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

 The intensity of the polarized light in each beam being 



/I 1-w 2 _ 1 l-^\ 

 \2*l + 7w* 2'l + 7vV' 



Q 2 



the intensity of natural light in the reflected beam is , , y v 



and in the refracted beam is ^ — —~ 9 * 



l+7v z 



Hence the degree of polarization in the refracted beam is 

 1-^2 i_ v z 



l+7w 2 \+7v* 8(v 2 -w 2 ) 



1-w 2 l-v 2 - (1 + TV) (1 -w 2 ) + (1 + 7w*) (1 -v 2 ) 

 1 + 7W 2 " 1 " l + 7u 2 



Let sin (<£—<£]) =y ; and sin (^ + 0^=^ ; then v= -, and 



1 .. «■ - 1 tan 2 W> + <*>,) ' U-2/V 1-2/ 2 



\1— yv 1-y 2 1-y 2 



and 



1-y 



l— V 2 . 

 Dividing out by the common fraction 8 in numerator and 



denominator, and calling p and rc the intensities of polarized and 

 natural light, we get 



p 8y 2 4y 2 



p + n " (l + 7v 2 ) +(l + 7v 2 -8y 2 ) ~~ l + 7v 2 -4y 2. 



From the above relations it appears that 



also 



«*nd 



l4^-2y 2 =(l +«;*). cos 2 (<£-&), 



l + 3i; 2 -4y 2 =(l+3^ 2 ).cos 2 (</>-</>,), 



1 + 7^ _ 8y 2 = (1 + 7w 2 ) cos 2 (0 - <fo) . 



