22 Mb GREEN, ON THE REFLEXION 



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



a Sin e = — A . -"Hj -^ a. 



and therefore 



/3 s 



a COS e = ^ . f m 2 + — j a , 

 _ . . (m 2 - l) 2 6 



fieose = |. (m 2 - J) «,; 



,.+ ir ,(„.-sy + () ,.- 1) .g 



"^v + i)..(„. + |)' + („'-ir^ 



(25). 



(26). 



When the refractive power in passing from the upper to the lower 

 medium is not very great, p. does not differ much from 1. Hence, sin e 

 and sin e t are small, and cos e, cos e t do not differ sensibly from unity ; 

 we have, therefore, as a first approximation, 



a sin 2 9 cot 9, 



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

 ized perpendicular to the plane of reflexion. This result is only a near 



approximation : but the formula (26) gives the correct value of Ej , or 



the ratio of the intensity of the reflected to the incident light; sup- 

 posing, with all optical writers, that the intensity 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 re- 

 flected light never becomes absolutely null, but attains a minimum 

 value nearly when 



