INTENSITY OF REFLECTED AND REFRACTED LIGHT. 



401 



= nf {af + h^) 

 we reduce the two equations to these 



/" + F"=/" 



= \ if" + F" +/") + ^, {af -a ¥'-a,f:} 



f" + F" - /" = ?i^ {af -aF- a J',) 



c 



or 



whence 



which equations give 



y;"_F"-/"= ^ {af'-a V'-aj;) 



/" + F"-/"=0 

 a/'-«F'-«,/'=0 



F" = 



i + a, ■' 



a + a, 

 by differentiating the second and eliminating successively//' and F". 



4. Now if <p be the angle of incidence, 

 <p. that of refraction, 



r=xcos(f)+ysm(p is the space described in a given time without 

 the medium, 



r, — x,co%^,+y,&m(p, within ; 



X, - ( = ■ . sin (p^ be the lengths of the waves respectively, 



and if 





SlVKp 



_j cos 0, sin ^ I. sin (p cos (^, 

 ' X sin <p^~ \ sin cp, 



, sind), . , Isind) 

 A sm ^, A. 



„„ _ sin <p cos 0,— sin (p, cos <^ ,„ 

 sin (p cos ^, + sin <p, cos ^ 



_ sin ((p — (p,) 

 sin {(p + (p) 



f" 



2coscpsmcp, 

 •'' sin (0 + (/),) ■•' 



The notation F, &c. is the same as that used by Mr Gkeen, and the present page 

 is added merely to make the suljject complete. 



5. These are the results deduced, in a manner apparently widely different, 

 by M. Fresnel. That the results should coincide is not by any means a matter 



VOL. XIV. PART II. 3 K 



