ON THE EEFLEXION AND REFRACTION OF LIGHT. 287 



lent to that marked (A) in our paper on Sound ; and the 

 general equations in ^ and w being the same, we may im- 

 mediately obtain the intensity of the reflected or refracted 

 waves, by merely writing in the simple formulae contained in 

 that paper, 



A = 1 and A, = 1 for light polarized in the plane of inci- 

 dence ; 



or A = - 2 and A, = ^ for light polarized perpendicular to the 

 / // 



plane of incidence. 



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

 refracted w^ave for both kinds of light. 



Eepresenting, therefore, the parts of w and w t due to the 

 disturbances in the Incident Reflected and Refracted waves by 



f(ax + by + ct), F(- ax + ly + ct), and / (a t x + ly + ct) 



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

 paper on Sound, viz. 



2 a 



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



A = A, = 1, 

 f t _ 2 2 



a 1 , 



* a "*" cot 



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



For light polarized perpendicular to the plane of incidence 

 we have A = 2 and A, = . If, therefore, we here represent the 



parts of A/T and ^ due to the same disturbances by /, .Fand f lt 



we get 



// 2 ^sin0 y cos0 2 



/' ~ 7 2 cot^ ! sin cos 6, ' cos 6 sin 6 

 cot 6 cos 6 t sin t 



[* Airy, u&t sup. p. 109.] 



