Page:Elementary Text-book of Physics (Anthony, 1897).djvu/486

472 to its optic axis suffers no change. If, however, the plate between the crossed polarizer and analyzer be inclined to the direction of the beam, light passes through the analyzer. It is generally colored, the color changing with the obliquity of the plate. If a system of lenses be used to convert the polarized beam into a conical pencil and the plate be placed in this perpendicular to its axis, the central ray of the pencil will be unchanged, but the oblique rays will be resolved except in and at right angles to the plane of vibration, and there will appear beyond the analyzer a system of colored rings surrounding a dark centre, and intersected by a black cross. If the analyzer be turned through 90°, a figure complementary to the first in all its shades and tints is obtained: the black cross and centre become white, and the rings change to complementary colors.

384. Biaxial Crystals.—Most crystals have two optic axes or lines of no double refraction, instead of one. They are biaxial crystals. Tlieir optic axes may be inclined to each other at any angle from 0° to 180°. The wave surfaces within these crystals are no longer the sphere and the ellipsoid, but surfaces of the fourth order with two nappes tangent to each other at four points where they are pierced by the optic axes. Neither of the two rays in such a crystal follows the law of ordinary refraction. The outer wave surface around one of the points of tangency has a depression something like that of an apple around the stem. By reference to the method already employed for constructing a wave front, it will be seen that there may be such a position for the incident wave that, when the elementary wave surfaces are constructed, the resultant wave will be a tangent to them in the circle around one of these depressions where it is pierced by the optic axis. Now since the direction of a ray of light is from the centre of an elementary wave surface to the point of tangency of that surface and the resultant wave, we shall have in this case an infinite number of rays forming a cone, of which the base is the circle of tangency. In other words, one ray entering the plate in a proper direction may be resolved into an infinite number of rays