ELLIPTIC POLARIZATION. 191 



It follows from these researches, that the phase of the ray 

 polarized perpendicularly to the plane of incidence is always 

 retarded, relatively to the other. The difference of phase 

 increases regularly with the incidence, being equal to TT at a 

 perpendicular incidence, and to 2n- at an incidence of 90. 

 At the angle of maximum polarization, E = f TT. This angle 

 is, of course, different for different metals : it is, however, 

 not far in any from 75. 



(202) It follows from the preceding, that there are n - 1 

 incidences between and 90, for which the ray is restored 

 to the condition of plane polarization by successive reflexions. 

 For the ray becomes plane-polarized, as often as the differ- 

 ence of phase of the two components is a multiple of TT. 

 But, with a single reflexion, the difference of phase increases 

 by TT between and 90 of incidence. Consequently with 

 n reflexions, the difference increases by mr ; and between 

 these limits of incidence there are n - 1 multiples of TT, and 

 therefore n - 1 angles of incidence at which the polarization 

 is restored. 



The plane of polarization of the restored ray will be on 

 the same side of the plane of incidence, as the plane of polari- 

 zation of the incident ray, or on the opposite, according as the 

 difference of phase is an even or odd multiple of TT. 



(203) It would appear from the foregoing, that metals 

 differ from transparent bodies, in their action upon light, in 

 two particulars namely, 1st, that they do not polarize com- 

 mon light completely at any incidence ; and 2ndly, that they 

 alter plane-polarized light by reflexion into light elliptically 

 polarized. It will be seen, presently, that these differences 

 are only differences in degree. 



It was long since observed by M. Biot, that diamond and 

 sulphur did not polarize the light completely at any angle ; and 



