ON THE REFLEXION AND REFRACTION OF LIGHT. 267 



Again, the systems (23) and (24) readily give 



a sm e = * . 



a"' 



en cos e = -J . f yu, 2 + - J a, 



/8 cos , = !. 



- a 



(25); 



and therefore 



(26). 



When the refractive power in passing from the upper to the 

 lower medium is not very great, ^ does not differ much from 1. 

 Hence, sine and sine, are small, and cose, cos e, do not differ 

 sensibly from unity; we have, therefore, as a first approxima- 

 tion, 



a. sin 2 cot 0. 



cot 6 _ sin 2(9 - sin 2#, _ tan (0 - 0,) 

 ~ sin 26 + sin 20, " tan (0 + 0j 



sin 2 0, 



a ~ , a, ~ sin 2 cot 

 a sin 2 , cot 



which agrees with the formula in Airy's Tracts, p. 358*, for light 

 polarized perpendicular to the plane of reflexion. This result is 

 only a near approximation: but the formula (26) gives the correct 



value of -5 , or the ratio of the intensity of the reflected to the 



incident light ; supposing, with all optical writers, that the in- 

 tensity of light is properly measured by the square of the actual 

 velocity of the molecules of the luminiferous ether. 



From the rigorous value (26), we see that the intensity of the 

 reflected light never becomes absolutely null, but attains a mini- 

 mum value nearly when 



* [Airy, ubi sup. p. no.] 



