24 REFLEXION AND REFRACTION. 



second surfaces, respectively, and let m and mi be the indices 

 of refraction at the two surfaces. Then, 



sin u sin 



sin Ui sin u z 



and multiplying 



_ sin u _ 



fj. denoting the ratio of the sines from the first medium into 

 the third. 



It is obvious that this result may be generalized ; and 

 that, when there is any number of successive media, bounded 

 by parallel surfaces, the index of refraction from the first into 

 the last is the continued product of the indices from the first 

 into the second, from the second into the third, and so on. 



When the first medium is a vacuum, m and /u will be the 

 absolute indices of refraction of the second and third media, 

 respectively. Hence m\^ the relative index of refraction from 

 the second medium into the third, is equal to the quotient 

 arising from the division of the absolute index of the latter 

 by that of the former. 



(29) When light traverses a prism, that is, a medium 

 bounded by two inclined plane surfaces, the total deviation of 

 the refracted ray is the sum of the deviations at incidence and 

 emergence. Let u and u' denote the angles which the inci- 

 dent and emergent rays make with the perpendiculars to the 

 faces at the points of incidence and emergence, v and v' the 

 angles which the portion of the ray within the prism forms 

 with the same, then the deviations at incidence and emergence 

 are, respectively, u - v, and u' - v' ; and the total deviation 

 A = u + u' - (v+ v'). Now, it is easily shown that the alge- 

 braic sum of the angles, which the portion of the ray within 

 the prism makes with the two perpendiculars, is equal to the 



