Page:Elementary Text-book of Physics (Anthony, 1897).djvu/488

474 planes of polarization of its constituents rotated through different angles, and the effect of rotating the analyzer is to quench one after another of the colors as the plane of polarization for each is reached. The result is a colored beam which changes its tint continuously as the analyzer rotates.

The best explanation of these phenomena was given by Fresnel. It is found that neither of the two beams from a quartz crystal is plane polarized. The polarization is in general elliptical, but becomes circular for waves perpendicular to the axis of the crystal, the motion in one ray being right-handed and in the other left-handed. Each particle of ether in the path of the light within the crystal is actuated at the same time by two circular motions in opposite directions. Its real motion is in the diameter which bisects the chord joining any two simultaneous hypothetical positions of the particle in the two circles. In Fig. 152 let $$P$$ and $$Q$$ represent these two simultaneous positions. It is plain that the two components in the direction $$AB$$ have the same value and are added, while those at right angles to $$AB$$ are equal and opposite and annul each other. So long as the two components retain the same relation as that assumed, the real motion of the particle is in the line $$AB$$ But in the quartz plate one of the motions is propagated more rapidly than the other, and another particle farther on in the path of the light may reach the point $$P$$ in one of its circular vibrations at the same time that it reaches $$Q'$$ in the other. This will give $$CD$$ as its real path, and the plane of its vibration has been rotated through the angle $$BOD.$$ When the light finally emerges from the plate its plane of vibration will have been rotated through an angle which is proportional to the thickness of the plate and depends upon the wave length of the light employed. A plate of quartz one millimetre in thickness rotates the plane of polarization of red light corresponding to Fraunhofer's line $$B,$$ 15° 18', of blue light corresponding to the line $$G,$$ 43° 12'. Some specimens of quartz rotate