THE REFLEXION AND REFRACTION OF LIGHT. 117 



When light is polarized in the plane of incidence, the conditions 

 at the surface of junction have been shewn to be 



w — w t 



(32) dy^ ' dw^ \ (when x = 0). 



dx dx 



Since in these conditions we may differentiate or integrate relative 

 to any of the independent variables except x, we see that the expressions 

 (30) and (32) are reduced to a form equivalent to that marked (A) in 

 our paper on Sound ; and the general equations in >// and w being the 

 same, we may immediately obtain the intensity of the reflected or re- 

 fracted waves, by merely writing in the simple formulae contained in 

 that paper, 



A = 1 and A, = 1 for light polarized in the plane of incidence; 



or A = -5 and A, = — 5 for light polarized perpendicular to the plane of 



7 y ' • -a 



incidence. 



As an example, we will here deduce the intensity of the refracted 

 wave for both kinds of light. 



Representing, therefore, the parts of w and w, due to the distur- 

 bances in the Incident Reflected and Refracted waves by 



f(ax + by + ct), F(- ax + by + ct), and f^ap + by + ct) 



respectively, and resuming the first of our expressions (7) in the paper 

 on Sound, viz. — 



f = * I A + a ) S" 

 we get for light polarized in the plane of incidence, where A = A, = 1, 



2 cos 9 sin 0, 



sin (0, + 0) ' 

 which agrees with the value given in Airy's Tracts, p. 356. 



