Page:Elementary Text-book of Physics (Anthony, 1897).djvu/480

466 right angles to the principal plane. The latter is reflected to one side and absorbed, and the former is transmitted. As the angle between the two principal planes increases, the transmitted component diminishes in intensity, until when this angle becomes 90° it disappears entirely. In this position the polarizer and analyzer are said to be crossed.

380. Effects of Plates of Doubly Refracting Crystals on Polarized Light.—If a plate cut from a doubly refracting crystal so that its faces are parallel to the optic axis, or at least not at right angles to it, be placed between the crossed polarizer and analyzer, and the principal plane of the plate coincide with, or be at right angles to, the plane of vibration, no effect is perceived. But if the plate be rotated so that its principal plane makes an angle with the plane of vibration, the motion may be considered as resolved into two components, one in, and the other at right angles to, the principal plane of the plate, and these two components on reaching the analyzer are again resolved each into two others, one in, and the other at right angles to, the principal plane of the analyzer. The vibrations in the principal plane of the analyzer are transmitted through it, and hence, in general, the introduction of the plate restores the light which the crossed polarizer and analyzer had extinguished. It is easy to see that the restored light will be most intense when the principal plane of the plate makes an angle of 45° with the plane of vibration of the polarized ray.

It is not to be understood that in the plate there are two separate beams of light, in one of which one set of particles is vibrating in one plane, and in the other another set in another plane. What really takes place is that each particle in the path of the light describes a path which is the resultant of the two components spoken of above. Let $$ab$$ (Fig. 145) be a plate of Iceland spar, and $$cd$$ the direction of its optic of the light perpendicular to the plane of the paper, and $$ef$$ to represent the direction of the disturbance produced by the entrance of a plane polarized wave. A motion in the direction of $$ef$$ is