POLARISED LIGHT AND ITS APPLICATIONS

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although his efforts at explanation did not stand the test of time, Malus accumulated a mass of results from minute and accurate observation on the behaviour of polarised light which furnished conclusive evidence for the law which bears his name.

The asymmetry of a ray polarised by reflection becomes very evident when the ray suffers reflection from a second surface, and Malus found that the intensity of the final ray was dependent upon the plane of incidence at the second surface. He attributed to each ray a plane passing through its path which bore a definite relation to its asymmetric properties ; this he called the Plane of Polarisation of the ray, and defined it as the plane of incidence of a polarised ray upon a surface when the reflected ray was of maximum intensity. The angle of reflection from a surface for which the polarisation of the light was most complete he termed the Angle of Polarisation. His Law of Polarisation could then be stated as follows :

When a ray of light polarised by reflection at one surface falls upon a second surface at the angle of polarisation, the intensity of the twice-reflected ray varies as the square of the cosine of the angle between the two planes of reflection.

The foundations of the theory of polarisation which holds to the present time were laid by Young and Fresnel in their conception of light transmission by transverse wave motion. Fresnel saw the immediate application of the conception to the case of polarised light, and suggested the restriction of the vibrations to a definite unchanging path at right angles to the direction of propagation. Accepting his hypothesis, we shall for the moment consider only light whose vibrations are linear and take place in ono definite direction. To this has been given the name of Plane Polarised Light.

A crucial test of Frcsnel's theory lay in the investigation of the behaviour of two plane polarised rays under conditions which might be expected to produce interference. Fresnel and Arago carried out this work, and their results added evidence in favour of the wave motion hypothesis, and led to the establishment of the following five laws governing the interference of polarised rays, known as the Fresn&l-Arago Laws:

1. Two rays polarised in the same plane interfere

with each other under the same conditions as for ordinary light.

2. Two rays polarised at right angles to one another

do not interfere under these conditions.

3. Two rays polarised at right angles, if obtained

from unpolarised light, may subsequently be brought into the same plane of polarisation without acquiring the power of interference.

4. Two such rays derived from plane polarised

light will, under the same conditions, show interference.

5. In the latter case a phase difference of tr,

equivalent to half a wave-length, must be added to the estimation of the path difference.

At about the same time Brewster deduced

from experimental data another law governing the size of the angle of polarisation. Brewster's Law may be expressed simply in the statement that the tangent of the angle of polarisation is equal to the index of refraction of the reflecting substance. Prom this it follows that at the polarising angle the sum of the angles of incidence and refraction is 90°, or that the reflected ray is perpendicular to the refracted ray, and that when light travelling in a medium is polarised by reflection from the bounding air-surface of the medium the refractive index is the cotangent of the polarising angle. Evidently, therefore, the polarising angle will vary with the wavelength of the light used. With most substances the dispersion is too low to show the effects of this law, but with substances of very high dispersive power, such as nitroso-dimethyl-aniline, the effect is visible in the distinct coloration of the image of a white source of light, and in the variation of the colour with the angle of incidence.

By the examination of light polarised by refraction through a crystal or by reflection at a glass surface various definite facts were deduced. The two rays emerging from a crystal of calcite were found to be polarised with their planes of polarisation parallel and perpendicular respectively to the plane containing the incident ray and the crystal-lographic axis. The ray reflected from a polished non-metallic surface was polarised in the plane of incidence and the refracted portion was partially polarised in a perpendicular plane. After a second refraction at the polarising angle the percentage of polarised light in the refracted ray was increased, while again the reflected ray was wholly polarised in a perpendicular plane, and this process could be repeated at any number of surfaces until the final refracted beam contained no appreciable amount of unpolarised light. These facts are capable of simple explanation on the wave theory of light propagation.

§ (3) EXPLANATION ON WAVE THEOIIY.—A transverse vibration in any direction may be resolved into two component vibrations at right angles in the same plane ; moreover, it can be shown that an elliptical or circular vibration can be resolved into two simultaneous linear vibrations at right angles to each other differing in phase. It may be supposed that a crystal such as calcite has an inherent power of resolving light vibrations in this way ; a separation of the two rays would be effected if we suppose that the one set of vibrations possesses a different rate of propagation through the crystal from that of the perpendicular set. This subject will be investigated more fully a little later in the general discussion of the behaviour of crystals in transmitting light. Turning now to the question