ON THE REFLEXION AND REFRACTION OF LIGHT. 289 



regular series of gradations, 



T being the common thickness of each of these successive media. 

 Then it is clear we should have to replace the last system by 



and 



- (33), 



and 



But it is evident from the form of the equations on the right 

 side of system (33), that the total effect due to the last terms of 

 their second members will be far less when n is great, than that 

 due to the corresponding term in the second equation of system 

 (29)*. If, therefore, we reject these second terms, and conceive 

 the common interval r so small that the result due to the first 

 terms may not differ very sensibly from that which would be 

 produced by a single refraction, we should have to replace 

 the system (29) by (30), and the intensity of the reflected 

 wave would then agree with the law assigned by Fresnel. In 

 virtue of this law, however highly refracting any substance 

 may be, homogeneous light will always be completely polarized 

 at a certain angle of incidence ; and Sir David Brewster states 



* In fact, in the system (33) each of the last terms will, in consequence of the 

 factors (/-li 2 - /i 2 ), &c. be quantities of the order compared with the last term of 

 (29'), and as their number is only n, their joint effect will be a quantity of the 

 order - compared with that of the term just mentioned. 



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