Maxwell's Theory of Light. 289 



the specific inductive capacities of the first and second media 

 respectively. Let i be the angle of incidence, r the angle of 

 refraction ; and let fi 1} fi 2 be the coefficients of magnetic in- 

 duction in the two media. 



The electric displacement perpendicular to the surface of 

 separation must be the same in both media ; 



.*. (cli + a 2 ) sin t=a s sin r 



(it should be noticed that this makes the magnetic force 

 parallel to the surface of separation the same in both media) ; 

 and the electromotive force along the surface is the same in 



A.ITT 



both media. Now electromotive force = -w- (electric displace- 

 ment) ; 



, v cos i a* 



.'. («!— 02)—-= j^cosr; 



«! + a 2 __ K 2 tan r 

 a±— a 2 Extant' 



(K 2 tan r—K-i tan 1) 



2 l K 2 tan r + K x tan 1 



__ 2K 2 % sin 1 



3 ~~ (K 2 tan r + K x tan t) cos r 



Now the energy is half electric and half magnetic, the energy 



f 2 

 due to an electric displacement /= l~ ; therefore if a*, «J, a* 



be the intensities of the incident, reflected, and refracted rays 

 respectively; since aj, a*, ol\ are respectively proportional to 

 the energy in unit volume along these rays, 



«! a 2 d% 



«i : «s : «3- ^ : ^ : -^ 



(K 2 tan r — Ki tan t) 

 2 ~~ * K 2 tan r + K x tan t 



_o s/(KiK 2 )sin^ 



a 3— ai ^K 2 tan r + Ki tan tj- cost* 



Now 



sinfc \/K 2 /x 2 . 



and if, as is very nearly the case for transparent dielectrics 

 yu, 1= =/>i 2 , we may put 



sin 



sin 



r-VEi' 



