Page:The American Cyclopædia (1879) Volume X.djvu/454

LIGHT If a plate of a double-refracting crystal, cut parallel to its axis, is interposed between the polarizer and analyzer of any polarizing ap- paratus, certain effects are produced when a strong beam of light is sent through it, which depend upon the position of the inter- posed plate as well as upon the relative posi- tions of the polarizer and analyzer. When the interposed plate has its axis parallel or perpendicular to the plane of the polarizer or analyzer, and these have their planes crossed at right angles, no change will take place in the phenomena, although in fact, when the axis of the interposed plate is perpendicular to the polarizer, it becomes itself an analyzer, and intercepts the polarized ray. When turned through an angle of 90, it allows it to pass and be intercepted by the analyzer proper; but if it is turned around gradually, a portion of light will pass through the analyzer, which increases in quantity till it has been turned through an angle of 45, when on further turning the light will gradually diminish till the plate has been turned through an addi- tional angle of 45, when it will vanish. This phenomenon has been called depolartzation, though' improperly, and has been made use of by Malus to detect double-refracting sub- stances in which no bifurcation of the rays could in any other way be detected. When the interposed plate is moderately thick, the transmitted light is white ; but when reduced to a very thin plate or film, the most gorgeous colors appear, which vary with every change of inclination of the interposed plate. Thin plates of mica or selenite, from fa to fa of an inch thick, are the most convenient for exhib- iting these effects. If the thickness of the plate is uniform, the transmitted light will be of a uniform color, differing however with plates of different thickness, the intensity being greatest when the axis of the plate is inclined at an angle of 45 with the plane of primitive polarization, and the color vanishing altogether when the axis of the plate coincides with the plane of primitive polarization or is perpen- dicular to it. But if the interposed plate be fixed and the analyzer turned, the color will change through every grade of tint into the complementary color. Suppose the position of the plate to be that in which the color is the brightest, viz., at an angle of 45, and sup- pose the color to be red ; now on turning the analyzer the color will grow fainter till it has moved through an angle of 45, when it dis- appears, and no light is transmitted ; on con- tinuing to tarn the analyzer, the complementary color green makes its appearance, increasing in intensity till a further angle of 45 is reached, when it will also begin to diminish, and finally vanish at a further angle of 45, or 135 from the first position, when the red will again ap- pear and attain its greatest brightness at 180 from the first position. Whatever may be the color at one position of the analyzer, the com- plementary color will appear on turning it through an angle of 90. To prove that the colors are complementary, a double-refracting prism may be used as the analyzer, in which two rays will be transmitted, each of which will exhibit alternately the same changes of color ; and if they are near enough together to overlap, the overlapping space will exhibit white light. When a plate is used which varies in thickness, the tints follow the laws of the colors of Newton's rings. The thick- ness producing corresponding tints, however, is much greater in crystalline plates exposed to polarized light than in thin plates of air or any other uniform medium. The black of the first order appears in a plate of sulphate of lime when its thickness is ^Vo f an i ncn ? an d between that and -fa of an inch is contained the whole succession of colors of Newton's scale. The color produced by a plate of mica in polar- ized light is the same as that reflected from a plate of air only ^-^ as thick. With Iceland spar the same color is produced when the thickness is about 13 times that of the plate of air. The physical explanation of these phe- nomena may be briefly stated as follows : A ray of light striking a double-refracting crystal is divided into two of unequal velocities, thus seemingly affording the conditions of inter- ference if the plate is sufficiently thin; but if these conditions were sufficient, the phe- nomena of interference ought to be produced without the polarizing apparatus. But in polarized light the case of interference is dif- ferent from that in ordinary light. In the latter the rays lie in planes of all azimuths, while in polarized light they lie only in two planes at right angles, and therefore they can- not interfere with each other. The subject was examined with reference to this point by Fresnel and Arago, who found that two rays polarized in the same plane interfere like two rays of ordinary light, and produce fringes, and that when the planes of polarization are inclined to each other the interference will be diminished until the angle between them is 90. It was further found that two oppositely polarized rays will not interfere when their planes are made to coincide, unless they are derived from a pencil originally polarized in one plane, and which has lost or gained half an undulation in passing from one plane to the other. If now the planes of polarization of two rays which have been made to differ in length by half an undulation, or any odd num- ber of half undulations, can be brought to co- incide, interference will follow; and this is accomplished by interposing the thin plate of double-refracting crystal which causes the light that has been reduced to one plane by the polarizer to be divided into two rays, one or- dinary and the other extraordinary, and differ- ing in phase by half a wave length. Colored Rings. If a thin plate of a double-refracting crystal, as Iceland spar, cut perpendicular to its axis, be substituted for the thin plate cut parallel with its axis used in the experiment