380 SiE David Brewster on the Compensations of Polarized Light. 



Ratio of common to 

 Refracted Pencil, polarized Light. 



1/9.6 

 920 , 1/11.6 

 1/11.5 



Hence, a pencil reflected at an incidence of 15° 40', compensates another re- 

 flected at 87° 51', and each of them compensates a pencil refracted at the 

 polarizing angle 56° 45', and the ratio of the common to the polarized light is 

 nearly the same. 



In support of the same views we shall examine what takes place at other three 

 remarkable angles of incidence. 



1. At 78° 7' where the quantity of polarized light is a maximum, or 158 

 rays, the power of compensation by reflexion is less than at every angle of inci- 

 dence between 78° 7', and 30° where the quantity of polarized light varies from 

 158 to 17 rays. 



At 78° 7' the quantity of refracted light is double that of the reflected light, 

 and is equal to two-thirds of the Incident light, and the quantity of polarized 

 light is nearly one-fourth of the reflected, and one-half of the refracted, light. 

 Now, at this angle the power of compensation by reflexion and refraction is 

 nearly in the inverse ratio of the quantity of light in the reflected and refracted 

 beams, and not as the quantities of common light, which they are supposed to 

 contain. For the powers of compensation are as 6° 50' to 14° 7' ; the ratio of light 

 in each beam as 666 + 333, and the proportion of common light as 508 to 175. 



2. At 85° 50' 40", when i — i' = 45°, when the refracted is one-half of the 

 reflected light, and the quantity of polarized light one-third of the refracted 

 light, one-sixth of the reflected light, and one-ninth of the incident light, the 

 power of compensation by refraction is nearly double of that by reflexion,* being 

 nearly in the inverse ratio of the quantities of light in the reflected and refracted 

 beams, and not of the quantities of common light which they contain. 



At other angles of incidence beside these two, the powers of compensation 

 have no such relations. 



3. At 82° 44', a very remarkable angle, where cos (i -\- i') = cos.'' {i — i'), 

 and where the reflected is equal to the refracted light, the compensation by re- 

 flection is equal to the compensation by refraction, and the ratio of the polarized 



* The one is 9° 44', and the other 4° 48'. 



