Sir David Brewster on the Compensations of Polarized Light. 389 



In the case of light polarized by refraction, the action of several surfaces may 

 and must often be necessary to produce compensation, and in this case, or when 

 the light compensated is polarized by successive refractions, we may find the 

 angle of incidence by means of the formulae 



cot r: cos" (i — i'), and sin i' z= . 



m 



And since v' cot0= cos (i — i'), we have for n refractions,f 



.in,:-— "L_ / "-^;^^an0-] 



Vtan0 



When the light has passed through a prism whose angle is ^, then if the 

 angle of the prism is equal to the angle of refraction, or ^ = i', or sin -f = 



SlH Z 



, the incidence i will be found from the formula for one refraction, because 



m 



the ray will emerge perpendicularly from the second surface of the prism, and 



suffer no change in its planes of polarization. 



If the angle of the prism is double the angle of refraction, or -^ = 2i', and the 

 deviation i — i' a minimum, the incidence i will be found from the formula when n, 

 the number of refractions, is two ; the refraction, and consequently, the polari- 

 zation at each surface being equal, and, therefore, the same, as for a plate when 

 ^ = 0. 



Having thus determined the laws of the compensation of polarized light, I 

 shall conclude this paper by pointing out a few of their numerous applications. 



1. The first and most important result of this inquiry is, that it aifords a 

 new and independent demonstration of the laws of the polarization of light by 

 reflexion and refraction, given in my papers of 1830. As this result has been 

 already referred to, I shall merely mention the following general proposition. 



When a ray of common light is incident at any angle upon the polished 

 surface of a transparent body, the whole of the reflected pencil suffers a physical 

 change, bringing it more or less into a state of complete polarization ; in virtue 

 of which change, its planes of polarization are more or less turned into the plane 



* See Phil. Trans. 1830, p. 137. 



