REPORT ON PHYSICAL OPTICS. 407 



from left to right, and the other in the opposite direction. A 

 plane-polarized ray, in fact, is equivalent to two circularly- 

 polarized rays of half the intensity, in one of which the vibra- 

 tions are from left to right, and in the other in the opposite di- 

 rection. When a plane-polaiized ray, therefore, is incident 

 perpendicularly upon a plate of rock ciystal, cut perpendicu- 

 larly to the axis, it may be resolved into two such circularly- 

 polarized rays. These are supposed to be transmitted with dif- 

 ferent velocities ; so that when they assume a common velocity 

 at emergence, one of them is in advance of the other. They 

 then compound a single ray polarized in a single plane ; and 

 this plane, it can be shown, is removed from the plane of pri- 

 mitive polarization through an angle proportional to the interval 

 of retardation of the two pencils, and therefore measured by the 

 thickness of the crystal. But this interval varies also with the 

 colour of the light ; and we are obliged to suppose that it is the 

 same for a given nmnher of waves, whatever be their length, — 

 so that, for a given thickness of the crystal, it varies inversely 

 as the length of a wave. From this supposition it will follow 

 that the deviation of the plane of polarization of the emergent 

 ray is inversely as the square of that length, agreeably to the 

 experimental results of M. Biot*. 



The laws of rotatory polarization are then completely ex- 

 plained ; and it only remained to prove the truth of the hypo- 

 thesis, — that two circularly-polarized pencils, whose vibrations 

 are in opposite directions, will actually be transmitted along the 

 axis of quartz with different velocities. This supposition is 

 easily put to the test of experiment -, since such a difference of 

 velocities must give rise to a difference of refraction, when the 

 surface of emergence is oblique to the direction of the ray. Ac- 

 cording to the hypothesis, therefore, a plane-polarized ray, 

 transmitted through a prism of rock crystal in the direction of 

 the optic axis, should undergo double refraction at emergence ; 

 and the two pencils into which it is divided should be circularly- 

 polarized. This has been completely verified by Fresnel, by an 

 achromatic combination of right-handed and left-handed prisms 

 arranged so as to double the separation ; and he has shown 

 that the two pencils are neither common nor plane-polarized 

 light, but possess all the characters which are impressed upon a 

 polarized ray by two total reflexions from glass at an anijle of 

 about 50°. 



The refraction of quartz, then, in the direction of its axis is 

 wholly different from that of every other known crystal. In 



* Annaks dc Cliimic, torn, xxviii. p, 117. 



