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592 ON THE OPTICAL CHARACTEK [438
incident at this angle with the normal and vibrating in the plane of incidence is not reflected. In this observation the reflected light (if there were any) would be deviated from its original direction through an angle of 2 (90° — 57°) = 66°, and this is the direction in which light initially unpolarized would appear completely polarized. Now replace the flat glass by a sphere of the same material, whose diameter is small in comparison with the wave-length. Light is now scattered in various directions, but the direction in which light originally unpolarized becomes completely polarized is at 90° with the original direction, instead of 66°. As the sphere grows, the polarization ceases to be complete, and the direction of best polarization moves oppositely to what would be expected—that is, still further away from 60°. When the circumference of the sphere is equal to twice the wave-length, the polarization, still pretty good, occurs at an angle of 135° with the original direction of the light *. In order to carry out the suggestion, we must abandon the supposition of uniform plane strata, inapplicable anyhow in its integrity to the case where one of the alternate plates is of air, and substitute a structure in which one' of the alternatives takes a form such as the spherical. A layer of equal spheres, with centres disposed upon a plane, would give a specular reflexion and a polarizing angle dependent upon the diameter of the spheres and upon the intervals between them. In certain cases, e.g. when the circumference of the sphere (of glass) is equal to l-75 x wave-length, the polarization is very imperfect. To explain a brilliant and highly-coloured reflexion there would need to be several layers of spheres, and it might be supposed that the diameter varied in different layers. In this way it would seem possible to combine a specular and highly-coloured reflexion with a very imperfectly developed polarization, and thus to evade the difficulty which meets us when we confine ourselves to " thin plates." Spheres have been spoken of for simplicity and because some of the effects have been calculated in this case, but it is evident that similar phenomena would be produced by obstacles of other and perhaps more probable forms. The obstacles must have a different index from that of the medium in which they are embedded, and there is no need for absorption.
It may perhaps be objected that though a layer of spheres may give a specular reflexion there would be an accompaniment of light dispersed at other angles, forming in the case of a regular pattern " diffraction spectra." It is uncertain whether or not this occurs. If it does not, the explanation may be that the pattern is too fine.
The above remarks are intended merely to attenuate the difficulty arising
* Phil Mag. Vol. xn. p. 81 (1881) j Proc. Roy. Soc. A, Vol. LXXXIV. p. 25 (1910) ; Scientiiic Papers, Vol. r. p. 518; Vol. v. p. 564.
[It would appear that for " 135° " we should read " 120°." According to the diagram on p. 564 of Vol. v. the maximum polarization for 7? = 27rJR/X = 2 occurs when //= +-5, where /u, is the cosine of the angle between the secondary (or scattered) ray and the backward direction of the incident ray. W. F. S.]spheres are easily demonstrated.