Page:Elementary Text-book of Physics (Anthony, 1897).djvu/483

§ 381] equal to a certain number of wave lengths, wbich we will assume to be ten, of the shortest waves of the visible spectrum. Since the longest waves of the visible spectrum are about twice the length of the shortest, they will suffer a retardation of five wave lengths. Other waves will suffer a retardation of nine, eight, seven, and six wave lengths. But, as was seen above, a retardation of one or more whole wave lengths of any kind of light causes extinction of that kind of light in the beam transmitted by the crossed analyzer. In the case considered the transmitted beam will lose six kinds of light distributed at about equal distances along the spectrum. The light remaining will consist of the different colors in about the same proportions as they exist in white light, and the beam will therefore be white but diminished in intensity. Hence, when a thick plate is interposed between the crossed polarizer and analyzer the restored light is white.

381. Elliptic and Circular Polarization.—In the last section, in discussing the effects of a thin plate, we considered the two components of the vibratory motion propagated from it. It was stated that the real motion of the vibrating particles was in general elliptical. Let us consider more fully the real motion. Let us suppose that the light is light of one wave length only, and that, as before, the principal plane of the plate makes an angle of 45° with the plane of vibration of the incident light. In Fig. 148 let $$yy$$ represent the original plane of vibration, and $$ab$$ and $$cd$$ the planes of maximum and minimum elasticity in the plate. As already explained, the first disturbance as the light enters the plate is in the direction $$yy;$$ but as the disturbance is propagated into the plate, each disturbed particle receives an impulse first of all in the direction $$cd$$ of greatest elasticity, then in other directions between $$cd$$ and $$ab,$$ and finally in the direction $$ab.$$ From this results an elliptical orbit with the major axis in the direction $$yy.$$ To determine this orbit exactly it is