Page:Elementary Text-book of Physics (Anthony, 1897).djvu/481

§ 380] of two motions, one along the axis, and the other perpendicular to it. In the propagation of this motion to the next particle, the motion in the direction of the optic axis will begin a little sooner than that at right angles because of the greater elasticity in the former direction, and this difierence becomes greater as the light is propagated into the plate. This is equivalent to a change in the relative phases of two vibrations at right angles, and this causes the path of a vibrating particle to change from the straight line to an ellipse. The result is, therefore, that, when the initial disturbance has any direction except in or at right angles to the principal plane of the plate, the motion of the vibrating particles within the plate becomes elliptical, the ellipses changing form as the distance from the front surface of the plate increases. It is entirely admissible, however, in the discussion of the problem to substitute for the actual motion its two components, as was done above.

It remains to consider what is the effect of the retardation or change of phase of one of the components with respect to the other. It will be remembered that in the analyzer each ray from the plate is again resolved into two components, and that two of these components are in the principal plane of the analyzer and are transmitted. These two components will evidently differ in phase just as did the two motions from which they were derived, and since they are in the same plane their resultant is represented by their algebraic sum. If they differ in phase by half a period their algebraic sum will be zero, and no light will be transmitted by the analyzer. This will occur for a certain thickness of the interposed plate. If the light experimented upon be white, it may occur for some wave lengths and not for others. Hence, some of the constituents of white light may fail in the beam transmitted by the analyzer, the image of the plate will then appear colored. A study of the resolution of the vibrations for this case shows that, of the two beams formed in the analyzer, one contains just that portion of the