at a Twin Plane of a Crystal. 255 



If, on the oilier hand, the incident light be polarized, 

 whether phme or elliptically, the character of the emergent 

 light must depend upon the precise thickness of the crystalline 

 layer, and will vary rapidly from one part of the spectrum to 

 another. The simplest case that we can consider is when the 

 polarization of the incident rays is such that one or other of 

 0], 2 vanish. TTe will suppose that it is 2 ; so that after 

 reflexion, 



Intensity of & _ p 2 -fr* + /V 6' 2 



Intensity of 6" ~~ f + r* + tf ' 6" 2 



_P\—P\\t"2. 4/^Vs 2 _. — 4/^2 



P-2—PiH /^iVi + HY (^i + /^) : 



(68) 



by (54), (55). This is the ratio of intensities that would be 

 observed with an analyzing nicol held so as to retain in suc- 

 cession 6' and 6" . If the crystalline layer be moderately 

 thick, and the light be of mixed wave-lengths, there will be 

 no interference observable between 6' and 6", and thus the 

 ratio just found is the extreme ratio of intensities. By means 

 of ((52) we may express it in terms of the angle of incidence 

 (<£), and of the fundamental optical constants of the crystal. 

 Thus 



V IC^ + ft,) 2 / (A-C)r 2 +(D-CV 

 _ B sin <f) 



~(A-C)sin 2 + (D-C)cos 2 f 



(69) 



This expression shows that in general the emergent light will 

 be fully polarized only when <j> is very small. In this case 

 we virtually fall back upon our original investigation where 

 the thickness of the layer was neglected. Since only 0j is 

 present, there is no depolarization in the first passage ; and 

 when <f) = there is no depolarization upon the return passage 

 in consequence of the disappearance of 6 r . The polarizations 

 corresponding in this case to 0,, 2 are obviously those in 

 and perpendicular to the plane of incidence ; and we learn 

 that, when the angle of incidence is small, polarizations in and 

 perpendicular to the plane of incidence are reversed in the 

 reflected ray. If the incident ray be polarized in other direc- 

 tions than these, the reflected ray is in general not fully 

 polarized, even though the angle of incidence be small. 



