554 



zation of the transmitted light, without any greater loss of illumination, 

 by employing a larger number of plates of a more transparent kind. 



Let us now confine our attention to perfectly transparent plates, 

 and consider the manner in which the degree of polarization of the 

 transmitted light varies with the angle of incidence. 



The degree of polarization is expressed by the ratio of ^ to ^/ 2 , 

 which for brevity will be denoted by x- When x=l there is no 

 polarization; when x=0 the polarization is perfect, in a plane per- 

 pendicular to the plane of incidence. Now // (which is used to 

 denote ^ or \// 2 as the case may be) is given in terms of p by one 

 of the equations (20), and p is given in terms of ii' and i+i' by 

 Fresnel's formulae (2). Put 



ii'=d, i+i<= ff >, 

 then, from (1), 



di di' dO da 



whence 



.... (22) 



and we see that i and w increase together from z=0 to =~' 

 have also 



cos Odd-sin 6 cos ado) = (cos 6-cos a 



l 

 sm a sm a sin a 



fl 0)<fwa= _ 



cos 3 ^ r 



Now cos 6 cos o- or 2 sin i sin f is positive ; and cos a is positive from 

 t'=0 to t'=cr, and negative from Z=TO- to =-. But (20) shows 



that $ decreases as p increases. From z'=0 to i=vr, p } increases and 

 p 2 decreases, and therefore ^ decreases and ^ 2 increases, and therefore 



on both accounts x decreases. When i=m, -^ is still positive, and 

 therefore -p negative, but i// a has its maximum value 1, so that on 

 passing through the polarizing angle x still decreases, or the polari- 



