ON THE LIGHT REFLECTED 



tan A' = - 



17. The intensities of the two component pencils are 



(tV cos 7 ) 8 j, = (^V 2 sin T ) 2 _ ^ 



" 1 + 2w , cos a + rV 1 + 2'Wa cos a + ftr a 8 ' 



And denoting the ratio of the amplitudes by tan 7', as before, 



llflDz V 1 + 2W 2 COS a + V^'V-i 



tan 7 ' = tan 7 7^1 + 2tnc z cos a + w 



When the thickness of the plate is that corresponding to the maxi- 

 mum difference of phase, this expression is reduced to 



18. When the media are the same on the two sides of the 

 plate, ih = - v, ? a = - w, and the preceding formulas for the maxi- 

 mum difference of phase are reduced to 



r + w , 



cos a = , tan A = 



which are identical with those already obtained for the reflected 

 light. Accordingly, the difference of phase of the two portions of the 

 polarized beam is the same in the reflected and in the transmitted 

 pencils. 



In the same case the ratio of the amplitudes is 



tan 7 ' = tan 7 



In resuming the theory of the rings in polarized light, I was 

 under the impression that the knowledge of the subject was still 

 confined to the general principles laid down by myself, many years 

 ago. Since the foregoing paper was read, however, I have learned 

 that the problem has been discussed by M. Jamin, in an interest- 

 ing memoir published in the Annales de Chimie in 1822. In this 

 memoir the author has confined himself to the case in which the 

 media are the same on the two sides of the plate. In another 

 respect, he has treated the problem more generally than it has 

 been considered in the foregoing paper, having based it upon the 

 theory of Cauchy, instead of that of Fresnel. lie has thus been 



