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



first surface, then 



r= sin (<£-&) 



The ray of intensity \, which is polarized in a plane perpendi- 

 cular to the plane of incidence, will give rise to a reflected ray of 

 intensity \w 2 , and a refracted ray of intensity \{\ — w q ) at the 

 first surface, where 



rc = tan(ft-«k) T 

 tan($-Hk) 

 Now consider first only the light polarized in the plane of in- 

 cidence. 



The ray refracted into the first plate is divided up at its second 

 surface into an internally reflected ray of intensity i(l— -v 2 )vV 

 and a refracted ray of intensity 4(1— i> 2 ) 2 . 



A similar division will take place at each surface with every 

 successive internally reflected ray. 



The intensity of the light passing out of the plate on the side 

 on which it entered will be 



i(l-vY{v 2 + v 6 + v™ + kc.}, 

 and therefore the whole intensity of the reflected beam is 

 i^ + i(l-t; 2 )V + ^ 6 + ^ +&c.) 



1 1 V 2 



2 + 2 l V) 1-v* 



1 2 f\ . 1-trH 1 2v* 



I 1 + ^ 2 J 2 



2 L ' 1 + ^ 2 J 2 l+i; 2 

 Hence the intensity of the beam which is refracted through the 

 plate is 



no light being supposed to be absorbed by the plate. 



Let the part which is reflected be represented by \k* ; then 

 the portion which passes through will be represented by J(l — k*). 



Now consider the action of the second plate on this portion, 

 which has been refracted by the first plate. The successive re- 

 flections and refractions by the two plates will be of the same 

 character as the successive reflections and refractions by the two 

 surfaces of the first plate ; also the intensities of the portions 

 reflected and refracted by the two plates will bear the same rela- 

 tion to A 2 , that the intensities of the portions reflected and re- 

 fracted from the two surfaces bear to v 2 . Therefore as the intensity 

 of the beam refracted through the two surfaces was changed from 



1 1 1 — v 2 



o to o • i 2J so tne ^tensity of the beam refracted through two 



