176 TRANSVERSAL VIBRATIONS : 



refracted rays would be unpolarized : but this, in general, is 

 not the case. 



In the case of the reflected beam, the inten sities of the 

 two portions are 



/*; 



the whole intensity of the reflected light is their sum, or 



J= 1 (; + t/ 8 ). 



Now, the first thing to be observed is, that the quantities 

 v 2 and v fz are unequal ; or, that the two portions of which the 

 reflected light consists, and which are polarized in opposite 

 planes, are different in intensity. Hence the reflected light 

 will not be of the nature of common, or unpolarized light ; 

 but will have -an excess of light polarized in the plane of inci- 

 dence, the former quantity being always greater than the 

 latter. This is otherwise expressed by saying, that the light 

 is partially polarized in the plane of incidence. The quantity 

 of polarized light is measured by the difference of the two 

 portions, or by 



Again, the intensities of the two refracted portions are 



As the latter of these quantities is greater than the former, 

 the refracted beam always contains an excess of light po- 

 larized perpendicularly to the plane of incidence. Their dif- 

 ference, \ (tf - v' 2 ), is the same as in the former case ; and 

 accordingly, the reflected and refracted pencils contain equal 

 quantities of oppositely polarized light. Thus, the experi- 

 mental law of Arago is a necessary consequence of theory. 



