CIRCULAR POLARIZATIOX. 



117 



'^L 





R 



Vh 



48. 



imiUi})le of i. It is tlicreforc cvidcait tli;it, at cadi r(.'fle(;tion in tlio rlioml), ono 

 of tlic component waves is accclonitcd or retarded oiie-eigljlli of an undulation 

 upon the other. 



The restoration of the ])lane ])olariz;ition, after four nsfiections, in an azimutli 

 00° removed from tJie azinuitli of incidence, may he understood hy C(jnsid(!ring 

 f the iollowinj^ ilhistration. Let the, 



arrow I'P' represent the amplitude 

 of movem(int in a ])ohirized wave at 

 a given moment. L(;t this he re- 

 solved into two rectangular compo- 

 nents 45*^ inclined to it on each side, 

 represented hy the arrows QQ' and 

 liU'. Suppose the molecule, at a 

 given instant, to he situated at the 

 point C* of its path. CJ" is tlie direction in wliich it is moving, and tlie length 

 of tlie line is the extent of its range. By two reflections in I''resn(d's rhomh, 

 or hy any other cause, let the component JIU' he so advanced upon QQ' that, 

 at some future instant, the molecule shall have reached the limit of its rangi; in 

 the hori:iontal dir(!Ction, and shall be ahout to return (as at U in the second 

 system of arrows) when, in the V(;rtical direction it is in the middle point, and 

 going toward Q' as hefon;. This would be in C, but for the horizoiital displacc- 

 jueut. In point of fact, it is at 11. The vei'tical vcdocity, (represented hy the 

 dotted arrow Q"Q"',) is at its maximum, and the horizontal velocity is zciro. 

 The conditions are such as, in the section on vibration, are shown to produce a 

 revolution of the molecule in a circle. The path of the molecule will accord- 

 ingly be ItQ'R'Q. After two additional reflections in the rhomb, the horizont.al 

 movement will be advanced over the vertical by another quarter of its doul)lc 

 vibration, and will bring the molecule, in its progress from right to left, to the 

 middle point, C", in the third system of arrows, at the same instant at which 

 the vertical movement, in the direction Q', brings it to the same point. The 

 velocities are now both at their maximum, and are equal. The molecule takes 

 the m(;an direction, V"V", betwecm them, and the ray is plane polarized in an 

 azimuth 90'^ from the original plane. 



Suppose the eye of the observer to be at E, the I'evolutiou of the molecule; is 

 dcxtrogyre, or, as it is also called, dcxlrorsum. Conceived as viewed in the oppo- 

 site direction, it would be laivogyre, or sinistra rsum. \\\ the earlier historv of 

 this subject, some confusion arose from the fact that different observers applied 

 these terms in different ways. Since observation, however, is only made upon 

 rays ajiprojichiiig the observer, this is the point of view now universally adopted 

 in naming the direction of gyration. Jt appears, then, that the advance of the, 

 left-hand component, by a quarter undulation, produces a dextrogyration, and 

 vice versa. If the plane of original polarization were P'T'", then, in the resolu- 

 tif^n. It 1 1' would be reversed, and the advance of Illl' would be the advance of 

 the right-hand component, producing lajvogyration. In this case, after four 

 reflections in Fresnel's rhomb, the resultant plane of polarization would be Vl". 

 If we distinguish, as positive, the azimuths to the right of the plane of reflec- 

 tion, and, as negative, those to the left, we may say that a plane polarized ray 

 in original azimuth — H'P, is circularly polarized dextrorsum by passing through 

 one of I'resnel's rhombs; and becom(;s plane polariz(fd again in azimuth +4-3'^, 

 after passing through two. If the original azimuth he -{-4-'3, the circular polar- 

 ization is sinistrorsum, and the hnal azimuth of plane polarization, negative. 

 One of these rhomhs may, therefore, be used as a polariscope, to detect the 

 direction of rotation of a circularly polarized ray. 



If two rays, one; in azimuth +45°, and the other in azimuth — i'P, were to 

 be reflected simultaneously in one of Fresnel's rhombs, the two consequent 



*Tliu loitois C, C, C", are accidentally omitted from the diagram. Tbey should be jjlaced 

 oii tJic dotted hue at the intersections of the .successive systcm.s of arrow.s. 



