﻿212 Prof. W. G. Adams on the Polarization of a ray of 



That the reasoning from the analogy between plates and re- 

 fractive surfaces is correct will readily appear ; and the law of 

 intensities may at once be deduced. 



Consider only the ray of intensity \ which is polarized in the 

 plane of incidence, ^k 2 is reflected by the first plate, and 

 ■J(l — k 2 ) is refracted through it. Of this latter portion, which 

 falls on a 'third refracting surface, (1 — v 2 ) is refracted and 

 v 2 is reflected; so that i(l— k 2 )(l — v 2 ) is the intensity of the 

 refracted portion, and ^v 2 (l — k 2 ) of the reflected portion. In 

 these are included all the rays arising from the successive internal 

 reflections inside the plate which take place before reflection by 

 the third surface. 



The reflected portion J v 2 (l — k 2 ) falls upon the first plate ; and 

 the portion of it refracted by the plate is ^ v 2 (l — A; 2 ) 2 , the por- 

 tion reflected being \v 2 k 2 {\ — A; 2 ). These portions include all 

 the rays, however internally reflected, which have only been once 

 reflected by the third surface. The reflected portion \v 2 k 2 {\ — k 2 ) 

 falls on the third surface ; and 



•J v 4 k 2 (l—k 2 ) is reflected back to the plate, 

 while 



^v 2 k 2 (l-— & 2 )(1— v 2 ) is refracted through the surface; 



similar reflections and refractions take place; and the whole 

 intensities of the refracted beams will be 



±(l—k 2 )(l-v 2 {l+v 2 k 2 + v 4 k 4 +kc.\ 



of the reflected beams will be 



\v 2 + l{l-k 2 ). {v 2 + v 4 k 2 + v 6 k 4 +8cc.\ 



^{i+(i-^(T=y> 



Of the portion J(l— k 2 ) which falls on a second refracting 

 plate, the intensity of the reflected portion will be 



and of the refracted portion 



In these are included all the rays, however internally reflected, 

 which have only been once reflected at the outside of the first 

 surface of the second plate. 



The portion again reflected by the first plate is 



and the portion refracted is 



±k 2 {l-k 2 ) 2 



