Page:The American Cyclopædia (1879) Volume X.djvu/453

LIGHT 447 dron of Iceland spar has its natural faces, which make an angle with the obtuse edges a and 5, fig. 20, of 71, cut to an angle of 68. It is then cut in a section ef, at right angles to the new faces a 5 and c d. The two parts are again joined together in their original position with Canada balsam, and mounted in a manner con- venient for use. The index of refraction in Ice- land spar for the ordinary ray is 1*654, and for the extraordinary 1'483. The refractive index of Canada balsam is 1'549, so that when a ray of light m o enters the crystal at o and is divided into two rays, o i and o A, the ordinary ray o i is totally reflected by the surface of the Canada balsam in the direction i g, and refracted out of the crystal in g Ic ; while the extraordinary ray o h passes through the balsam in the direc- tion Ti n, and is refracted in the direction n p, parallel to m o. A beam of light therefore, passed through a Nicol's prism in this direc- tion, will cast but one image upon a screen. This combination has been improved by Fou- cault by dispensing with the Canada balsam, FIG. 21. FIG. 22. Malus's Polariscope. thus having nothing between the divided sur- faces except a film of air. If the length of the prism is such that the two rays may fall upon the divided surface at angles interme- diate to those corresponding to the indices of refraction, the ordinary ray will be whol- ly reflected, while the extraordinary ray will be refracted, and therefore transmitted. Ma- lus's polariscope, figs. 21 and 22, consists of two reflectors, A, the analyzer, and J5, the polarizer. They are each composed of a pile of glass plates which may be turned about a horizontal axis, the analyzer also turning about a vertical axis, the angle of ro- tation being measured on the horizontal circle G C, which also holds the substance to be ex- perimented upon. The polarizer is set so that a beam of light reflected at the polarizing an- gle shall be thrown vertically upward. If the analyzer is set at an angle of about 35 25' from the perpendicular (the precise angle de- pending on the refractive index of the glass), the polarized ray will be reflected when the 498 VOL. x. 29 angles of incidence and refraction of the two mirrors are in the same plane, as shown in fig. 22, but will not be reflected when they are at right angles to each other, as in fig. 21. It is not necessary that both mirrors should have the same inclination to the verti- cal, the position given in the cut ; that will depend on the direction of the incident ray. Elliptic and Circular Polarization; Inter- ference of Polarized Light. So far we have been considering cases in which the particles of ether in the polarized ray move in parallel straight lines at right angles to the direction of the ray, so that this lies in one plane ; such is called plane polarized light. But when the ethereal particles are acted on by forces tend- ing to alter their planes of vibration, they are supposed to describe curves which may be either ellipses or circles, depending on the components forming the resultant. An elliptic vibration may result from the action of two rectilinear vibrations at right angles to each other which differ in phase, as in the ordinary and the ex- traordinary ray; therefore, when a plane po- larized ray is reflected from a surface, or pass- ed through a double-refracting plate cut paral- lel to its axis and placed in certain positions, it is either elliptically or circularly polarized. In the case of polarization by reflection, when the azimuth of the plane of polarization of the incident ray is 45, we may conceive this re- solved into two rays, one in the plane of inci- dence and the other in the perpendicular plane, which are equal to each other ; and if they dif- fer in phase by one quarter of an undulation, the light will be circularly polarized. Accord- ing to the theory of Fresnel, the change of phase is produced at the moment of reflection, and the amount of change has been deduced by him through the most ingenious mathemati- cal reasoning. In reflection from St. Gobain glass Fresnel found the difference of phase in the two rays was one eighth of an undula- tion when the angle of incidence was 54 37'. Therefore, if a rhomb of this glass is formed with its faces of incidence and emergence in- clined to the other faces at this angle, and a ray is sent into it perpendicular to one of the faces, it will take the direction a & c d, fig. 23, being reflected at the inner surfaces of the crystal at & and c, and emerge perpendicularly at the oppposite face, with a difference in phase of a quarter of an undulation. If there- fore the inci- c dent ray is po- larized in a plane inclined at an angle of 45 to the plane of reflec- tion, the emergent light will be circularly polarized. This theory, the result of pure mathematical reasoning, was verified by ex- periment. If this circularly polarized ray is transmitted through a second rhomb parallel to the first, it will become plane-polarized. FIG. 28. Fresnel's Ehomb.