AND TRANSMITTED BY THIN PLATES. 167 



When the media are the same on the two sides of the plate, 2 ' = 0, 

 and u z = - u. In this case, therefore, u'tt 2 ' = 1 - 2 , and the gene- 

 ral expression for the intensity becomes 



(1 - ')' 



I' 



I - 2'U? COS a + U* ' 



Comparing this with the expression for the intensity of the reflected 

 light (5), we learn that 



/+/' = !; 



or that the intensities of the reflected and transmitted lights are 

 complementary, the maximum of the former corresponding to the 

 minimum of the latter, and vice versa. This law explains the rela- 

 tions of the reflected and transmitted rings observed by Newton 

 and Arago. 



The greatest and least intensities are 



1 - tt'V 

 1 + U-) ' 



1 and 



Accordingly, the intensity of the light in the bright rings is equal 

 to that of the incident light. 



16. When the incident light is polarized in any plane, inclined 

 at the angle y to the plane of incidence, the transmitted light is 

 composed of two portions, polarized in the plane of incidence, and 

 in the perpendicular plane, respectively. The phases of these two 

 portions are given by the formulas, 



- W 2 sin a , ww-t sin a 



tan w = - , tan v = -: - ; 

 l + ta*oea 1 + ww 2 cos a 



and as these are in general unequal, the light will be elliptically- 

 polarized. The difference of phase is given by the formula 



f 

 (r X. ) ~ j + ^p a 



Hence the ellipticity varies with a, and therefore with the thick- 

 ness of the plate. 



The difference, \J/ - x'> will be a maximum, when 



cos a = 



Substituting in the preceding formula, and denoting the greatest 

 difference of phase by A', we have 



