THE LAW OF MINIMUM DEVIATION OF 

 LIGHT BY A PRISM.* 



Francis E. Nipher. 



An elementary proof of the law of minimum deviation of 

 light by a prism may be obtained as follows : — 



Let i and r represent the angles of incidence and refrac- 

 tion at the point where the light enters the prism, and let i' 

 and ?•' represent these angles where the same ray leaves the 

 prism. The angles i and r' are in air and r and i' are in the 

 glass. Then by geometry, calling d the angle of deviation 

 of the ray, 



d = i—r-\-r'—i'=i-\-r' — A (1) 



where A=r -\- i' ,\^ the 

 angle of the prism. If 

 we lay off the angles d, 

 i and r' on three rec- 

 tangular axes, (1) is 

 the equation of a plane. 

 The trace of this plane 

 on the plane d, i is 

 obtained from (1) by 

 making r' = 0. If i be 

 made zero we shall have 

 the trace on the plane 

 d, r,' 



These traces make an 

 angle of 45° with the 

 axes which they inter- 

 sect, and the distance 

 of each point of inter- 

 section, from the ori- 

 gin, is A. The position 

 of this plane is wholly 

 independent of the re- 

 fractive properties of 

 the prism. Any two 

 prisms having equal Fig. i. 



* Read before Regular Academy Meeting, November 4, 1895. Approved 

 by Council, November 18, 1895. 



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