Page:Elementary Text-book of Physics (Anthony, 1897).djvu/482

468 light that the other lacks; hence if the analyzer be turned through 90°, the image will change to the complementary color. In Fig. 146, let $$ab$$ represent the plane of the vibrations in the polarized ray, and let $$cd$$ and $$ef$$ represent the two planes of vibration of the rays in the interposed plate. At the instant of entering the plate the primary vibration and its two components will have the relation shown in the figure. The two components are then in the same phase. As the movement penetrates the plate, one component falls behind the other, and the relation of their phases changes, until, with a retardation of one wave length, the phases are again as in the figure. Suppose the thickness of the plate such that this retardation occurs for some constituent of white light. After leaving the plate the relative phases of the components remain unchanged, and the constituent in question enters the analyzer as two vibrations at right angles and in the same phase. In Fig. 147 let $$oe$$ and $$od$$ represent the two components, and $$xx$$ and $$yy$$ the two planes of vibration in the analyzer. $$oe$$ will give the components $$om$$ and $$on,$$ and $$od$$ the components $$om'$$ and $$on'.$$ Since the components $$om$$ and $$om'$$ annul each other, the color to which they correspond is wanting in the light resulting from vibrations in the plane $$xx,$$ while since the components $$on$$ and $$on'$$ are added, this color is found in full intensity among the vibrations in the plane $$yy.$$ For light of other wave lengths, the relative retardation is different, but for each vibration period, the component in the direction $$xx$$ combined with that in the direction $$yy$$ represents the total light for that period in the beam entering the analyzer; that is, the total effect of vibrations in the direction $$xx$$ combined with that of vibrations in the direction $$yy$$ must produce white light, and one effect must, therefore, be the complement of the other.

Let us suppose the plate thick enough to cause a retardation