensible magnitude, the
rays from its extremities will cross each other within the prism, and
hence the object will appear inverted when looked at through the
prism. Dove has applied the ' reversion prism ' to render erect
the inverted images of the astronomical telescope.
151. The mirage of the desert and various other phantasmal
appearances in the atmosphere are, in part, due to total reflexion.
When the sun heats an expanse of sand, the layer of air in contact
with the sand becomes lighter than the superincumbent air. The
rays from a distant object, a tree for example, striking very obliquely
upon the upper surface of this layer, may be totally reflected, thus
showing images similar to those produced by a surface of water. The
thirsty soldiers of the French army were tantalised by such ap-
pearances in Egypt.
152. Gases, like liquids and solids, can refract and reflect light;
but, in consequence or the lowness of their refractive indices, both
reflection and refraction are feeble. Still atmospheric refraction has
to be taken into account by the astronomer, and by those engaged in
trigonometrical surveys. The refraction of the atmosphere causes the
sun to be seen before it actually rises, and after it actually sets.
153. The quivering of objects seen through air rising over a
heated surface is due to irregular refraction, which incessantly shifts
the directions of the rays of light. In the air this shifting of the
rays is never entirely absent, and it is often a source of grievous
annoyance to the astronomer who needs a homogeneous atmosphere.
154. The flame of a candle or of a gas-lamp, and the column of
heated air above the flame ; the air rising from a red-hot iron ; the
pouring of a heavy gas, such as carbonic acid, downwards into air; and
the issue of a lighter one, such as hydrogen, upwards, — may all be
made to reveal themselves by their action upon a sufficiently intense
light. The transparent gases interposed between such a light and
22 Notes on Light.
a white screen are seen to rise like smoke upon the screen through
the effects of refraction.
Lenses.
155. A lens in optics is a portion of a refracting substance such
as glass, which is bounded by curved surfaces. If the surface be
spherical the lens is called a spherical lens.
156. Lenses divide themselves into two classes, one of which
renders parallel rays convergent, the other of which renders such rays
divergent. Each class comprises three kinds of lenses, which are
named as follows : —
Converging Lenses.
1. Double convex, with both surfaces convex.
2. Plano-convex, with one surface plane and the other convex.
3. Concavo-convex (Meniscus), with a concave and a convex
surface, the convex surface being the most strongly curved.
Diverging Lenses.
1 . Double concave, with both surfaces concave.
2. Plano-concave, with one surface plane and the other concave.
3. Convexo-concave, with a convex and a concave surface, the
concave surface being the most strongly curved.
157. A straight line drawn through the centre of the lens, and per-
pendicular to its two convex surfaces, is the principal axis of the lens.
158.. A luminous beam falling on a convex lens parallel to the axis,
has its constituent rays brought to intersection at a point in the axis
behind the lens. This point is the principal focus of the lens. As
before, the principal focus is the focus of parallel rays.
159. The rays from a luminous point placed beyond the focus
intersect at the opposite side of the lens, an image of the point being
formed at the place of intersection. As the point approaches the
principal focus its image retreats from it, and when the point actually
reaches the principal focus, its image is at an infinite distance.
160. If the principal focus be passed, and the point come between
that focus and the lens, the rays after passing through the lens will be
still divergent. Producing them backwards, they will intersect on
that side of the lens on which stands the luminous point. The focus
here is virtual. A body of sensible magnitude placed between the
focus and the lens would have a virtual image.
161. When an object of sensible dimensions is placed anywhere
beyond the principal focus, a real image of the object will be formed
in the air behind the lens. The image may be either greater or less
than the object in size, but the image will always be inverted.
162. The positions of the image and the object are, as before,
convertible.
Diverging Lenses. 23
1G3. In the case of concave lenses the images are always virtual.
104. A spherical lens is incompetent to bring all the rays that
fall upon it to the same focus. The rays which pass through the lens
near its circumference are more refracted than those which pass
through the central portions, and they intersect earlier. Where per-
fect definition is required it is therefore usual, though at the expense
of illumination, to make use of the central rays only.
165. This difference of focal distance between the central and cir-
cumferential rays is called the spherical aberration of the lens. A
lens so curved as to bring all rays to the same focus is called
aplanatic; a spherical lens cannot be rendered aplanatic.
166. As in the case of spherical mirrors, spherical lenses have their
caustic curves and surfaces (diacaustics) formed by the intersection
of the refracted rays.
Vision and the Eye.
167. The human eye is a compound lens, consisting of three
principal parts : the aqueous humour, the crystalline lens, and the
vitreous humour.
168. The aqueous humour is held in front of the eye by the
cornea, a transparent, horny capsule, resembling a watch-glass in shape.
Behind the aqueous humour, and immediately in front of the crystal-
line lens, is the iris, which surrounds the pupil. Then follow the
lens and the vitreous humour, which last constitutes the main body
of the eye. The average diameter of the human eye is 10*9 lines.*
169. When the optic nerve enters the eye from behind, it divides
into a series of filaments, which are woven together to form the
retina, a delicate network spread as a screen at the back of the eye.
The retina rests upon a black pigment, which reduces to a minimum
all internal reflexion.
170. By means of the iris the size of the pupil may be caused to
vary within certain limits. When the light is feeble the pupil
expands, when it is intense the pupil contracts ; thus the quantity of
light admitted into the eye is, to some extent, regulated. The pupil
also diminishes when the eye is fixed upon a near object, and expands
when it is fixed upon a distant one.
171. The pupil appears black; partly because of the internal
black coating, but mainly for another reason. Could we illuminate
the retina, and see at the same time the illuminated spot, the pupil
would appear bright. But the principle of reversibility, so often
spoken of, comes into play here. The light of the illuminated spot
in returning outwards retraces its steps, and finally falls upon the
source of illumination. Hence, to receive the returning rays, the
observer's eye ought to be placed between the source and the retina.
But in this position it would cut off the illumination. If the light
be thrown into the eye by a mirror pierced with a small orifice, or
* A line is ^th of an inch.
24 Notes on Light.
with a small portion of the silvering removed, then the eye of the
observer placed behind the mirror, and looking through the orifice,
may see the illuminated retina. The pupil under these circumstances
glows like a live coal. This is the principle of the Ophthalmoscope
(Augenspiegel, Helmholtz), an instrument by which the interior of
the eye may be scanned, and its condition in health or disease noted.
172. In the case of albinos, or of white rabbits, the black pigment
is absent, and the pupil is seen red by light which passes through the
sclerotica, or white of the eye. When this light is cut off, the pupil
of an albino appears black. In some animals the black pigment is
displaced by a reflecting membrane, the tapetum. It is the light
reflected from the tapetum which causes a cat's eye to shine in par-
tial darkness. The light in this case is not internal, for when the
darkness is total the cat's eyes do not shine.
173. In the camera obscura of the photographer the images of
external objects formed by a convex lens are received upon a plate
of ground glass, the lens being pushed in or out until the image upon
the glass is sharply defined.
174. The eye is a camera obscura, with its refracting lenses, the
retina playing the part of the plate of ground glass in the ordinary
camera. For perfectly distinct vision it is necessary that the image
upon the retina should be perfectly defined ; in other words, that the
rays from every point of the object looked at should be converged to
a point upon the retina.
175. The image upon the retina is inverted.
Adjustment of the Eye : use of Spectacles.
176. If the letters of a book held at some distance from the eye
be looked at through a gauze veil placed nearer the eye, it will be
found that when the letters are seen distinctly the veil is seen indis-
tinctly ; conversely, if the veil be seen distinctly, the letters will be
seen indistinctly. This demonstrates that the images of objects at
different distances from the eye cannot be defined at the same time
upon the retina.
177. Were the eye a rigid mass, like a glass lens, incapable of
change of form, distinct vision would only be possible at one particular
distance. We know, however, that the eye possesses a power of
adjustment for different distances. This adjustment is effected, not
by pushing the front of the eye backwards or forwards, but by
changing the curvature of the crystalline lens.
178. The image of a candle reflected from the forward or back-
ward surface of the lens is seen to diminish when the eye changes
from distant to near vision, thus proving the curvature of the lens to
be greater for near than for distant vision.
179. The principal refraction endured by rays of light in crossing
the eye occurs at the surface of the cornea, where the passage is from
Adjustment of the Eye : use of Spectacles. 25
air to a much denser medium. The refraction at the cornea alone
would cause the rays to intersect at a point nearly half an inch behind
the retina. The convergence is augmented by the crystalline lens,
which brings the point of intersection forward to the retina itself.
180. A line drawn through the centre of the cornea and the centre
of the whole eye to the retina is called the axis of the eye. The
length of the axis, even in youth, is sometimes too small; in other
words, the retina is sometimes too near the cornea ; so that the
refracting part of the organ is unable to converge the rays from a
luminous point so as to bring them to a point upon the retina. In
old age also the refracting surfaces of the eye are slightly flattened,
and thus rendered incompetent to refract the rays sufficiently. In
both these cases the image would be formed behind the retina, instead
of upon it, and hence the vision is indistinct.
181. The defect is remedied by holding the object at a distance
from the eye, so as to lessen the divergence of its rays, or by placing
in front of the eye a convex lens, which helps the eye to produce the
necessary convergence. This is the use of spectacles.
182. The eye is also sometimes too long in the direction of the
axis, or the curvature of the refracting surfaces may be too great. In
either case the rays entering the pupil are converged so as to intersect
before reaching the retina. This defect is remedied either by holding
the object very close to the eye, so as to augment the divergence of its
rays, thus thro wing back the point of intersection ; or by placing in front
of the eye a concave lens, which produces the necessary divergence.
183. The eye is not adjusted at the same time for equally- distant
horizontal and vertical objects. The distance of distinct vision is
greater for horizontal lines than for vertical ones. Draw with ink two
lines at right angles to each other, the one vertical, the other horizontal:
Bee one of them distinctly black and sharp ; the other appears indis-
tinct, as if drawn in lighter ink. Adjust the eye for this latter line,
the former will then appear indistinct. This difference in the cur-
vature of the eye in two directions may sometimes become so great
as to render the application of cylindrical lenses necessary for its
correction.
The Punctum Caecum.
184. The spot where the optic nerve enters the eye, and from
which it ramifies to form the network of the retina, is insensible to
the action of light. An object whose image falls upon that spot is
not seen. The image of a clock-face, of a human head, of the moon,
may be caused to fall upon this * blind spot,' and when this is the
case the object is not visible.
185. To illustrate this point, proceed thus: — Lay two white
wafers on black paper, or two black ones on white paper, with an
interval of 3 inches between them. Bring the right eye at a height
of 10 or 11 inches exactly over the left-hand wafer, so that the line
26 Notes on Light.
joining the two eyes shall be parallel to the line joining the two
wafers. Closing the left eye, and looking steadily with the right at
the left-hand wafer, the right-hand one ceases to be visible. In this
position the image falls upon the ' blind spot ' of the right eye. If
the eye be turned in the least degree to the right or left, or if the
distance between it and the paper be augmented or diminished, the
wafer is immediately seen. Preserving these proportions as to size
and distance, objects of far greater dimensions than the wafer may
have their images thrown upon the blind spot, and be obliterated.
Persistence of Impressions.
186. An impression of light once made upon the retina does not
subside instantaneously. An electric spark is sensibly instantaneous ;
but the impression it makes upon the eye remains for some time after
the spark has passed away. This interval of persistence varies with
different persons, and amounts to a sensible fraction of a second.
187. If, therefore, a succession of sparks follow each other at
intervals less than the time which the impression endures, the separate
impressions will unite to form a continuous light. If a luminous point
be caused to describe a circle in less than this interval, the circle will
appear as a continuous closed curve. From this cause also, the spokes
of a rapidly rotating wheel blend together to a shadowy surface.
Wheatstone's Photometer is based on this persistence. It also explains
the action of those instruments in which a series of objects in dif-
ferent positions being brought in rapid succession before the eye, the
impression of motion is produced.
188. A jet of water descending from an orifice in the bottom of a
vessel exhibits two distinct parts : a tranquil pellucid portion near the
orifice, and a turbid or untranquil portion lower down. Both parts
of the jet appear equally continuous. But when the jet in a dark
room is illuminated by an electric spark, all the turbid portion reveals
itself as a string of separate drops standing perfectly still. It is their
quick succession that produces the impression of continuity. The
most rapid cannon-ball, illuminated by a flash of lightning, would be
seen for the fraction of a second perfectly motionless in the air.
189. The eye is by no means a perfect optical instrument. It
suffers from spherical aberration ; a scattered luminosity, more or
less strong, always surrounding the defined images of luminous objects
upon the retina. By this luminosity the image of the object is sensibly
increased in size ; but with ordinary illumination the scattered light
is too feeble to be noticed. When, however, bodies are intensely
illuminated, more especially when the bodies are small, so that a
slight extension of their images upon the retina becomes noticeable,
such bodies appear larger than they really are. Thus, a platinum-
wire raised to whiteness by a voltaic current has its apparent diameter
enormously increased. Thus also the crescent moon seems to belong
Persistence of Impressions. 27
to a larger sphere than the dimmer mass of the satellite which it par-
tially clasps. Thus also, at considerable distances, the parallel flashes
sent from a number of separate lamps and reflectors in a lighthouse
encroach upon each other, and blend together to a single flash. The
white-hot particles of carbon in a flame describe lines of light, because
of their rapid upward motion. These lines are widened to the eye ;
and thus a far greater apparent solidity is imparted to the flame than
in reality belongs to it.
189a. This augmentation of the true size of the optical image i»
called Irradiation.
Bodies seen within the Eye.
190. Almost every eye contains bodies more or less opaque dis-
tributed through its humours. The so-called muscce volitantes are of
this character ; so are the black dots, snake-like lines, beads, and rings,
which are strikingly visible in many eyes. Were the area of the pupil
contracted to a point, such bodies might produce considerable annoy-
ance ; but because of the width of the pupil the shadows which these
small bodies would otherwise cast upon the retina are practically obli-
terated, except when they are very close to the back of the eye.* It
is only necessary to look at the firmament through a pinhole to give
these shadows greater definition upon the retina.
191. The veins and arteries of the retina itself also cast their
shadows upon its posterior surface ; but the shaded spaces soon become
so sensitive to light as to compensate for the defect of light falling upon
them. Hence under ordinary circumstances the shadows are not seen.
But if the shadows be transported to a less sensitive portion of the
retina, the image of the vessels becomes distinctly visible.
192. The best mode of obtaining the transference of the shadow
is to concentrate in a dark room, by means of a pocket lens of short
focus, a small image of the sun or of the electric light upon the white
of the eye. Care must be taken not to send the beam through the
pupil. When the small lens is caused to move to and fro, the
shadows are caused to travel over different portions of the retina, and
a perfectly defined image of the veins and arteries is seen projected
in the darkness in front of the eye.
193. Looking into a dark space, and moving a candle at the same
time to and fro beside the, eye, so that the rays enter the pupil very
obliquely, the shadow of the retinal vessels is also obtained. In some
eyes the suddenness and vigour with which the spectral image displays
itself are extraordinary ; others find it difficult to obtain the effect.
194. Finally, a delicate image of the vessels may be obtained by
looking through a pinhole at the bright sky, and moving the aperture
to and fro.
See Notes 18 and 19.
28 Notes on Light.
The Stereoscope.
195. Look with one eye at the edge of the hand, so that the
finger nearest the eye shall cover all the others. Then open the
second eye ; by it the other fingers will be seen foreshortened. The
images of the hand therefore within the two eyes are different.
196. These two images are projected on the two retinae; if by
any means we could combine two drawings, executed on a flat surface,
so as to produce within the two eyes two pictures similar to the two
images of the solid hand, we should obtain the impression of solidity.
This is done by the stereoscope.
197. The first form of this instrument was invented by Sir Charles
Wheatstone. He took drawings of solid objects as seen by the two
eyes, and looked at the images of these drawings in two plane mirrors.
Each eye looked at the image which belonged to it, and the mirrors
were so arranged that the images overlapped, thus appearing to come
from the same object. By this combination of its two plane projec-
tions, the object sketched was caused to start forth as a solid.
198. In looking at and combining two such drawings, the eyes
receive the same impression, and go through the same process as when
they look at the real object. We see only one point of an object
distinctly at a time. If the different points of an object be at different
distances from the eyes, to see the near points distinctly requires a
greater convergence of the axes of the eyes than to see the distant ones.
Now, besides the identity of the retinal images of the stereoscopic
drawings with those of the real object, the eyes, in order to cause the
corresponding pairs of points of the two drawings to coalesce, have
to go through the same variations of convergence that are necessary to
see distinctly the various points of the actual object. Hence the
impression of solidity produced by the combination of such drawings.
199. Measure the distance between two pairs of points, which
when combined by the stereoscope present two single points at
different distances from the eye. The distance between the one pair
will be greater than that between the other pair. Different degrees
of convergence are therefore necessary on the part of the eye to
combine the two pairs of points. It is to be noted that the coales-
cence produced in the stereoscope at any particular moment is only
partial. If one pair of corresponding points be seen singly, the
others must appear double. This is also the case when an actual
solid is looked at with both eyes ; of those points of it which are at
different distances from the eyes one only is seen singly at a time.
200. The impression of solidity may be produced in an exceed-
ingly striking manner without any stereoscope at all. Most easily,
thus : — Take two drawings — projections, as they are called — of the
frustum of a cone ; the one as it is seen by the right eye, the other
as it is seen by the left. Holding them at some distance from the
eyes, let the left-hand drawing be looked at by the right eye, and the
The Stereoscope. 29
right-hand drawing by the left. The lines of vision of the two eyes
here cross each other ; and it is easy, after a few trials with a pencil-
point placed in front of the eyes, to make two corresponding points
of the drawings coincide. The moment they coincide, the combined
drawings start forth as a single solid, suspended in the air at the
place of intersection of the lines of vision. It depends upon the
character of the drawings whether the inside of the frustum is seen,
or the outside, whether its base or its top seems nearest to the
eye. For this experiment the drawings are best made in simple
outline, and they may be immensely larger than ordinary stereoscopic
drawings.
Take notice that here also the different pairs of the corresponding
points are at different distances apart. Two corresponding points,
for example, of the top of the frustum will not be the same distance
asunder as two points of the base.
201. Wheatstone's first instrument is called the Reflecting Stereo-
scope ; but the methods of causing drawings to coalesce so as to
produce stereoscopic effects are almost numberless. The instrument
most used by the public is the Lenticular Stereoscope of Sir David
Brewster. In it the two projections are combined by means of two
half lenses with their edges turned inwards. The lenticular stereo-
scope also magnifies.*
202. It has been stated in note 198 that for the distinct vision of
a near point a greater convergence of the lines of vision of the two
eyes is necessary than for that of a distant one. By an instru-
ment in which two rectangular prisms are employed,! the rays from
two points may be caused to cross before they enter the eyes, the
convergence being thus rendered greater for the distant point than
for the near one. The consequence of this is, that the near point
appears distant, and the distant point near. This is the principle of
Wheatstone's pseudoscope. By this instrument convex surfaces are
rendered concave, and concave surfaces convex. The inside of a hat
or teacup may be thus converted into its outside, while a globe may
be seen as a concave spherical surface.
Nature of Light ; Physical Theory of Reflexion and Refraction.
It is now time to redeem to some extent the promise of our first
note, that the ' something ' which excites the sensation of light should
be considered more closely subsequently.
203. Every sensation corresponds to a motion excited in our
nerves. In the sense of touch, the nerves are moved by the contact
of the body felt ; in the sense of smell, they are stirred by the infini-
tesimal particles of the odorous body ; in the sense of hearing, they
are shaken by the vibrations of the air.
* Fuller and clearer information regarding the stereoscope -will be found in
the Journal of the Photographic Society, vol. iii. pp. 96, 116, and 167-
f See Note 150.
30 Notes on Light.
Theory of Emission.
204. Newton supposed light to consist of small particles shot out
with inconceivable rapidity by luminous bodies, and fine enough to
pass through the pores of transparent media. Crossing the humours
of the eye, and striking the optic nerve behind the eye, these particles
were supposed to excite vision.
205. This is the Emission Theory or Corpuscular Theory of Light.
206. Considering the enormous velocity of light, the particles, if
they exist, must be inconceivably small ; for if of any conceivable
weight, they would infallibly destroy so delicate an organ as the eye.
A bit of ordinary matter, one grain in weight, and moving with the
velocity of light, would possess the momentum of a cannon-ball
150 Ibs. weight, moving with a velocity of 1000 feet a second.
207. Millions of these light particles, supposing them to exist,
concentrated by lenses and mirrors, have been shot against a balance
suspended by a single spider's thread ; this thread, though twisted
18,000 times, showed no tendency to untwist itself; it was therefore
devoid of torsion. But no motion due to the impact of the particles
was even in this case observed.*
208. If light consists of minute particles, they must be shot out
with the same velocity by all celestial bodies. This seems ex-
ceedingly unlikely, when the different gravitating forces of such
different masses are taken into account. By the attractions of such
diverse masses, the particles would in all probability be pulled back
with different degrees of force.
209. If, for example, a fixed star of the sun's density possessed
250 times the sun's diameter, its attraction, supposing light to be
acted on like ordinary matter, would be sufficient to finally stop the
particles of light issuing from it. Smaller masses would exert cor-
responding degrees of retardation ; and hence the light emitted by
different bodies would move with different velocities. That such is
not the case — that light moves with the same velocity whatever be
its source — renders it probable that it does not consist of particles
thus darted forth.
But a more definite and formidable objection to the Emission
Theory may be stated after we have made ourselves acquainted with
the account it rendered of the phenomena of reflexion and refraction.
210. In direct reflexion, according to the emission theory, the light
particles are first of all stopped in their course by a repellent force
exerted by the reflecting body, and then driven in the contrary direc-
tion by the same force.
211. This repulsion is however selective. The reflecting substance
singles out one portion of the group of particles composing a luminous
beam and drives them back ; but it attracts the remaining particles
of the group and transmits them.
212. When a light particle approaches a refractive surface
* Bennett, Phil. Trans. 1792.
Theory of Emission. 31
obliquely, if the particle be an attracted one, it is drawn towards the
surface, as an ordinary projectile is drawn towards the earth. Re-
fraction is thus accounted for. Like the projectile, too, the velocity
of the light particle is augmented during its deflection; it enters the
refracting medium with this increased velocity, and once within the
medium, the attractions before and behind the particle neutralising
each other, the increased velocity is maintained.
213. Thus, it is an unavoidable consequence of the theory of
Newton, that the bending of a ray of light towards the perpendicular
is accompanied by an augmentation of velocity — that light in water
moves more rapidly than in air, in glass more rapidly than in water,
in diamond more rapidly than in glass. In short, that the higher the
refractive index, the greater the velocity of the light.
214. A decisive test of the emission theory was thus suggested,
and under that test the theory has broken down. For it has been
demonstrated, by the most rigid experiments, that the velocity of
light diminishes as the index of refraction increases. The theory,
however, had yielded to the assaults made upon it long before this
particular experiment was made.
Theory of Undulation.
215. The Emission Theory was first opposed by the celebrated
astronomer Huygens and the no less celebrated mathematician Euler,
both of whom held that light, like sound, was a product of ivave motion.
Laplace, Malus, Biot, and Brewster supported Newton, and the emis-
sion theory maintained its ground until it was finally overthrown by
the labours of Thomas Young* and Augustin Fresnel.
216. These two eminent philosophers, while adducing whole classes
of facts inexplicable by the emission theory, succeeded in establishing
the most complete parallelism between optical phenomena and those
of wave motion. The justification of a theory consists in its exclu-
sive competence to account for phenomena. On such a basis the
Wave Theory, or the Undulatory Theory of light, now rests, and
every day's experience only makes its foundations more secure. This
theory must for the future occupy much of our attention.
* Dr. Young was appointed Professor of Natural Philosophy in the Koyal
Institution, Aiigust 3, 1801. From a marble slab in the village church of
Earnborough, near Bromley, Kent, I copied, on the llth of April, the following
inscription : —
' Near this place are deposited the remains of THOMAS YOUNG, M.D., Fellow
and Foreign Secretary of the Koyal Society, Member of the National Institute
of France. A man alike eminent in almost every department of human
learning, whose many discoveries enlarged the bounds of Natural Science, and
who first penetrated the obscurity which had veiled for ages the Hieroglyphics
of Egypt.
' Endeared to his friends by his domestic virtues, Honoured by the world for
his unrivalled acquirements, He died in the hope of the resurrection of the just.
'Born at Milverton, in Somersetshire, June 13th, 1773.
' Died in Park Square, London, May 29th, 1829,
' In the 66th year of his age.'
32 Notes on Light.
217. In the case of sound, the velocity depends upon the relation
of elasticity to density in the body which transmits the sound. The
greater the elasticity the greater is the velocity, and the less the
density the greater is the velocity. To account for the enormous
velocity of propagation in the case of light, the substance which
transmits it is assumed to be of both extreme elasticity and of extreme
tenuity. This substance is called the iMminiferous ether.
218. It fills space ; it surrounds the atoms of bodies ; it extends,
without solution of continuity, through the humours of the eye. The
molecules of luminous bodies are in a state of vibration. The vibra-
tions are taken up by the ether, and transmitted through it in waves.
These waves impinging on the retina excite the sensation of light.
219. In the case of sound, the air-particles oscillate to and fro in
the direction in which the sound is transmitted ; in the case of light,
the ether particles oscillate to and fro across the direction in which
the light is propagated. In scientific language the vibrations of sound
are longitudinal , while the vibrations of light are transversal. In fact,
the mechanical properties of the ether are rather those of a solid than
of an air.
220. The intensity of the light depends on the distance to whicli
the ether particles move to and fro. This distance is called the am-
plitude of the vibration. The intensity of light is proportional to the
square of the amplitude; it is also proportional to the square of the
maximum velocity of the vibrating particle.
221. The amplitude of the vibrations diminishes simply as the
distance increases ; consequently the intensity, which is expressed by
the square of the amplitude, must diminish inversely as the square of
the distance. This, in the language of the wave theory, is the law
of inverse squares.
222. The reflexion of ether waves obeys the law established in
the case of light. The angle of incidence is demonstrably equal to
the angle of reflexion.
223. To account for refraction, let us for the sake of simplicity
take a portion of a circular wave emitted by the sun or some other
distant body. A short portion of such a wave would be straight.
Suppose it to impinge from air upon a plate of glass, the wave being
in the first instance parallel to the surface of the glass. Such a wave
would go through the glass without change of direction.
224. But as the velocity in glass is less than the velocity in air,
the wave would be retarded on passing into the denser medium.
225. But suppose the wave, before impact, to be oblique to the
surface of the glass ; that end of the wave which first reaches the
glass will be first retarded, the other portions being held back in
succession. This retardation of one end of the wave causes it to
swing round ; so that when the wave has fully entered the glass its
course is oblique to its first direction. It is refracted.
226. If the glass into which the wave enters be a plate with
Theory of Undulation. 33
parallel surfaces, the portion of the wave which reached the upper
surface first, and was first retarded, will also reach its under surface
first, and escape earliest from the retarding medium. This pro-
duces a second swinging round of the wave, by which its original
direction is restored. In this simple way the Wave Theory accounts
for Kefraction.
227. The convergence or divergence of beams of light by lenses
is immediately deduced from the fact that the different points of the
ether wave reach the lens, and are retarded by the lens in succession.
228. The density of the ether is greater in liquids and solids than
in gases, and greater in gases than in vacuo. A compressing force
seems to be exerted on the ether by the molecules of these bodies.
Now if the elasticity of the ether increased in the same proportion as
its density, the one would neutralise the other, and we should have
no retardation of the velocity of light. The diminished velocity in
highly refracting bodies is accounted for by assuming that in such
bodies the elasticity in relation to the density is less than in vacuo.
The observed phenomena immediately flow from this assumption.
229. The case is precisely similar to that of sound in a gas or
vapour which does not obey the law of Mariotte. The elasticity of
such a gas or vapour, when compressed, increases less rapidly than
the density ; hence the diminished velocity of the sound.
230. But we are able to give a more distinct statement as to the
influence which a refracting body has upon the velocity of light.
Regard the lines o m and np in Fig. 2, Note 113. These two lines
represent the velocities of light in the two media there considered ;
or, expressed more generally, the sine of the angle of incidence
represents the velocity of light in the first medium, while the sine of
the angle of refraction represents the velocity in the second. The
index of refraction then is nothing else than the ratio of the two velo-
cities. Thus in the case of water where the index of refraction is f
the velocity in air is to its velocity in water as 4 is to 3. In glass also,
where the index of refraction is f the velocity in air is to the velo-
city in glass as 3 is to 2. In other words the velocity of light in
air is 1^- times its velocity in water, and !•§• times its velocity in
glass. The velocity of light in air is about 2 J times its velocity in
diamond, and nearly three times its velocity in chromate of lead,
the most powerfully refracting substance hitherto discovered.
Strictly speaking, the index of refraction refers to the passage of a
ray of light, not from air, but from a vacuum* into the refracting
body. Dividing the velocity of light in vacuo by its velocity in the
refracting substance, the quotient is the index of refraction of that
substance.
231. In the wave theory, the rays of light are perpendiculars to
the waves of ether. Unlike the wave, the ray has no material
existence ; it is merely a direction.
* That is to say, a vacuum save as regards the ether itself.
D
34 Notes on Light.
Prisms.
232. It has been stated in note 129, that in the case of a plate of
glass with parallel surfaces, the direction possessed by an oblique
ray, prior to its meeting the glass, is restored when it quits the glass.
This is not the case if the two surfaces at which the ray enters and
emerges be not parallel.
233. When the ray passes through a wedge-shaped transparent
substance, in a direction perpendicular to the edge of the wedge, it
is permanently refracted. A body of this shape is called a prism in
optics, and the angle enclosed by the two oblique sides of the wedge
is called the refracting angle.
234. The larger the refracting angle the greater is the deflection
of the ray from its original direction. But with the self-same prism
the amount of the refraction varies with the direction pursued by the
ray through the prism.
235. When that direction is such that the portion of the ray'
within the prism makes equal angles with the two sides of the prism,
or what is the same, with the ray before it reaches the prism and
after it has quitted it, then the total refraction is a minimum. This
is capable both of mathematical and experimental proof; and on
this result is based a method of determining the index of refraction.
236. The final direction of a refracted ray being unaltered by its
passage through glass plates with parallel surfaces, we may employ
hollow vessels composed of such plates and filled with liquids, thus
obtaining liquid prisms.
Prismatic Analysis of Light: Dispersion.
237. Newton first unravelled the solar light, proving it to be com-
posed of an infinite number of rays of different degrees of refrangi-
bility; when such light is sent through a prism, its constituent rays
are drawn asunder. This act of drawing apart is called dispersion.
238. The waves of ether generated by luminous bodies are not all
of the same length ; some are longer than others. In refracting
substances the short waves are more retarded than the long ones ;
hence the short waves are more refracted than the long ones. This
is the cause of dispersion.
239. The luminous image formed when a beam of white light is
thus decomposed by a prism is called a spectrum. If the light em-
ployed be that of the sun, the image is called the solar spectrum.
240. The solar spectrum consists of a series of vivid colours,
which, when reblended, produce the original white light. Com-
mencing with that which is least refracted, we have the following
order of colours in the solar spectrum : — Red, Orange, Yellow,
Green, Blue, Indigo, Violet.
Prismatic Analysis of Light : Dispersion. 35
241. The Colour of Light is determined solely by its Wave-length.
—The ether waves gradually diminish in length from the red to the
violet. The length of a wave of red light is about ^-g-oir °f an mcn ?
that of a wave of violet light is about -g-y-g^th of an inch. The
waves which produce the other colours of the spectrum lie between
these extremes.
242. The velocity of light being 192,000 miles in a second, if
we multiply this number by 39,000 we obtain the number of waves
of red light in 192,000 miles; the product is 474,439,680,000.000.
All these waves enter the eye in a second. In the same interval
699,000,000,000,000 waves 'of violet light enter the eye. At this
prodigious rate is the retina hit by the waves oflight.
243. Colour, in fact, is to light what pitch is to sound. The pitch
of a note depends solely on the number of aerial waves which strike
the ear in a second. The colour of light depends on the number of
ethereal waves which strike the eye in a second. Thus the sensation
of red is produced by imparting to the optic nerve four hundred and
seventy-four millions of millions of impulses per second, while the
sensation of violet is produced by imparting to the nerve six hundred
and ninety-nine millions of millions of impulses per second. In the
Emission Theory numbers not less immense occur, ' nor is there any
mode of conceiving the subject which does not call upon us to admit
the exertion of mechanical forces which may well be termed infinite.' *
Invisible rays : Calorescence and Fluorescence.
244. The spectrum extends in both directions beyond its visible
limits. Beyond the visible red we have rays which possess a high
heating power, though incompetent to excite vision ; beyond the
violet we have a vast body of rays which, though feeble as regards
heat, and powerless as 'regards light, are of the highest importance
because of their capacity to produce chemical action.
245. In the case of the electric light, the energy of the non-
luminous calorific rays emitted by the carbon points is about eight
times that of all the other rays taken together. The dark calorific
rays of the sun also probably exceed many times in power the lumi-
nous solar rays. It is possible to sift the solar or the electric beam
so as to intercept the luminous rays, while the non-luminous rays
are allowed free transmission.
246. In this way perfectly dark foci may be obtained where com-
bustible bodies may be burned, non-refractory metals fused, and
refractory ones raised to the temperature of whiteness. The non-
luminous calorific rays may be thus transformed into luminous ones,
Avhich yield all the colours of the spectrum. This passage, by the
intervention of a refractory body, from the non-luminous to the lumi-
nous state, is called Calorescence.
* Sir John Herschel.
36 Notes on Light.
247. So also as regards the ultra-violet rays; when they are
permitted to fall upon certain substances — the disulphate of quinine
for example — they render the substance luminous ; invisible rays are
thereby rendered visible. The change here receives the name of
Fluorescence.
248. In calorescence the atoms of the refractory body are caused
to vibrate more rapidly than the waves which fall upon them ; the
periods of the waves are quickened by their impact on the atoms.
The refrangibility of the rays is, in fact, exalted. In fluorescence, on
the contrary, the impact of the waves throws the molecules of the
fluorescent body into vibrations of slower periods than those of the
incident waves ; the refrangibility of the rays is in fact lowered.
Thus by exalting the refrangibility of the ultra-red, and by lower-
ing the refrangibility of the ultra-violet rays, both classes of rays are
rendered capable of exciting vision.
249. Though the term is by no means faultless, those rays, both
ultra-red and ultra-violet, which are incompetent to excite vision, are
called invisible rays. In strictness we cannot speak of rays being
either visible or invisible; it is not the rays themselves but the objects
they illuminate that become visible. ' Space, though traversed by
the rays from all suns and all stars, is itself unseen. Not even the
ether which fills space, and whose motions are the light of the world,
is itself visible.' *
Doctrine of Visual Periods.
250. A string tuned to a certain note resounds when that note is
sounded. If you sing into an open piano, the string whose note is in
unison with your voice will be thrown into sonorous vibration. If
there be discord between the note and the string, there is no re-
sonance, however powerful the note may be. A particular church-pane
is sometimes broken by a particular organ-peal, through the coinci-
dence of its period of vibration with that of the organ.
251. In this way it is conceivable that a feeble note, through the
coincidence of its periods of vibration with those of a sounding body,
may produce effects which a powerful note, because of its non-
coincidence, is unable to produce.
252. This, which is a known phenomenon of sound, helps us to
a conception of the deportment of the retina towards light. The
retina, or rather the brain in which its fibres end, is, as it were,
attuned to a certain range of vibrations, and it is dead to all vibra-
tions which lie without that range, however powerful they may be.
253. The quantity of wave motion sent to the eye at night, by
a candle a mile distant, suffices to render the candle visible. Em-
ploying the powerful ultra-red rays of the sun, or of the electric light,
* ' Proceedings of the Eoyal Institution,' vol. v., p. 456.
Doctrine of Visual Periods. 37
it is demonstrable that ethereal waves possessing many millions of
times the mechanical energy of those which produce the candle's
light, maybe caused to impinge upon the retina without exciting any
sensation whatever. The periods of succession of the waves, rather
than their strength, are here influential.
254. When in music two notes are separated from each other by
an octave, the higher note vibrates with twice the rapidity of the lower.
In Note 241 the lengths of the wave of red light and of violet
light are set down as 33-^5- of an inch and ^T^VTTTF of an inch
respectively; but these numbers refer to the mean red and the mean
violet. The waves of the extreme violet are about half the length
of those of the extreme red, and they strike the retina with double
the rapidity of the red. While, therefore, the musical scale, or the
range of the ear, is known to embrace nearly eleven octaves, the optical
scale, or range of the eye, is comprised within a single octave.
Doctrine of Colours.
255. Natural bodies possess the power of extinguishing, or, as it is
called, absorbing the light that enters them. This power of absorption
is selective, and hence, for the most part, arise the phenomena of
colour.
256. When the light which enters a body is wholly absorbed the
body is black ; a body which absorbs all the waves equally, but not
totally, is grey; while a body which absorbs the various waves
unequally is coloured. Colour is due to the extinction of certain
constituents of the white light within the body, the remaining con-
stituents which return to the eye imparting to the body its colour.
257. It is to be borne in mind that bodies of all colours, illuminated
by white light, reflect white light from their exterior surfaces. It is
the light which has plunged to a certain depth within the body, which
has been sifted there by elective absorption, and then discharged
from the body by interior reflexion that, in general, gives the body its
colour.
258. A pure red glass interposed in the path of a beam decomposed
by a prism, either before or after the act of decomposition, cuts off all
the colours of the spectrum except the red. A glass of any other
pure colour similarly interposed would cut off all the spectrum except
that particular portion which gives the glass its colour. It is, how-
ever, extremely difficult, if not impossible, to obtain pure pigments of
any kind. Thus a yellow glass not only allows the yellow light
of the spectrum to pass, but also a portion of the adjacent green and
orange ; while a blue glass not only allows the blue to pass, but also
a portion of the adjacent green and indigo.
259. Hence, if a beam of white light be caused to pass through a
yellow glass and a blue glass at the same time, the only transmissible
colour common to both is green. This explains why blue and yellow
38 Notes on Light.
powders, when mixed together, produce green. The white light
plunges into the powder to a certain depth, and is discharged by
internal reflexion, minus its yellow and its blue. The green alone
remains.
260. The effect is quite different when, instead of mixing blue and
yellow pigments, we mix blue and yellow lights together. Here the
mixture is a pure white. Blue and yellow are complementary colours.
261. Any two colours whose mixture produces white are called
complementary colours. In the spectrum we have the following
pairs of such colours : —
Ked and greenish Blue.
Orange and cyanogen Blue.
Yellow and indigo Blue.
Greenish yellow and Violet.
262. A body placed in a light which it is incompetent to transmit
appears black, however intense may be the illumination. Thus, a
stick of red sealing-wax, placed in the* vivid green of the spectrum,
is perfectly black. A bright red solution similarly placed cannot be
distinguished from black ink ; and red cloth, on which the spectrum
is permitted to fall, shows its colour vividly where the red light falls
upon it, but appears black beyond this position.
263. We have thus far dealt with the analysis of white light. In
reblending the constituent colours, so as to produce the original, we
illustrate, by synthesis, the composition of white light.
264. Let the beam analyzed be a rectangular slice of light. By
means of a cylindrical lens we can recombine the colours, and produce
by their mixture the original whita. It is also possible, by the com-
bination of the colours of its spectrum, to build up a perfect image
of the source of light. The persistence of impressions on the retina
also offers a ready means of blending colours.
Chromatic Aberration. Achromatism.
265. Owing to the different refrangibility of the different rays of
the spectrum, it is impossible by a single spherical lens to bring them
all to a focus at the same point. The blue rays, for example, being
more refracted than the red will intersect sooner than the red.
266. Hence, when a divergent cone of white light is rendered
convergent by a lens, the convergent beam, as far as the point of
intersection of the rays, will be surrounded by a sheath of red ; while
beyond the focus the divergent cone will be surrounded by a sheath of
blue. Hence, when the refracted rays fall upon a screen placed
between the lens and the focus of blue rays, a white circle with a red
border is obtained, while if the screen be placed beyond the focus of
red rays the white circle will have a blue border. It is impossible
to produce a colourless image in these positions of the screen.
267. This lack of power on the part of a lens to bring its differently
Chromatic Aberration. Achromatism. 31)
coloured constituents to a common focus, is called the Chromatic aber-
ration of the lens.
268. Newton considered it impossible to get rid of chromatic
aberration ; for he supposed the dispersion of a prism or lens to be
proportional to its refraction, and that if you destroyed the one you
destroyed the other. This, however, was an error.
'269. For two prisms producing the same mean refraction may
produce very different degrees of dispersion. By diminishing the
angle of the more highly dispersive prism we can make its dispersion
sensibly equal to that of the feebly dispersive one ; and we can neu-
tralize the colours of both prisms by placing them in opposition to
each other, without neutralizing the refraction.
270. When, for example, a prism of water is opposed to a prism
of flint-glass, after the dispersion of the water, which is small, has
been destroyed, the beam is still refracted. If a prism of crown-glass
be substituted for the prism of water, substantially the same effect is
produced. The flint-glass is competent to neutralize the dispersion
of the crown before it neutralizes the refraction.
271. What is here said of prisms applies equally to lenses. A
convex crown-glass lens, opposed to a concave flint-glass lens, may
have its dispersion destroyed, and still images may be formed by the
combination of the two lenses, because of the residual refraction.
272. A combination of lenses wherein colour is destroyed while a
certain amount of refraction is preserved, is called an achromatic com-
bination, or more briefly an achromatic leus.
273. The human eye is not achromatic. It suffers from chromatic
aberration as well as Irorn spherical aberration.
Subjective Colours.
274. By the action of light the optic nerve is rendered less sensi-
tive. When we pass from bright daylight into a moderately lighted
room, the room appears dark.
275. This is also true of individual colours ; when light of any
particular colour falls upon the eye the optic nerve is rendered less
sensitive to that colour. It is, in fact, partially blinded to its per-
ception.
276. If the eyes be steadily fixed upon a red wafer placed on
white paper, after a little time the wafer will be surrounded by a
greenish rim, and if the wafer be moved away, the place on which it
rested will appear green.
277. This is thus explained: — the eye by looking at the wafer has
its sensibility to red light diminished; hence, when the wafer is
removed, the white light falling upon the spot of the retina on which
the image of the wafer rested, will have its red constituent virtually
removed, and will therefore appear of the complementary colour.
The first rim of green light observed is due to the extension of the red
40 Notes on Light.
light of the wafer a little beyond its geometrical image on the retina,
in consequence of the spherical aberration of the eye.
278. Coloured shadows are reducible to the same cause. Let a
strong red light, for example, fall upon a white screen. A body in-
terposed between the light and the screen will cast a shadow, and if
this shadow be moderately illuminated by a second white light it will
appear green. If the original light be bluo, the shadow will appear
yellow ; if the original light be green, the shadow will appear red.
The reason is, that the eye in the first instance is partially blinded
to the perception of the colour cast upon the screen ; hence the white
light, which reaches the eye from the shadow, will have that colour
partially withdrawn, and the shadow will appear of the complementary
colour.
279. Colours of this kind are called subjective colours; they depend
upon the condition of the eye, and do not express external facts of
colour.
Spectrum Analysis.
280. Metals and their compounds impart to flames peculiar colours,
which are characteristic of the metals. Thus the almost lightless
flame of a Bunsen's burner is rendered a brilliant yellow by the metal
sodium, or by any volatilizible compound of that metal, such as
chloride of sodium or common salt. The flame is rendered green by
copper, purple by zinc, and red by strontian.
281. These colours are due to the vapours of the metals which are
liberated in the flame.
282. When such incandescent metallic vapours are examined by
the prism, it is found that instead of emitting rays which form a
continuous spectrum, one colour passing gradually into another, they
emit distinct groups of rays of definite, but different refrangibilities.
The spectrum corresponding to these rays is a series of coloured bands,
separated from each other by intervals of darkness. Such bands are
characteristic of luminous gases of all kinds.
283. Thus the spectrum of incandescent sodium-vapour con-
sists of a brilliant band on the confines of the orange and yellow ;
and the vapour is incompetent to shed forth any of the other light of
the spectrum. When this band is more accurately analyzed it resolves
itself into two distinct bands ; greater delicacy of analysis resolves
it into a group of bands with fine dark intervals between them.
The spectrum of copper-vapour is signalized by a series of green
bands, while the incandescent vapour of zinc produces brilliant bands
of blue and red.
284. The light of the bands produced by metallic vapours is very
intense, the whole of the light being concentrated into a few narrow
strips, and escaping in a great measure the dilution due to dispersion.
285. These coloured bands are perfectly characteristic of the
Spectrum Analysis. 41
vapour ; from their position and number the substance that produces
them can be unerringly inferred.
286. If two or more metals be introduced into the flame at the
same time, prismatic analysis reveals the bands of each metal as if
the others were not there. This is also true when a mineral contain-
ing several metals is introduced into the flame. The constituent
metals of the mineral will give each its characteristic bands.
287. Hence, having made ourselves acquainted with the bands
produced by all known metals, if entirely new bands show themselves,
it is a proof that an entirely new metal is present in the flame. It
is thus that Bunsen and KirchhofF, the founders of spectrum analysis,
discovered Rubidium and Caesium; and that Thallium, with its superb
green band, was discovered by Mr. Crookes.
288. The permanent gases when heated to a sufficient temperature,
as they may be by the electric discharge, also exhibit characteristic
bands in their spectra. By these bands they may be recognized, even
at stellar distances.
289. The action of light upon the eye is a test of unrivalled
delicacy. In spectrum analysis this action is brought specially into
play ; hence the power of this method of analysis.*
Further Definition of Radiation and Absorption.
290. The terms ray, radiation, and absorption, were employed
long prior to the views now entertained regarding the nature of light.
It is necessary more clearly to understand the meaning attached by the
undulatory theory to those terms.
291. And to complete our knowledge it is necessry to know that
all bodies, whether luminous or non-luminous, are radiants ; if they
do not radiate light they radiate heat.
292. It is also necessary to know that luminous rays are also heat
rays ; that the self-same waves of ether falling on a thermometer
produce the effects of heat ; and impinging upon the retina produce
the sensation of light. The rays of greatest heat however, as already
explained, lie entirely without the visible spectrum.
293. The radiation both of light and heat consists in the commu-
nication of motion from the vibrating atoms of bodies to the ether
which surrounds them. The absorption of heat consists in the accept-
ance of motion, on the part of the atoms of a body, from ether which
* Many persons are incompetent to distinguish one colour of the spectrum
from another ; red and green, for example, are often confounded. Dalton, the
celebrated founder of the Atomic Theory, could only distinguish by their form
ripe red cherries from the green leaves of the tree. This point is now attended
to in the choice of engine-drivers, who have to distinguish one coloured signal
from another. The defect is called colour-blindness, and sometimes Daltonism.
42 Notes on Light.
has been already agitated by a source of light or heat. In radiation,
then, motion is yielded to the ether; in absorption, motion is received
from the ether.
294. When a ray of light or of heat passes through a body without
loss ; in other words, when the waves are transmitted through the ether
which surrounds the atoms of the body, without sensibly imparting
motion to the atoms themselves, the body is transparent. If motion
be in any degree transferred from the ether to the atoms, in that
degree is the body opaque.
295. If either light or radiant heat be absorbed, the absorbing
body is warmed] if no absorption takes place, the light or radiant
heat, whatever its intensity may be, passes through the body without
affecting its temperature.
296. Thus in the dark foci referred to in Note 246, or in the focus
of the most powerful burning mirror which concentrates the beams
of the sun, the air might be of a freezing temperature, because the
absorption of the heat by the air is insensible. A plate of clear rock-
salt, moreover, placed at the focus, is scarcely sensibly heated, the
absorption being small ; while a plate of glass is shivered, and a plate
of blackened platinum raised to a white heat, or even fused, because
of their powers of absorption.
297. It is here worth remarking that calculations of the tempera-
tures of comets, founded on their distances from the sun, may be, and
probably are, entirely fallacious. The comet, even when nearest to
the sun, might be intensely cold. It might carry with it round its
perihelion the chill of the most distant regions of space. If trans-
parent to the solar rays it would be unaffected by the solar heat, as
long as that heat maintained the radiant form.
The pure Spectrum : Fraunhofer^ s Lines.
298. When a beam of white light issuing from a slit is decomposed,
the spectrum really consists of a series of coloured images of the slit
placed side by side. If the slit be wide, these images overlap ; but
in a pure spectrum the colours must not overlap each other.
299. A pure spectrum is obtained by making the slit through
which the decomposed beam passes very narrow, and by sending
the beam through several prisms in succession, thus augmenting the
dispersion.
300. When the light of the sun is thus treated, the solar spectrum
is found to be not perfectly continuous ; across it are drawn innume-
rable dark lines, the rays corresponding to which are absent. Dr.
Wollaston was the first to observe some of these lines. They were
afterwards studied with supreme skill by Fraunhofer, who lettered
them and made accurate maps of them, and from him they have been
called Fraunhofer s lines.
Reciprocity of Radiation and Absorption. 43
Reciprocity of Radiation and Absorption.
301. To account for the missing rays of the lines of Fraunhofer
was long an enigma with philosophers. By the genius of KirchhofF
the enigma was solved. Its solution carried with it a new theory of
the constitution of the sun, and a demonstration of a method which
enables us to determine the chemical composition of the sun, the
stars, and the nebulae. The application of Kirchhoff's principles by
Messrs. Huggins, Miller, Secchi, Janssen, and Lockyer has been of
especial interest and importance.
302. Kirchhoff's explanation of the lines of Fraunhofer is based
upon the principle that every body is specially opaque to such rays
as it can itself emit when rendered incandescent.
303. Thus the radiation from a carbonic oxide flame, which con-
tains carbonic acid at a high temperature, is intercepted in an astonish-
ing degree by carbonic acid. If the rays from a sodium flame be sent
through a second sodium flame, they will be stopped with particular
energy by the second flame. The rays from incandescent thallium
vapour are intercepted by thallium vapour, those from lithium vapour
by lithium vapour, and so of the other metals.
304. In the language of the undulatory theory, waves of ether are
absorbed with special energy — their motion is taken up with special
facility — by atoms whose periods" of vibration synchronise with the
periods of the waves. This is another way of stating that a body
absorbs with special energy the rays which it can itself emit.
305. If a beam of white light be sent through the intensely yellow
flame of sodium vapour, the yellow constituent of the beam is inter-
cepted by the flame, while rays of other refrangibilities are allowed
free transmission.
306. Hence, when the spectrum of the electric light is thrown
upon a white screen, the introduction of a sodium flame into the path
of the rays cuts off the yellow component of the light, and the spec-
trum is furrowed by a dark band in place of the yellow.
307. Introducing other flames in the same manner in the path of
the beam, if the quantity of metallic vapour in the flame be sufficient,
each flame will cut out its own bands. And if the flame through
which the light passes contain the vapours of several metals, we shall
have the dark characteristic bands of all of them upon the screen.
308. Expanding in idea our electric light until it forms a globe
equal to the sun in size, and wrapping round this incandescent globe
an atmosphere of flame, that atmosphere would cut off those rays of
the globe which it can itself emit, the interception of the rays being
declared by dark lines in the spectrum.
309. We thus arrive at a complete explanation of the lines of
Fraunhofer, and a new theory of the constitution of the sun. The
orb consists of a solid or molten nucleus, in a condition of intense
44 Notes on Light.
incandescence, but it is surrounded by a gaseous photosphere con-
taining vapours which absorb those rays of the nucleus which they
themselves emit. The lines of Fraunhofer are thus produced.
310. The lines of Fraunhofer are narrow bands of partial dark-
ness ; they are really illuminated by the light of the gaseous envelope
of the sun. But this is so feeble in comparison with the light of the
nucleus intercepted by the envelope, that the bands appear dark in
comparison with the adjacent brilliance.
311. Were the central nucleus abolished, the bands of Fraunhofer
on a perfectly dark ground, would be transformed into a series of
bright bandy. These would resemble the spectra obtained from a
flame charged with metallic vapours. They would constitute the
spectrum of the solar atmosphere.
312. It is not necessary that the photosphere should be composed
of pure vapour. Doubtless it contains vast masses of incandescent
cloudy matter, composed of white hot molten particles. These
intensely luminous white hot clouds may be the main origin of
the light which the earth receives from the sun, and with them
the true vapour of the photosphere may be more or less confusedly
mingled. But the vapour which produces the lines of Fraunhofer
must exist outside the clouds, as assumed by Kirchhoff.
Solar Chemistry.
313. From the dark bands of the spectrum we can determine
what substances enter into the composition of the solar atmosphere.
314. One example will illustrate the possibility of this. Let the
light from the sun and the light from incandescent sodium vapour
pass side by side through the same slit, and be decomposed by the
same prism. The solar light will produce its spectrum, and the
sodium light its yellow band. This yellow band will coincide
exactly in position with a characteristic dark band of the solar
spectrum, which Fraunhofer distinguishes by the letter D.
315. Were the solar nucleus absent, and did the vaporous photo-
sphere alone emit light, the dark line D would be a bright one. Its
character and position prove it to be the light emitted by sodium.
This metal, therefore, is contained in the atmosphere of the sun.*
316. The result is still more convincing when a metal which
gives a numerous series of bright bands finds each of its bands
exactly coincident with a dark band of the solar spectrum. By this
method Kirchhoff, to whom we owe, in all its completeness, this
splendid generalization, established the existence of iron, calcium,
* By reference to note 283 it will be seen that the sodium line is resolved by
delicate analysis into a group of lines. The Fraunhofer dark band D is similarly
resolved. It ought to be mentioned that both Mr. Talbot and Sir John Herschel
clearly foresaw the possibility of employing spectrum analysis in detecting
minute traces of bodies.
Solar Chemistry. 45
magnesium, sodium, chromium, and other metals in the solar
atmosphere ; and Mr. Huggins has extended the application of the
method to the light of the planets, fixed stars, and nebulae.*
Planetary Chemistry.
317. The light reflected from the moon and planets is solar light;
and, if unaffected by the planet's atmosphere, the spectrum of the
planet would show the same lines as the solar spectrum.
318. The light of the moon shows no other lines. There is no
evidence of an atmosphere round the moon.
319. The lines in the spectrum of Jupiter indicate a powerful
absorption by the atmosphere of this planet. The atmosphere of
Jupiter contains some of the gases or vapours present in the earth's
atmosphere. Feeble lines, some of them identical with those of
Jupiter, occur in the spectrum of Saturn.
320. The lines characterizing the atmospheres of Jupiter and
Saturn are not present in the spectrum of Mars. The blue portion
of the spectrum is mainly the seat of absorption ; and this, by giving
predominance to the red rays, may be the cause of the red colour of
Mars.
321. All the stronger lines of the solar spectrum are found in the
spectrum of Venus, but no additional lines.
Stellar Chemistry.
322. The atmosphere of the star Aldebaran contains hydrogen
sodium, magnesium, calcium, iron, bismuth, tellurium, antimony,
mercury. The atmosphere of the star Alpha in Orion contains
sodium, magnesium, calcium, iron, and bismuth.
323. No star sufficiently bright to give a spectrum has been
observed to be without lines. Star differs from star only in the
grouping and arrangement of the numerous fine lines by which their
spectra are crossed.
324. The dark absorption lines are strongest in the spectra of
yellow and red stars. In white stars the lines, though equally
numerous, are very poor and faint.
325. A comparison of the spectra of stars of different colours
suggests that the colours of the stars may be due to the action of
their atmospheres. Those constituents of the white light of the star
on which the lines of absorption fall thickest are subdued, the star
being tinted by the residual colour.
Father Secchi, of Rome, has studied the light of many hundreds
of stars, and has divided them into four classes.
* Professor Stokes foresaw the possible application of spectrum analysis to
solar chemistry.
46 Notes on Light.
Nebular Chemistry.
326. Some nebulae give spectra of bright 'bands, others give con-
tinuous spectra. The light from the former emanates from intensely
heated matter existing in a state of gas. This may in part account
for the weakness of the light of these nebulas.
327. It is probable that two of the constituents of the gaseous
nebula? are hydrogen and nitrogen.
The Red Prominences and Envelope of the Sun.
328. Astronomers had observed during total eclipses of the sun
vast red prominences extending from the solar limb many thousand
miles into space. The intense illumination of the circum-solar
region of our atmosphere masks, under ordinary circumstances, the
red prominences. They are quenched, as it were, by excess of light.
329. But when, by the intervention of the dark body of the moon,
this light is cut off, the prominences are distinctly seen.
330. It was proved by Mr. De la Rue and others that the red
matter of the prominences was wrapped round a large portion of the
sun's surface. According to the observations of Mr. Lockyer, the
red matter forms a complete envelope round the sun.
331. Examined by the spectroscope the matter of the prominences
shows itself to be, for the most part, incandescent hydrogen. With
it are mixed the vapours of sodium and magnesium.
332. Mr. Janssen in India, and Mr. Lockyer subsequently, but
independently, in England proved that the bright bunds of the
prominences might be seen without the aid of a total eclipse. The
explanation of this discovery is glanced at in Note 284, where the
intensity of the bright bands of incandescent gases was referred to
the practical absence of dispersion.
333. By sending the light, which under ordinary circumstances
masks the hydrogen bands, through a sufficient number of prisms it
may be dispersed, and thereby enfeebled in any required degree.
When sufficiently enfeebled the undispersed light of the incandescent
hydrogen dominates over that of the continuous spectrum. By going
completely round the periphery of the sun Mr. Lockyer found this
hydrogen atmosphere everywhere present, its depth, generally about
5,000 miles, being indicated by the length of its characteristic bright
lines. Where the hydrogen ocean is shallow the bright bands are
short, where the prominences rise like vast waves above the level of
the ocean the bright lines are long. The prominences sometimes
reach a height of 70,000 miles.
The Rainbow.
334. A beam of solar light, falling obliquely on the surface of a
rain- drop, is refracted on entering the drop; it is in part reflected
The Rainbow. 47
at the back of the drop, and on emerging from the drop it is again
refracted.
335. By these two refractions on entrance and on emergence the
beam of light is decomposed, and it quits the drop resolved into its
coloured constituents. It is received by the eye of an observer who
laces the dr6p and turns his back to the sun.
336. In general the solar rays, when they quit the drop, are
divergent, and therefore produce but a feeble effect upon the eye.
But at one particular angle the rays, after having been twice refracted
and once reflected, issue from the drop almost perfectly parallel.
They thus preserve their intensity like rays reflected from a parabolic
mirror, and produce a corresponding effect upon the eye. The angle
at which this parallelism is established varies with the refrangibility
of the light.
337. Draw a line from the sun to the observer's eye and prolong
this line beyond the observer. Conceive another line drawn from
the eye enclosing an angle of 42° 30' with the line drawn to the sun.
The rain-drop struck by this second line will send to the eye a
parallel beam of red light. Every other drop similarly situated, that
is to say, every drop at an angular distance of 42° 30' from the line
drawn to the sun will do the same. We thus obtain a circular band
of red light, forming part of the base of a cone, of which the eye of
the observer is the apex. Because of the angular magnitude of the
sun the width of this band will be half a degree.
338. From the eye of the observer conceive another line to be
drawn enclosing an angle of 40° 30' with the line drawn to the sun.
A drop struck by this line will send along the line an almost per-
fectly parallel beam of violet light to the eye. All drops at the same
angular distance will do the same, and we shall obtain a band of
violet light of the same width as the red. These two bands consti-
tute the limiting colours of the rainbow, and between them the
bands corresponding to the other colours lie.
339. The rainbow is in fact a spectrum, in which the rain-drops
play the part of prisms. The width of the bow from red to violet is
about two degrees. The size of the arc visible at any time mani-
festly depends upon the position of the sun. The bow is grandest
when it is formed by the rising or the setting sun. An entire semi-
circle is then seen by an observer on a plain, while from a mountain-
top a still greater arc is visible.
340. The angular distances and the order of colours here given
correspond to the primary bow, but in addition to this we usually see
a secondary bow of weaker hues, and in which the order of the colours
is that of the primary inverted. In the primary the red band forms the
convex surface of the arch ; it is the largest band ; in the secondary
the violet band is outside, the red forming the concavity of the bow.
341. The secondary bow is produced by rays which have under-
gone two reflexions within the drop, as well as two refractions at its
48 Notes on Light.
surface. It is this double internal reflexion that weakens the colour.
In the primary bow the incident rays strike the upper hemisphere of
the drop, and emerge from the lower one ; in the secondary bow the
incident rays strike the lower hemisphere of the drop, emerge from
the upper one, and then cross the incident rays to reach the eye of
the observer. The secondary bow is 3J degrees wideband it is 7-|-
degrees higher than the primary. From the space between the two
bows part of the light reflected from the anterior surfaces of the rain-
drops reaches the eye ; but no light whatever that enters the rain-
drops in this space is reflected to the eye. Hence this region of the
falling shower is darkest.
Interference of Light.
342. In wave motion we must clearly distinguish the motion of
the wave from the motion of the individual particles which at any
moment constitute the wave. For while the wave moves forward
through great distances, the individual particles of water concerned
in its propagation perform a comparatively short excursion to and
fro. .A sea-fowl, for example, as the waves pass it, is not carried
forward, but moves up and down.*
343. Here, as in other cases, the distance through which the indi-
vidual water particles oscillate, or through which the fowl moves
vertically up and down, is called the amplitude of the oscillation.
344. When light from two different sources passes through the
same ether, the waves from the one source must be more or less
affected by the waves from the other. This action is most easily
illustrated by reference to water-waves.
345. Let two stones be cast at the same moment into still water.
Eound each of them will spread a series of circular waves. Let us
fix our attention on a point A in the water, equally distant from
the two centres of disturbance. The two first crests of both systems
of waves reach this point at the same moment, and it is lifted by
their joint action to twice the height that it would attain through the
action of either wave taken singly.
346. The first depression, or sinus as it is called, of the one system
of waves also reaches the point A at the same moment as the first
sinus of the other, and through their joint action the point is de-
pressed to twice the depth that it would attain by the action of either
sinus taken singly.
347. What is true of the first crest and the first depression is also
true of all the succeeding ones. At the point A the successive crests
will coincide, and the successive depressions will coincide, the agita-
tion of the point being twice what it would be if acted upon by one
only of the systems of waves.
* Strictly speaking the water particles describe closed curves, and not straight
vertical lines.
Interference of Light. 49
348. The length of a wave is the distance from any crest, or any
sinus, to the crest or sinus next preceding or succeeding. In the
case of the two stones dropped at the same moment into still water, it
is manifest that the coincidence of crest with crest and of sinus with
sinus would also take place if the distance from the one stone to the
point A exceeded the distance of the other stone from the same point
by a whole wave-length. The only difference would be, that the
second wave of the nearest stone would then coincide with the first
wave of the most distant one. The one system of waves would here
be retarded a whole wave-length behind the other system.
349. A little reflection will also mnke it clear that coincidence
of crest with crest and of sinus with sinus will also occur at the
point A when the retardation of the one system behind the other
amounts to any number of whole ivave-lengths.
350. But if we suppose the point A to be half a wave-length more
distant from the one stone than from the other, then as the waves
pass the point A the crests of one of the systems will always coincide
with the sinuses of the other. When a wave of the one system tends
to elevate the point A, a wave from the other system will, at the same
moment, tend to depress it. As a consequence the point will neither
rise nor sink, as it would do if acted upon by either system of waves
taken singly. The same neutralization of motion occurs where the
difference of path between the two stones and the point A amounts to
any odd number of half wave-lengths.
351. Here, then, by adding motion to motion, we abolish motion
and produce rest. In precisely the same way we can, by adding
sound to sound, produce silence, one system of sound-waves being
caused to neutralize another. So also by adding heat to heat we can
produce cold, while by adding light to light we can produce darkness.
It is this perfect identity of the deportment of light and radiant heat
with the phenomena of wave-motion that constitutes the strength of
the Theory of Undulation.
352. This action of one system of waves upon another, whereby
the oscillatory motion is either augmented or diminished, is called
Interference. In relation to optical phenomena it is called the Inter-
ference of Light. We shall henceforth have frequent occasion to
apply this principle.
Diffraction, or the Inflexion of Light.
353. Newton, who was familiar with the idea of an ether, and
indeed introduced it in some of his speculations, objected that if
light were propagated by waves, shadows could not exist ; for that
the waves would bend round opaque bodies, and abolish the shadows
behind them. According to the wave theory this bending round of
the waves actually occurs, but the different portions of the inflected
waves destroy each other by their interference.
E
50 Notes on Light.
354. This bending of the waves of light round the edges of
opaque bodies, receives the name of Diffraction or Inflexion (Ger-
man, Beugung). We have now to consider some of the effects of
diffraction.
355. And for this purpose it is necessary that our source of light
should be a physical point or a fine line : for when an extensive
luminous surface is employed, the effects of its different points in
diffraction phenomena neutralize each other.
356. A point of light may be obtained by converging, by a lens
of short focus, the parallel rays of the sun, admitted through a small
aperture into a dark room. The small image of the sun formed at
the focus is here our luminous point. The image of the sun formed
on the surface of a silvered bead, or indeed upon the convex surface
of a glass lens, or of a watch-glass blackened within, also answers the
purpose.
357. A line of light is obtained by admitting the sunlight through
a slit, and sending the slice of light through a cylindrical lens. The
rectangular beam is contracted to a physical line at the focus of the
lens. A glass tube blackened within and placed in the light, reflects
from its surface a luminous line which also answers the purpose. For
many experiments, indeed, the circular aperture, or the slit itself,
suffices without any condensation by a lens.
358. In the experiment now to be described, a slit of variable
width is placed in front of the electric lamp, and this slit is looked at
from a distance through another slit, also of variable aperture. The
light of the lamp is rendered monochromatic by placing a pure red
glass in front of the slit.
359. With the eye placed in the straight line drawn through both
slits from the incandescent carbon points of the electric lamp an extra-
ordinary appearance is observed. Firstly, the slit in front of the lamp
is seen as a vivid rectangle of light ; but right and left of it is a
long series of rectangles, decreasing in vividness, and separated from
each other by intervals of absolute darkness.
360. The breadth of the bands varies with the width of the slit
placed in front of the eye. If the slit be widened the images become
narrower, and crowd more closely together; if the slit be narrowed,
the images widen and retreat from each other.
361. It may be proved that the width of the bands is inversely
proportional to the width of the slit held in front of the eye.
362. Leaving everything else unchanged, let a blue glass or a
solution of ammonia sulphate of copper, which gives a very pure blue,
be placed in the path of the light. A series of blue bands is thus
obtained, exactly like the former in all respects save one ; the blue
rectangles are narrower, and they are closer together than the red
ones.
363. If we employ colours of intermediate refrangibilities between
red and blue, which we may do by causing the different colours of a
Diffraction, or the Inflexion of Light. 51
spectrum to shine through the slit, we should obtain bands of colour
intermediate in width and occupying intermediate positions between
those of the red and blue. Hence when white light passes through the
slit the various colours are not superposed, and instead of a series of
monochromatic bands, separated from each other by intervals of dark-
ness, we have a series of coloured spectra placed side by side, the
most refrangible colour of each spectrum being nearest to the slit.
364. When the slit in front of the camera is illuminated by a
candle flame, instead of the more intense electric light, substantially
the same effects, though less brilliant, are observed.
365. What is the meaning of this experiment, and how are the
lateral images of the slit produced? Of these and certain accompany-
ing results the emission theory is incompetent to offer any explanation.
Let us see how they are accounted for by the theory of undulation.
366. For the sake of simplicity, we will consider the case of
monochromatic light. Conceive a wave of ether advancing from the
first slit towards the second, and finally filling the second slit When
the wave passes through the latter it not only pursues its direct
course to the retina, but diverges right and left, tending to throw
into motion the entire mass of the ether behind the slit. In fact, every
point of the wave which Jills the slit is itself a centre of new wave-
systems , which are transmitted in all directions through the ether behind
the slit. We have now to examine how these secondary waves act upon
each other.
367. First, let us regard the central rectangle of the series. It is
manifest that the different parts of every transverse section of the
wave, which in this case fills our slit, reach the retina at the same
moment. They are in complete accordance, for no one portion is
retarded in reference to any other portion. The rays thus coming
direct from the source through the slit to the retina produce the
central band of the series.
368. But now let us consider those waves which diverge obliquely
from the slit. In this case, the waves from the two edges of the slit
have, in order to reach the retina, to pass over unequal distances. Let
us suppose the difference in path of the two marginal rays to be a
whole wave-length of the red light ; how must this difference affect
the final illumination of the retina ?
369. Fix your attention upon the particular ray or line of light that
passes exactly through the centre of the slit to the retina. The difference
of path between this central ray and the two marginal rays is, in the
case here supposed, half a wave-length. The least reflection will
make it clear that every ray on the one side of the central line finds a
ray upon the other side, from which its path differs by half an un-
dulation, with which, therefore, it is in complete discordance. The
consequence is that the light on the ©ne side of the central line will
completely abolish the light on the other side of that line, absolute
darkness being the result of their mutual extinction. The first dark
E 2
52 Notes on Light.
interval of our series of bands is thus accounted for. It is produced
by an obliquity which causes the paths of the marginal rays to be
a whole wave-length different from each other.
370. When the difference between the paths of the marginal rays
is half a wave-length, a partial destruction of the light is effected.
The luminous intensity corresponding to this obliquity is a little less
than one-half — accurately 0'4 — of that of the undiffracted light.
371. If the paths of the marginal rays be three semi-undulations
different from each other, and if the whole beam be divided into
three equal parts, two of these parts will completely neutralize each
other, the third only being effective. Corresponding, therefore, to
an obliquity which produces a difference of three semi-undulations
in the marginal rays, we have a luminous band, but one of consider-
ably less intensity than the undiffracted central band.
372. With a marginal difference of path of four semi-undulations
we have a second extinction of the entire beam, a space of absolute
darkness corresponding to this obliquity. In this way we might
proceed further, the general result being that, whenever the obliquity
is such as to produce a marginal difference of path of an even number
of semi-undulations, we have complete extinction ; while, when the
marginal difference is an odd number of semi-undulations, we have
only partial extinction, a portion of the beam remaining as a luminous
band.
373. A moment's reflection will make it plain that the shorter the
wave, the less will be the obliquity required to produce the necessary
retardation. The maxima and minima of blue light must therefore
fall nearer to the centre than the maxima and minima of red light.
The maxima and minima of the other colours fall between these
extremes. In this simple way the undulatory theory completely
accounts for the extraordinary appearance referred to in Note 359.
When a slit and telescope are used, instead of the slit and naked
eye, the effects are magnified and rendered more brilliant.
Measurement of the Waves of Light.
374. We are now in a condition to solve the important problem
of measuring the length of a wave of light.
375. The first of our dark bands corresponds, as already explained,
to a difference of marginal path of one undulation ; our second dark
band to a difference of path of two undulations ; our third dark
band to a difference of three undulations, and so forth. With a slit
I- 35* millimeter wide Schwerd found the angular distance of the
first dark band from the centre of the field to be 1' 38". The
angular distances of the other dark bands are twice, three times,
four times, &c., this quantity, that is to say they are in arithmetical
progression.
* The millimeter is about rth of an inch.
Measurement of the Waves of Light. 53
376. Draw a diagram of the slit E c with the beam passing through
it at the obliquity corresponding to the first dark band. Let fall a
perpendicular from one edge, E, of the slit on the marginal ray of
the other edge at d. The distance, c d, between the foot of this
perpendicular and the other edge is the length of the wave of light.
From the centre E, with the width E c as radius, suppose a semicircle
to be described ; its radius being 1*35, the length of this semicircle
is readily found to be 4*248 millimeters. Now, the length of this
semicircle is to the length c d of the wave as 180° to X'38", or as
048,000" to 98". Thus we have the proportion —
648,000 I 98 1 1 4*248 to the wave-length c d*
Making the calculation we find the wave-length for this particular
kind of light (red), to be 0'000643 of a millimeter, or 0-000026 of
an inch.
377. Instead of receiving them directly upon the retina, the
coloured fringes may be received upon a screen. In this case it is
desirable to employ a lens of considerable convergent power to bring
the beam from the first slit to a focus, and to place the second slit
or other diffracting edge or edges between the focus and the screen.
The light in this case virtually emanates from the focus.
378. If the edge of a knife be placed in the beam parallel to the
slit, the shadow of the edge upon the screen will be bounded by a
series of parallel coloured fringes. If the light be monochromatic
the bands will be simply bright and dark. The back of the knife
produces the same effect as its edge. A wooden or an ivory paper-
knife produces precisely the same effect as a steel knife. The fringes
are absolutely independent of the character of the substance round
the edge of which the light is diffracted.
379. A thick wire placed in the beam has coloured fringes on
each side of its shadow, if the wire be fine, or if a human hair be
employed, the geometric shadow itself will be found occupied by
parallel stripes. The former are called the exterior fringes, the
latter the interior fringes. In the hands of Young and Fresnel
all these phenomena received their explanation as effects of inter-
ference.
380. A slit consists of two edges facing each other. When a slit
is placed in the beam between the focus and the screen, the space
between the edges is occupied by stripes of colour.
381. Looking at a distant point of light through a small circular
aperture the point is seen encircled by a series of coloured bands.
If monochromatic light be used these bands are simply bright and
dark, but with white light the circles display iris-colours.
382. These results are capable of endless variation by varying
the size, shape, and number of the apertures through which the
* C d is so minute that it practically coincides with the circle drawn round E.
54 Notes on Light.
point of light is observed. The street lamps at night, looked at
through the meshes of a handkerchief, show diffraction phenomena.
The diffraction effects obtained by Schwerd in looking through a
bird's feathers are very gorgeous. The iridescence of Alpine clouds
is also an effect of diffraction.*
383. Following out the indications of theory Poisson was led to
the paradoxical result that in the case of an opaque circular disk the
illumination of the centre of the shadow, caused by diffraction at the
edge of the disk, is precisely the same as if the disk were altogether
absent. This startling consequence of theory was afterwards verified
experimentally by Arago.
Colours of Thin Plates.
384. When a beam of monochromatic light — say of pure red,
which is most easily obtained by absorption — falls upon a thin,
transparent film, a portion of the light is reflected at the first surface
of the film ; a portion enters the film, and is in part reflected at the
second surface.
385. This second portion having crossed the film to and fro is
retarded with reference to the light first reflected. The case resembles
that of our two stones dropped into still water at unequal distances
from the point A (Note 345).
386. If the thickness of the film be such as to retard the beam
reflected from the second surface a whole wave-length, or any number
of whole wave-lengths— or, in other words, any even number of half
wave-lengths — the two reflected beams, travelling through the same
ether, will be in complete accordance ; they will therefore support
each other, and make the film appear brighter than either of them
would do taken singly.
387. But if the thickness of the film be such as to retard the
beam reflected from the second surface half a wave-length, or any
odd number of half wave-lengths, the two reflected beams will be
in complete discordance ; and a destruction of light will follow. By
the addition of light which has undergone more than one reflexion
at the second surface to the light which has undergone only one
* This may be imitated by the spores of Lycopodium. The diffraction phe-
nomena of ' actinic clouds ' are exceedingly splendid. One of the most inte-
resting cases of diffraction by small particles that ever came before me was that
of an artist whose vision was disturbed by vividly-coloured circles. "When he
came to me he was in great dread of losing his sight ; assigning as a cause of
his increased fear that the circles were becoming largpr and the colours more
vivid. I ascribed the colours to minute particles in the humours of the eye, and
encouraged him by the assurance that the increase of size and vividness indi-
cated that the diffracting particles were becoming smaller, and that they might
finally be altogether absorbed. The prediction was verified. It is needless to
say one word on the necessity of optical knowledge in the case of the practical
oculist.
Colours of Thin Plates. 55
reflexion, the beam reflected from the first surface may be totally
destroyed. Where this total destruction of light occurs the film
appears black.
388. If the film be of variable thickness, its various parts will
appear bright or dark according as the thickness favours the accord-
ance or discordance of the reflected rays.
389. Because of the different lengths of the waves of light, the
different colours of the spectrum require different thicknesses to pro-
duce accordance and discordance ; the longer the waves, the greater
must be the thickness of the film. Hence those thicknesses which
effect the extinction of one colour will not effect the extinction of
another. When, therefore, a film of variable thickness is illuminated
by white light, it displays a variety of colours.
390. These colours are called the colours of thin plates.
391. The colours of the soap-bubble ; of oil or tar upon water ; of
tempered steel ; the brilliant colours of lead skimmings ; Nobili's
metallo- chrome ; the flashing colours of certain insects' wings, are all
colours of thin plates. The colours are produced by transparent films
of all kinds. In the bodies of crystals we often see iridescent colours
due to vacuous films produced by internal fracture. In cutting the
dark ice under the moraines of glaciers internal fracture often occurs,
and the colours of thin plates flash forth from the body of the ice with
extraordinary brilliancy.
392. Newton placed a lens of small curvature in optical contact
with a plane surface of glass. Between the lens and the surface he
had a film of air, which gradually augmented in thickness from the
point of contact outwards. He thus obtained in monochromatic light
a series of bright and dark rings, corresponding to the different thick-
nesses of the film of air, which produced alternate accordance and
discordance.
393. The rings produced by violet he found to be smaller than
those produced by red, while the rings produced by the other colours
fell between these extremes. Hence when white light is employed,
* Newton's Rings' appear as a succession of circular bands of colour.
A far greater number of the rings is visible in monochromatic than
in white light, because the differently coloured rings, after a certain
thickness of film has been attained, become superposed and re-blended
to form white light.
394. Newton, considering the means at his disposal, measured the
diameters of his rings with marvellous accuracy ; he also determined
from its focal length and its refractive index the diameter of the
sphere of which his lens formed a part. He found the squares of the
diameters of his rings to be in arithmetical progression, and conse-
quently that the thicknesses of the film of air corresponding to the -
diameters of the rings were also in arithmetical progression.
395. He determined the absolute thicknesses of the plates of air at
which the rings were formed. Employing the most luminous rays of
56 Notes on Light.
the spectrum, that is the rays at the common boundary of the yellow
and orange, he found the thickness corresponding to the first bright
ring to be TT^OTTO^ °f an inch.
396. The entire series of bright rings were formed at the following
successive thicknesses : —
SinnJ'J
and the series of dark rings, separating the bright ones, at the thick-
T78000>
397. To account for the rings, Newton assumed that the light
particles were endowed with Jits of easy transmission and of easy
reflexion. He probably figured those particles as endowed at the same
time with a motion of translation through space, and a motion of
•rotation round their own axes. If we suppose such particles to
resemble little magnets which present alternately attractive and
repulsive poles to the surface which they approach, we have a concep-
tion in conformity with the notion of Newton.
398. According to this conception ordinary reflexion and refrac-
tion would depend upon the presentation of the repulsive or the
attractive poles of the particles to the reflecting or refracting surface.
399. Figure then the rotating light particles entering the film of
air between Newton's lens and plate. If the distance between both be
such as to enable the light particle to perform a complete rotation, it
will present at the second surface of the film of air the same pole that
it presented at the first. It will therefore be transmitted, and will
not return to the eye.
400. This effect would also take place if the distance between the
plate and lens were such as to enable the light particle to perform
two, three, four, &c., complete rotations. The dark rings of Newton
were thus accounted for. They occurred at places where the light
particles, instead of being sent back to the eye from the second surface
of the film, were transmitted through that surface.
401. But if the thickness of the film be such as to allow the light
particle which has entered the first surface to perform only half a
rotation before it arrives at the second surface ; then a repulsive pole
will be presented to the latter, and the particle will be driven back
to the eye. The same will occur if the distance be such as to enable
the light particle to perform three, or five, or seven, &c., semi-rota-
tions. The bright rings of Newton were thus accounted for ; they
occurred at places where the light particles on reaching the second
surface of the film were reflected back to the eye.
402. The theory of emission is here at direct issue with the theory
of undulation. Newton assumes that the action which produces the
alternate bright and dark rings takes place at a single surface ; i. e.
the second surface of the film. The undulatory theory affirms that
the rings are caused by the interference of rays reflected from both
Colours of Thin Plates. 57
surfaces. This has been proved to be the case. By employing
polarised light (to be subsequently described and explained) we can
destroy the reflexion at the first surface of the film, and when this is
done the rings vanish altogether.
403. The beauty and subtlety of Newton's conception are, how-
ever, manifest ; and the theory was apparently supported by the fact
that rings of feeble intensity are actually formed by transmitted light,
and that the bright rings by transmitted light correspond to thick-
nesses which produce dark rings in reflected light.
404. The transmitted rings are referred by the undulatory theory
to the interference of rays which have passed directly through the
film, with others which have undergone two reflexions within the film.
They are thus completely accounted for.
NOTE. — The thickness -pr¥Vo-o' of an inch referred to in Note 396,
as that corresponding to the first bright ring, is one-fourth of the
length of an undulation of the light employed by Newton. Hence,
in passing to and fro through the film, the rays reflected at the
second surface are half an undulation behind those reflected at the
first surface. At this thickness, therefore, the ring ought, according
to the principles of interference, to be dark instead of bright. The
same remarks apply to the thicknesses yy-g^^, TT^xrnirj &c- *> ^e
former corresponds to a retardation of three, and the latter to a
retardation of five semi-undulations. With regard to the dark rings,
the first of them occurs at a thickness the double of which is the
length of a whole undulation ; the second of them occurs at a thick-
ness which, when doubled, is equal to two wave-lengths ; the third
at a thickness double of which is three wave-lengths. Hence, if we
take the thickness of the film alone into account, the bright rings ought
to be dark, and the dark rings bright.
But something besides thickness is to be considered here. In the
case of the first surface of the film the wave passes from the dense
ether of the glass into the rare ether of the air. In the case of the
second surface of the film the wave passes from the rare ether of
the air into the dense ether of the glass. This difference at the two
reflecting surfaces of the film can be proved to be equivalent to the
addition of half a wave-length to the thickness of the film. To the
absolute thickness, therefore, as measured by Newton, half a wave-
length is in each case to be added ; when this is done the rings follow
each other in exact accordance with the law of interference enunciated
in Notes 348 to 350.
Double Refraction.
405. In air, water, and well-annealed glass, the luminiferous ether
has the same elasticity in all directions. There is nothing in the
molecular grouping of these substances to interfere with the perfect
homogeneity of the ether.
406. But when water crystallizes to ice, the case is different ; here
58 Notes on Light.
the molecules are constrained by their proper forces to arrange them-
selves in a certain determinate manner. They are, for example,
closer together in some directions than in others. This arrangement
of the molecules carries along with it an arrangement of the sur-
rounding ether, which causes it to possess different degrees of elas-
ticity in different directions.
407. In a plate of ice, for example, the elasticity of the ether in a
direction perpendicular to the surface of freezing is different from its
elasticity in a direction parallel to the same surface.
408. This difference is displayed in a peculiarly striking manner
by Iceland spar, which is crystallized carbonate of lime ; and in con-
sequence of the existence of these two different elasticities, a wave of
light passing through the spar is divided into two ; the one rapid,
corresponding to the greater elasticity, and the other slow, corre-
sponding to the lesser elasticity.
409. Where the velocity is greatest, the refraction is least ; and
where the velocity is least the refraction is greatest. Hence in Ice-
land spar, as we have two waves moving with different velocities, we
have double refraction.
410. This is also true of the greater number of crystalline bodies.
If the grouping of the molecules be not in all directions alike, the
ether will not be in all directions equally elastic, and double re-
fraction will infallibly result.
411. In rock salt, alum, and other crystals this homogeneous
grouping of the molecules actually occurs, and such crystals behave
like glass, water, or air.
412. In certain doubly refracting crystals the molecules are
arranged in the same manner on all sides of a certain direction. For
example, in the case of ice the molecular arrangement is the same
all round the perpendiculars to the surface of freezing.
413. In like manner, in Iceland spar the molecules are arranged
symmetrically round the crystallographic axis, that is, round the
shortest diagonal of the rhomb into which the crystal may be
cloven.*
414. When a beam of light passes through ice perpendicular to
the surface of freezing, or through Iceland spar parallel to the crys-
tallographic axis, there is no double refraction. These cases are repre-
sentative ; that is to say, there is no double refraction in the direction
round which the molecular arrangement is in all directions the same.
* The arrangement of the molecules is such, that Iceland spar maybe cloven
with great and equal facility in three different directions. The planes of cleavage
are here oblique to each other. Eock salt also cleaves readily and equally in
three directions, the planes of cleavage being at right angles to each other.
Hence, while rock salt cleaves into cubes, Iceland spar cleaves into rhombs.
Many crystals cleave with different facilities in different directions. Selenite
and crystallized sugar (sugar-candy) are examples.
Double Refraction. 59
415. This direction of no double refraction is called the optic axis
of the crystal.
NOTE. — The vibrations of the ether being transverse to the di-
rection of the ray, the elasticity which determines the rapidity of
transmission is that at right angles to the ray's direction. In Iceland
spar the velocity is slowest in the direction of the axis ; hence the
elasticity at right angles to the axis is a minimum. The ray, on the
other hand, whose vibrations are executed along the axis is the most
rapid; hence the elasticity of the ether along the axis is a maximum.
In perfectly homogeneous bodies the surface of elasticity would be
spherical ; it would be measured by the same length of radius in all
directions. In the case of Iceland spar the surface of elasticity is an
ellipsoid whose longer axis coincides with the axis of the crystal.
Phenomena presented by Iceland Spar.
416. The two beams into which the incident beam is divided by
the spar do not behave alike. One of them obeys the ordinary law of
refraction ; its index of refraction is perfectly constant and indepen-
dent of its direction through the crystal. The angles of incidence
and refraction are in the same plane, as in the case of ordinary re-
fraction. The ray which behaves thus is called the ordinary ray.
In its case the sine of the angle of incidence is to the sine of the
angle of refraction, or the velocity of light in air is to its velocity in
the crystal, in the constant ratio of 1 "654 to 1. The number 1'654
is the ordinary index of Iceland spar.
417. But the other beam acts differently. Its index of refraction
is not constant, nor is the angle of refraction as a general rule in the
same plane as the angle of incidence. The ray which behaves thus
is called the extraordinary ray. If a prism be formed of the spar
with its refracting angle parallel to the optic axis, when the incident
beam traverses the prism at right angles to the optic axis, the separa-
tion of its two parts is a maximum. Here the full difference of
elasticity between the axial direction and that perpendicular to it
comes into play, and the extraordinary ray suffers its minimum re-
tardation, and therefore its minimum refraction. Its refractive index
is then 1-483.
418. The index of refraction of the extraordinary ray varies with
its direction through the crystal from 1'483 to T654. The mini-
mum value of the ratio of the two sines, or of the two velocities, viz.
1-483, is called the extraordinary index.
419. When a small aperture through which light passes is re-
garded through a rhomb of Iceland spar two apertures are seen. If
the rhomb be placed over a black dot on a sheet of white paper, two
dots will be seen ; and if the spar be turned, one of the images of
the aperture or of the dot will rotate round the other.
420. The rotating image is that formed by the extraordinary ray.
60 Notes on Light.
421 . One of the two images of the dot is also nearer than the other.
The ordinary ray behaves as if it came from a more highly refractive
medium, and the greater the refraction the nearer must the image
appear. The apparent shallowness of water is referred to in Notes
131 and 132. With bisulphide of carbon the shallowness would be
more pronounced, because the refraction is greater. In Iceland spar
the ordinary index bears nearly the same relation to the extraordi-
nary as the index of bisulphide of carbon to that of water ; hence the
ordinary image must appear nearer than the extraordinary one.
422. Brewster showed that a great number of crystals possessed
two optic axes, or two directions on which a beam passes through the
crystal without division. Crystallized sugar, mica, heavy spar, sul-
phate of lime and topaz are examples.
423. Thus crystals divide themselves into —
I. Single refracting crystals, such as rock salt, alum, and fluor spar;
and
IT. Double refracting crystals, of which we have two kinds, viz.
a. Uniaxal crystals, or those with a single optic axis, such as
Iceland spar, rock crystal, and tourmaline ; and
b. Biaxal crystals, or those which possess two optic axes, such as
arragonite, felspar, and those mentioned in 422.
424. When on a plate of Iceland spar cut perpendicular to the
axis, a beam of light falls obliquely, the ordinary ray being the more
refracted is nearer to the axis than the extraordinary. The extraor-
dinary ray is as it were repelled by the axis. But Biot showed that
there are many crystals in which the reverse occurs, in which, that is
to say, the extraordinary ray is nearer to the axis than the ordinary,
being as it were attracted. The former class he called repulsive or
negative crystals; Iceland spar, ruby, sapphire, emerald, beryl, and
tourmaline being examples. The latter class he called attractive or
positive crystals, rock crystal, ice, zircon being examples.
The Polarization of Light.
425. The double refraction of Iceland spar was discovered by
Erasmus Bartholinus, and was first described by him in a work pub-
lished in Copenhagen in 1669. The celebrated Huygens sought to
account for the phenomenon on the principles of a wave theory, and
he succeeded in doing so.
426. In his experiments on this subject, Huygens found that when
a common luminous beam passes through Iceland spar in any direction
save one (that of the optic axis), it is always divided into two beams
of equal intensity ; but that when either of these two half-beams is sent
through a second piece of spar, it is usually divided into two of unequal
intensity, and that there are two positions of the spar in which one of
the beams vanishes altogether.
The Polarization of Light. 61
427. On turning the spar round this position of absolute dis-
appearance, the missing beam appeared ; its companion at the same
time becoming dimmer; both of them then passed through a phase
of equal intensity, and when the rotation was continued, the beam
which was first transmitted disappeared.
428. Reflecting on this experiment Newton came to the conclusion,
that the divided beam had acquired sides by its passage through the
Iceland spar, and that its interception and transmission depended on the
way on which those sides presented themselves to the molecules of the
second crystal. He compared this two-sidedness of a beam of light to
the two-endedness of a magnet known as its polarity ; and a luminous
beam exhibiting this two-sidedness was afterwards said to be polarized.
429. In 1808, Malus, while looking through a birefracting prism
at one of the windows of the Luxembourg Palace, from which the
solar light was reflected, found that in a certain position of the spar,
the ordinary image of the window almost wholly disappeared ; while
in a position perpendicular to this, the extraordinary image dis-
appeared. He discerned the analogy between this action and that
discovered by Huygens in Iceland spar, and came to the conclusion
that the effect was due to some new property impressed upon the
light by its reflexion from the glass.
430. What is this property ? It may be most simply studied and
understood by means of the crystal called tourmaline. This crystal
is birefractive ; it divides a beam of light incident upon it into two,
but its molecular grouping, and the consequent disposition of the
ether within it, are such that one of these beams is rapidly quenched,
while the other is transmitted with comparative freedom.
431. It is to be borne in mind that the motions of the individual
ether particles are transverse to the direction in which the light is
propagated (read Note 219). In a beam of ordinary light the vibrations
occur in all directions round the line of propagation.
432. The change suffered by light in passing through a plate of
tourmaline, of sufficient thickness, and cut parallel to the axis is
this: — All vibrations save those executed parallel to the axis are
quenched within the crystal. Hence the beam emergent from the
plate of tourmaline has all its vibrations reduced to a single plane.
In this condition it is a beam of plane polarized light.
433. Imagine a cylindrical beam of light with all its ether
particles vibrating in the same direction — say horizontally — looked
down upon vertically, the ether particles, if large enough, would be
seen performing their excursions to and fro across the direction of the
beam. Looked at crosswise horizontally, the particles would be seen
advancing and retreating, but their paths would be invisible, every
ether particle covering its own path. In the one case we should see
the lines of excursion ; in the other case, the ends of the lines only.
In this, according to the undulatory theory, consists the two-sidedness
discovered by Huygens, and commented on by Newton.
62 Notes on Light.
Polarization of Light by Reflexion.
434. The quality of two-sidedness is also impressed upon light by
reflexion. This is the great discovery of Malus. A beam reflected
from glass is in part polarized at all oblique incidences, a portion of
its vibrations being reduced to a common plane. At one particular
incidence the beam is perfectly polarized, all its vibrations being
reduced to the same plane. The angle of incidence which corresponds
to this perfect polarization is called the polarizing angle.
435. The polarizing angle is connected with the index of refraction
of the medium by a very beautiful law discovered by Sir David
Brewster.* When a luminous beam is incident upon a transparent
substance, it is in part reflected and in part refracted. At one par-
ticular incidence the reflected and refracted portions of the beam are
at right angles to each other. The angle of incidence is then the polar-
izing angle. This is the geometrical expression of the law of
Brewster.
436. The polarizing angle augments with the refractive index of
the medium. For water it is 53°, for glass 58°, and for diamond
68°.
437. Thus a beam of ordinary light, whose vibrations are executed
in all directions, impinging upon a plate of glass at the polarizing
angle, has, after reflexion, all its vibrations reduced to a common plane.
The direction of the vibrations of the polarized beam is parallel to the
polarizing surface.
438. Let a beam thus polarized by reflexion at the surface of one
plate of glass impinge upon a second plate at the polarizing angle.
In one position of this plate the beam suffers its maximum reflexion.
In a certain other position the beam is wholly transmitted, there is
no reflexion. In this experiment the angle of incidence remains
unchanged, nothing being altered save the side of the ray which strikes
the reflecting surface.
439. The reflexion of the polarized beam is a maximum when
the lines along which the ether particles vibrate are parallel to the
reflecting surface. It is wholly transmitted when the lines of
vibration strike the reflecting surface at the polarizing angle. The
reflexion is then zero. By taking advantage of this fact, the re-
flexion from the first surface of a thin film has been abolished,
Newton's rings being thereby rendered incapable of formation, as
stated in Note 402.
440. A beam which meets the first surface of a plate of glass
with parallel sides at the polarizing angle meets the second surface
also at its polarizing angle, and is in part reflected there perfectly
polarized. Hence, by augmenting the number of plates, the
* The index of refraction of the medium is the tangent of the polarizing
angle.
Polarization of Light by Refraction. 63
repeated reflexions at their limiting surfaces furnish a polarized
beam of greater intensity than that obtained by reflexion at a single
surface.
Polarization of Light by Refraction.
441. We have hitherto directed our attention to the reflected
portion of the beam ; but the refracted portion, which enters the
glass, is also partially polarized. The quantities of polarized light
in the reflected and refracted beams are always equal to each other.
442. The plane of vibration in the refracted beam is at right
angles to that in the reflected beam.
443. When several plates of glass are placed parallel to each other,
and a beam is permitted to fall upon them at the polarizing angle, at
every passage from plate to plate a portion of light is reflected polar-
ized, an equal portion of polarized light entering the glass at the same
time. By duly augmenting the number of plates, the polarization by
the successive refractions may be rendered sensibly perfect. When
this occurs, if any further plates be added to the bundle, reflexion
entirely ceases at their limiting surfaces, the beam afterwards being
wholly transmitted.
Polarization of Light by Double Refraction.
444. In the case last considered the light was polarized by ordi-
nary refraction. The polarization of light by double refraction has
been already touched upon in Notes 432 and 433. We shall now
extend our examination of the crystal of tourmaline there referred to,
and turn it to account in the examination of other crystals.
445. If a beam of light which has passed through one plate of
tourmaline impinge' upon a second plate, it will pass through both, if
the axes of the two plates be parallel. But if they are perpendicular
to each other, then the light transmitted by the one is quenched
by the other, darkness marking the space where the two plates are
superposed.
446. If the two axes be oblique to each other, a portion of the
light will pass through both plates. For, in a manner similar to
the resolution of forces in ordinary mechanics, an oblique vibration
may be resolved into two, one parallel to the axis of the tourmaline,
the other perpendicular to the axis. The latter component is quenched,
but the former is transmitted.
447. Hence if the axes of two plates of tourmaline be perpen-
dicular to each other, a third plate of tourmaline introduced
obliquely between them, or a plate of any other crystal which acts
in a manner similar to the tourmaline, will transmit a portion of
the light emergent from the first crystal. The plane of vibration
of this light being oblique to the axis of the second crystal, a
portion of the light will also pass through the latter. By the intro-
64 Notes on Light.
duction, therefore, of a third crystal, with its axis oblique, we abolish
in part the darkness of the space where the two rectangular plates
are superposed.
Examination of Light transmitted through Iceland Spar.
448. We have now to examine, by means of a plate of tourmaline,
the two parts into which a luminous beam is divided in its passage
through Iceland spar.
449. Confining our attention to one of the two beams, it is imme-
diately found that in a certain position of the plate the light is
freely transmitted, while in the perpendicular position it is com-
pletely stopped. This proves the beam emergent from the spar to
be polarized.
450. From the position of the tourmaline we can immediately
infer the direction of vibration in the polarized beam. If trans-
mission occur when the axis of the plate of tourmaline is vertical,
the vibrations are vertical ; if transmission occur when the tourma-
line is horizontal, the vibrations are horizontal. The same mode of
investigation teaches us that the second beam emergent from the spar
is also polarized.
451. The vibrations of the ether particles in the two beams are
executed in planes which are at right angles to each other. If the
vibrations in the one beam be vertical, in the other they are hori-
zontal. A plate of tourmaline with its axis vertical transmits the
former and quenches the latter ; while the same plate held hori-
zontally, quenches the former and transmits the latter.
452. A tourmaline plate placed with its axis vertical, in front of
the electric lamp, has its image cast by a lens upon a screen. A
piece of Iceland spar, with one of its planes of vibration horizontal
and the other vertical, placed in front of the lens divides the beam
into two, and yields two images of the tourmaline. One of these
images is bright, the other is dark. The reason is that in the light
emergent from the tourmaline the vibrations are vertical, and they
can only be transmitted through the spar in company with its verti-
cally vibrating beam. In the horizontally vibrating beam the
tourmaline must appear black.
453. It is also black if the light emergent from it, and surrounding
it, meet, at the polarizing angle, a plate of glass whose plane of
reflexion is vertical • while it is bright when the light is reflected
horizontally. These effects are consequences of the law of polariza-
tion by reflexion.
454. Not only do crystallized bodies possess this power of double
refraction and polarization ; but all bodies whose atomic grouping is
such as to cause the ether within them to possess different elasticities
in different directions do the same.
455. Thus organic structures are usually double refracting. A
Action of Iceland Spar. 65
double refracting structure may also be conferred on ordinary glass
by either strain or pressure. Strains and pressures due to unequal
heating also produce double refraction. Unannealed jilass behaves
like a crystal. A plate of common window-glass, which under ordi-
nary circurristanees shows no trace of double refraction, if heated
at a single point, is rendered doubly refractive by the strains and
pressures propagated round the heated point. The Introduction
of any of these bodies between the crossed plates of tourmaline
partly abolishes the darkness caused by the superposition of the plates.
456. Two plates of tourmaline, between which bodies may be in-
troduced and examined by polarized light, constitute a simple form
of the polariscope. The plate at which the light first enters is called
the polarizer, while the second plate is called the analyzer.
457. But the tourmalines are small, usually coloured, and under
no circumstances competent to furnish an intense beam of polarized
light. If one of the parts into Avhich a prism of Iceland spar divides
a beam of light could be abolished, the remaining beam would be
polarized, and, because of the transparency of the spar, it would
be far more intense than any beam obtainable from tourmaline.
458. This has been accomplished with great skill by Nicol. He
cut a long parallelepiped of spar into two by a very oblique section ;
polished the two surfaces, and united them by Canada balsam. The
refrangibility of the balsam lies between those of the ordinary and
the extraordinary rays in Iceland spar, being less than the former
and greater than the latter. When, therefore, a beam of light is sent
along the parallelepiped, the ordinary ray, to enter the balsam, must
pass from a denser to a rarer medium. In consequence of the
obliquity of its incidence it is totally reflected, and is thus got rid of.
The extraordinary ray, on the contrary, in passing from the spar to
the balsam passes from a rarer to a denser medium, and is therefore
transmitted. In this way we obtain a single intense beam of polarized
light. (Read Notes 123, 141, and 142.)
459. A parallelepiped prepared in the fashion here described is
called a NicoVs prism.
460. Nicol's prisms are of immense use in experiments on polariza-
tion. With them the best polariscopes are constructed. Reflecting
polariscopes are also constructed, consisting of two plates of glass,
one of which polarizes the light by reflexion, the other examining
the light so polarized. The beam reflected from the polarizer is in
this case reflected or quenched by the analyzer according ao the
planes of reflexion of the two mirrors are parallel or at right angles
to each other.
Colours of Double-refracting Crystals in Polarized Light.
461. A large class of these colours may be illustrated and ex-
plained by reference to the deportment of thin plates of gypsum
66 Notes on Light.
(crystallized sulphate of lime, commonly called selenite) between
the polarizer and analyzer of the polariscope.
462. The crystal cleaves with great freedom in one direction ; it
cleaves with less freedom in two others ; the latter two cleavages are
also unequal. In other words, gypsum possesses three planes of
cleavage, no two of which are equal in value, but one of which
particularly signalizes itself by its perfection.
463. By following these three cleavages it is easy to obtain from
the crystal diamond-shaped laminae of any required thinness.
464. The crystal, as might be expected from the character of its
cleavages, is double-refracting. A beam of ordinary light imping-
ing at right angles on a plate of gypsum, whose surfaces are those of
most perfect cleavage, has its vibrations reduced to two planes at
right angles to each other ; that is to say, the beam whose ether,
prior to entering the gypsum, vibrates in all transverse directions,
after it has entered the gypsum, and after its emergence from it,
vibrates in two rectangular directions only.
465. The elasticity of the ether is different in these two rectan-
gular directions; consequently the one beam passes more rapidly
through the gypsum than the other.
466. In refracting bodies generally the retardation of the light
consists in a diminution of the wave-length of the light. The rate of
vibration is unchanged during the passage of the light through the
refracting body. The case is exactly similar to that of a musical
sound transmitted from water into air. The velocity is reduced to
one-fourth by the transfer, because the wave-length is reduced to
one-fourth. But the pitch, depending as it does on the number of
waves which reach the ear in a second, is unaltered.
467. Because of the difference of elasticity between the two rect-
angular directions of vibration in gypsum, the waves of ether in the
one direction are more shortened than in the other.
468. In the experiments with a plate of gypsum now to be de-
scribed and explained, we shall employ as polarizer a piece of Ice-
land spar, one of whose beams is intercepted by a diaphragm. A
Nicol's prism shall be our analyzer.
, 469. When the planes of vibration of the spar and of the Nicol
coincide, the light passes through both and may be received upon a
-screen. When the planes of vibration are at right angles to each
other, the light emergent from the spar is intercepted by the Nicol,
and the screen is dark.
470. If a plate of selenite be placed between the polarizer and
analyzer, with either of its planes of vibration coincident with that of
the polarizer or analyzer, it produces no change upon the screen.
If the screen be light, it remains light; if it be dark, it remains
dark after the introduction of the gypsum, which here behaves like
a plate of ordinary glass.
471. Let us assume the screen to be dark. Interposing a thick
Action of Selenite. 67
plate of gypsum with its directions of vibration oblique to that of the
polarizer or analyzer, ivhite light reaches the screen. If the plate
be thin, the light which reaches the screen is coloured. If the plate
be of uniform thickness, the colour is uniform. If of different
thicknesses, or if in cleaving thin scales cling to the surface of the
film, some portions of the plate will be differently coloured from the
rest.
472. When thick plates are employed, the different colours, as
in the case of thin plates, are superposed, and re-blended to white
light.
473. The quantity of light which reaches the eye is a maximum
when the planes of vibration of the gypsum enclose an angle of 45°
with those of the polarizer and analyzer.
474. If the plate of selenite be a thin wedge, and if the light be
monochromatic, say red, alternately bright (red) and dark bands are
thrown upon the screen.
475. If, instead of red light, blue be employed, the blue bands are
found to occur at smaller thicknesses than those which produced the
red : other colours occur at intermediate thicknesses. Hence when
white light is employed, instead of bands of brightness separated
from each other by bands of darkness, we have a series of iris-
coloured bands.
476. If, instead of a wedge gradually augmenting in thickness
from the edge towards the back, we employ a disk gradually augment-
ing in thickness from the centre outwards ; instead of a series of
parallel bands we obtain under similar circumstances, in white light,
a series of concentric iris-coloured circles.
477. Here then we have in the first instance a beam of plane
polarized light impinging on the selenite. The direction of vibration
of this beam is resolved into two others at right angles to each other;
namely, into the two directions in which the ether vibrates within
the crystal. One of these systems of waves is retarded with reference
to the other.
478. But as long as the rays vibrate at right angles to each
other, they cannot interfere so as to augment or diminish the inten-
sity. To effect such interference the rays must vibrate in the same
plane.
479. The function of the analyzer is to reduce the two rect-
angular wave-systems to a single plane. Here the effect of retarda-
tion is at once felt, and the wraves conspire or oppose each other
according as their vibrations are in the same phase or in opposite
phases.
• 480. When the vibration planes of the polarizer and analyzer are
parallel, a thickness of the gypsum crystal which produces a retarda-
tion of half an undulation causes the light to be extinguished by the
analyzer.
481. When the polarizer and analyzer are crossed, a retardation
F2
68 Notes on Light.
of half an undulation, or of any odd number of half undulations,
within the crystal does not produce extinction when these vibrations
are compounded by the analyzer. A retardation of a whole undu-
lation, or of any number of whole undulations, produces in this case
extinction. This, when followed out, is a plain consequence of the
composition of the vibrations.
482. Expressed generally, the phenomena exhibited by the parallel
and crossed polarizer and analyzer are complementary. If the field be
dark when they are crossed, it is bright when they are parallel. If
the field be green when they are crossed, it is red when they are
parallel; if yellow when they are crossed, it is blue when they are
parallel. Thus a rotation of 90° always brings out the complementary
colour.
483. If instead of the Nicol we employ a birefracting prism of
Iceland spar, the colours of the selenite produced by the two oppo-
sitely polarized beams will be complementary. The overlapping of
the two colours always produces white. Any other double-refracting
substance, whether crystallized, organized, mechanically pressed or
strained, exhibits, on examination by polarized light, phenomena
similar to those of the gypsurn.
484. A common beam of light is equivalent in all its effects to
two beams vibrating in two rectangular planes. As two such beams
cannot interfere, we c?nnot have the colours of the selenite in common
light.
Rings surrounding the Axes of Crystals in Polarized Light.
485. A pencil of rays passing along the axis through Iceland spar
suffers no division ; but if inclined to the axis, however slightly, the
pencil is divided into two, which vibrate in rectangular planes, and
one of which is more retarded than the other.
486. If the incident light be polarized, on quitting the spar,
oblique to the axis, it will be in a condition similar to the light
emergent from the plates of gypsum already referred to. When two
rectangular vibrations, passing through the same ether, are reduced
to the same plane by the analyzer, interference occurs; the two rays
either conspiring or opposing each other.
487 . Whether they conspire or not depends upon the amount of
relative retardation, and this again depends upon the thickness of the
spar traversed by the two rays. If they conspire at a certain thickness
they will also conspire at twice that thickness, thrice that thickness,
&c. Those thicknesses at which the rays conspire are separated by
others at which they oppose each other.
488. With a conical beam whose central ray passes along the axis,
the effects are symmetrical all round the axis ; and when the crystal,
illuminated by such a ray, is examined by monochromatic polarized
light, we have a series of bright and dark circles surrounding the
Rings round Axes ; Circular Polarization. 69
489. When the light is red the circles are larger than -when the
light is blue; the smaller the wave-length the smaller are the circles.
Hence, since the different colours are not. superposed, when white light
is employed instead of bands of alternate brightness and darkness we
have a series of iris-coloured circles.
When the polarizer and analyzer are crossed the system of bands
is intersected by a black cross, whose arms are parallel to the planes
of vibration in the polarizer and analyzer. Those rays, whose planes
of vibration within the crystal coincide with the planes of either the
polarizer or analyzer, cannot get through either, and their complete in-
terception forms the two arms of the cross. Those rays whose planes
of vibration enclose an angle of 45° with that of the polarizer or ana-
lyzer produce the greatest effect when they conspire. At this incli-
nation the bright ring is at its maximum brilliancy, from which,
right and left, it becomes more feeble, until it finally merges into the
darkness of the cross.
490. A rotation of 90° produces here, as in other cases, the com-
plementary phenomena : the black cross becomes white, and the
circles change their tints to complementary ones.
491. In crystals possessing two optic axes a series of iris- coloured
bands surround both axes, each band forming a curve, which its
discoverer, James Bernoulli, called a lemniscata.
Elliptic and Circular Polarization.
492. Two rays of light vibrating at right angles to each other, how-
ever the one system of vibrations may be retarded with reference to
the other, cannot, as already stated, interfere so as to produce either
an increase or a diminution of the light.
493. But though the intensity remains unchanged, the rays act
upon each other. If one of them differs from the other by any exact
number of semi-undulations, the two rays are compounded to a single
rectilinear vibration. In all other cases the resultant vibration is
elliptical; in one particular case the ellipse in which the individual
particles of ether move is converted into a circle. This occurs when
one of the systems of waves is an exact quarter of an undulation
behind the other ; we have then circular polarization.
494. This compounding of ethereal vibration is mechanically the
same as the compounding of the vibrations of an ordinary pendulum ;
or as the compounding of the vibrations of two rectangular tuning-
forks by the method of Lissajous.*
495. Elliptic polarization is the rule and not the exception. It is
particularly manifested in reflexion from metals, and from trans-
parent bodies which possess a high index of refraction. Jamin has
detected it in light reflected from all bodies.
* See Lectures on Sound, 1st ed., p. 307.
70 Notes on Light.
Rotatory Polarization.
496. A. polarized ray of monochromatic light, as already stated,
suffers no change during its transmission through Iceland spar in the
direction of the optic axis.
497. But if transmitted through rock-crystal (quartz) in the
direction of the optic axis, its plane of vibration is turned by the
crystal.* Supposing the polarizer and analyzer of the polariscope to
be crossed so as to produce perfect darkness before the crystal is
introduced between them, on its introduction light will pass, and to
quench the light the analyzer must be turned into a new position.
The angle through which the analyzer is turned measures the rota-
tion of the plane of vibration.
498. Some specimens of rock-crystal turn the plane of vibration
to the right, and others to the left. The former are called right-
handed and the latter left-handed crystals. Sir John Herschel
connected this optical difference with a visible difference of crystal-
line form.
499. In the celebrated experiment of Faraday, with a bar of
heavy glass, the plane of vibration was caused to rotate both by a
magnet and an electric current ; the direction of rotation bearing
a constant relation to the polarity of the magnet and to the direction
of the current.
500. The subject of rotatory polarization was examined with great
care and completeness by Biot, and he established certain laws re-
garding it, two of which may be enunciated here.
1. The amount of the rotation is proportional to the thickness of
the plate of rock-crystal.
2. The rotation of the plane of vibration is different for the different
rays of the spectrum, increasing with the refrangibility of the lig;ht.
Thus with a plate of rock- crystal one millimeter thick, he obtained
the following rotations for the mean rays of the respective colours of
the spectrum.
Red, 19°.
Orange, 21'
Green, 28°
Blue, 32°.
Indigo, 36°.
Violet, 41°.
Yellow, 23°.
With a plate two millimeters in thickness the rotation for red is 38°
a.nd for violet 82°.
501. Since, then, the rays of different colours emerge from the
rock-crystal vibrating in different planes, when such light falls upon
the analyzer that colour only whose plane of vibration coincides with
that of the analyzer will be transmitted. By turning the analyzer
we allow the other colours to pass in succession.
502. The phenomena of rotatory polarization are produced by the
interference of two circularly polarized pencils of light, which, are
Conclusion. 71
propagated along the axis with unequal velocities, the one revolving
from Jeft to right, and the other revolving in the opposite direction.*
CONCLUSION.
I have endeavoured in these lectures to bring before you the
views at present entertained by all eminent scientific thinkers regard-
ing the nature of light. I have endeavoured to make as clear to
you as possible that bold theory according to which space is filled
with an elastic substance capable of transmitting the motions of light
and heat. And consider how impossible it is to escape from this or
some similar theory, — to avoid ascribing to light, in space, a material
basis. Solar light and heat require about eight minutes to travel
from the sun to the earth. During this time the light and heat are
detached from both. Enclose, in idea, a portion of the intervening
space — say a cubic mile of it — occupied for a moment by light and
heat. Ask yourselves what they are. The first inquiry towards a
solution is, What can they do ? We only know things by their effects,
What, then, are the effects which this cubic mile of light and heat can
produce ? At the earth, where we can operate upon them, we find
theim capable of producing motion. We can lift weights with them ;
we can turn wheels with them ; we can urge locomotives with them ;
we can fire projectiles with them. What other conclusion can you
come to than that the light and heat which thus produce motion are
themselves motions ? f
Our cubic mile of space, then, is for a measurable time the
vehicle of motion. But is it in the human mind to imagine motion
without at the same time imagining something moved ? Certainly
not. The very conception of motion necessarily includes that of a
moving body. What, then, is the thing moved in the case of our
cubic mile of sunlight ? The undulatory theory replies that it is a
substance of determinate mechanical properties, a body which may or
may not be a form of ordinary matter, but to which, whether it is or
not, we give the name of ether. Let us tolerate no vagueness here ;
for the greatest disservice that could be done to science — the surest
way to give error a long lease of life — is to enshroud scientific
theories in vagueness. The motion of the ether communicated to
material substances throws them into motion. It is therefore itself
a material substance, for we have no knowledge that in nature any-
thing but a material substance can throw other material substances
into motion. Two modes of motion are possible to the ether. Either
it is shot through space as a projectile, or it is the vehicle of wave-
motion. The projectile theory, though enunciated by Newton, and
* See Lloyd, Wave Theory, p. 199, &c.
t Sir William Thomson has attempted to calculate ' the mechanical value of
a cubic mile of sunlight.'
72 Notes on Light.
supported by such men as Laplace, Biot, Brewster, and Malus, has
hopelessly broken down. Wave-motion, then, of one kind or another
we must fall back upon. But how does the Wave Theory account for
the phenomena ? Throughout the greater part of these lectures we
have been answering this question. The cases brought before you
are representative. Thousands of facts might be cited in illustration
of each of them, and not one of these facts is left unexplained by the
undulatory theory. It accounts for all the phenomena of reflexion ;
for all the phenomena of refraction, single and double ; for all the
phenomena of dispersion ; for all the phenomena of diffraction ; for
the colours of thick plates and thin, as well as for the colours of all
natural bodies. It accounts for all the phenomena of polarization ;
for all those wonderful affections, those chromatic splendours ex-
hibited by crystals in polarized light. Thousands of isolated facts
might, as I have said, be ranged under each of these heads ; the
undulatory theory accounts for them all. It traces out illuminated
paths through what would otherwise be the most hopeless jungle of
phenomena in which human thought could be involved. This is
why the foremost men of the age accept the ether not as a vague
dream, but as a real entity — a substance endowed with inertia, and
capable, in accordance with the established laws of motion, of im-
parting its thrill to other substances. If there is one conception more
firmly fixed in modern scientific thought than another, it is that heat
is a mode of motion. Ask yourselves how the va*t amount of
mechanical energy actually transmitted in the form of heat reaches
the earth from the sun. Matter must be its vehicle, and the matter
is according to theory the luminiferous ether.
Thomas Young never saw with his eyes the waves of sound ;
but he had the force of imagination to picture them and the intel-
lect to investigate them. And he rose from the investigation of the
unseen waves of air to that of the unseen waves of ether ; his belief
in the one being little, if at all, inferior to his belief in the other. One
expression of his will illustrate the perfect definiteness of his ideas.
To account for the aberration of light he thought it necessary to assume
that the ether which encompasses the earth does not partake of the
motion of our planet through space. His words are : — * The ether
passes through the solid mass of the earth as the wind passes through
a grove of trees.' This bold assumption has been shown to be unne-
cessary by Prof. Stokes, who proves that, by ascribing to the ether
properties analogous to those of an elastic solid, aberration would
be accounted for, without supposing the earth to be thus permeable.
Stokes believes in the ether as firmly as Young did.
I may add, that one of the most refined experimenters in France,
M. Fizeau, who is also a member of the Institute, undertook to
determine, some years ago, whether a moving body drags the ether
Conc'ltiMri. ' 73
along with it in its motion. 'Hi^'g^r-clusiDn is th>,f pdrt,of, the ether
adheres to the molecules of the body, and is transferred along with
them. This conclusion may or may not be correct ; but the mere
fact that such experiments were undertaken by such a man illustrates
the distinctness with which this idea of an ether is held by the most
eminent scientific workers of the age.
But while I have endeavoured to place before you with the utmost
possible clearness the basis of the undulatory theory, do I therefore
wish to close your eyes against any evidence that may arise of its in-
correctness ? Far from it. You may say, and justly say, that a hundred
years a^o another theory was held by the most eminent men, and that,
as the flieory then held had to yield, the undulatory theory may have
to yield also. This is perfectly logical. Just in the same way, a person
in the time of Newton, or even in our own time, might reason thus:
The great Ptolemy, and numbers of great men after him, believed that
the earth was the centre of the solar system. Ptolemy's theory had
to give way, and the theory of gravitation may, in its turn, have to give
way also. This is just as logical as the former argument. The strength
of the theory of gravitation rests on its competence to account for all
the phenomena of the solar system ; and how strong that theory is
will be understood by those who have heard in this room Professor
Grant's lucid account of all that it explains. On a precisely similar
basis rests the undulatory theory of light; only that the phenomena
which it explains are far more varied and complex than the pheno-
mena of gravitation. You regard, and justly so, the discovery of
Neptune as a triumph of theory. Guided by it, Adams and Leverrier
calculated the position of a planetary mass competent to produce
the disturbances of Uranus. Leverrier communicated the result of his
calculation to Galle of Berlin ; and that same night Galle pointed
the telescope of the Berlin Observatory to the portion of the heavens
indicated by Leverrier, and found there a planet 36,000 miles in
diameter.
It so happens that the undulatory theory has also its Neptune.
Fresnel had determined the mathematical expression for the wave-
surface in crystals possessing two optic axes; but he did not appear to
have an idea of any refraction in such crystals other than double re-
fraction. While the subject was in this condition the late Sir William
Hamilton, of Dublin, a profound mathematician, took it up, and proved
the theory to lead to the conclusion that at four special points of the
wave-surface the ray was divided not in two parts, but into ?n infinite
number of parts] forming at those points a continuous conical envelope
instead of two images. No human eye had ever seen this envelope
when Sir William Hamilton inferred its existence. If the theory of
gravitation be true, said Leverrier, in effect, to Dr. Galle, a planet
ought to be there: if the theory of undulation be true, said Sir William
74 Notes on Light.
Hamilton -to, Dr/ibloy.d, my hrtrJiions envelope ought to be there.
Lloyd took a crystal of Arragonite, and following with the most
scrupulous exactness the indications of theory, discovered the envelope
which had previously been an idea in the mind of the mathematician.
Whatever may be the strength which the theory of gravitation
derives from the discovery of Neptune, it is matched by the strength
which the tmdulatory theory derives from the discovery of conical
refraction.
NOTE.
I would strongly recommend for perusal the essay on
Light, published in Sir John Herschel's 'Familiar Lectures
on Scientific Subjects.'
J. T.
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