a maximum in an equatorial direction, its amplitude being, in fact, proportional to the sine of the polar distance. The polar line must, by considerations of symmetry, be the line of the incident vibration. Thus we see that none of the light scattered in the x-direction can come from that constituent of the incident. light which vibrates parallel to the x-axis, so the light observed in this direction must consist of vibrations parallel to the z-axis. But we have seen that the plane of polarization of the scattered light is the plane of xy; and therefore the vibration is at right angles to the plane of polarization.[1]
The phenomena of diffraction and of polarization by scattering thus agreed in confirming the result arrived at in Fresnel's and Green's theory of reflexion. The chief difficulty in accepting it arose in connexion with the optics of crystals. As we have seen, Green and Cauchy were unable to reconcile the hypothesis of aethereal vibrations at right angles to the plane of polarization with the correct formulae of crystal-optics, at any rate so long as the aether within crystals was supposed to be free from initial stress. The underlying reason for this can be readily In a crystal, where the elasticity is different in different. directions, the resistance to distortion depends solely on the orientation of the plane of distortion, which in the case of light. is the plane through the directions of propagation and vibration. Now it is known that for light propagated parallel to one of the axes of elasticity of a crystal, the velocity of propagation depends only on the plane of polarization of the light, being the same whichever of the two axes lying in that plane is the direction of propagation. Comparing these results, we see that. the plane of polarization must be the plane of distortion, and therefore the vibrations of the aether-particles must be executed parallel to the plane of polarization.[2]
- ↑ The theory of polarization by small particles was afterwards investigated by Lord Rayleigh, Phil. Mag. xli (1871).
- ↑ In Fresnel's theory of crystal-optics, in which the aether-vibrations are at right angles to the plane of polarization, the velocity of propagation depends only on the direction of vibration, not on the plane through this and the direction of transmission.
