482 Proofs of Elementarg Theorems of Oblique Refraction. 



and similarly from the triangle NPR, 



. AT cos 77'. sin y' 



sm N = ' — j-r- 1 - . 



sin 9 



Hence since fi sin <j>=fi' sin <f>', 



ifACOST) . sin y = // cos 7/ . sin7 / . ... (3) 



Putting PN = 90°, the third well-known theorem is 

 obtained as a particular case of (3). 



IV. The first step in the discussion of prismatic deviation 

 may be added for the sake of continuity. 



Let P represent the refracting edge of a prism, 

 Nj, N 2 the normals to the faces, 

 Tx the incident ray, 

 R the ray in the prism, 



I 2 the emergent ray. 



Let fJ>"= the refractive index of the third medium, 

 D— the total deviation =IiI 2 , 

 D = the angle I 1 PI 2 = the projection of I T I 2 on NiN 2 . 



Since PN! = PN 2 = 90°, the great circle NiN 2 represents 

 the principal plane, and the arc N X N 2 is equal to the angle 

 of the prism. 



Fig. 2. 



P 



From (2), (a cos VI 1 = /jl / cos PR=/i/' cos PI 2 . 



Therefore if the first and third media have the same index 



