Direct Vision Spectroscopes by Double Internal Reflection. 445 



At the same time the prism-face c D has been revolved an 

 equal amount. The ray is therefore refracted under the same 

 circumstances as before, at its emergence, but emerges parallel 

 to its original direction, d e parallel to s a. 



lb is evident that if i e are the original angles of incidence 

 and emergence in the uncorrected prism, these will still remain 

 the angles of incidence and emergence when the deviation is 

 removed. In this case i + e = c c being the principal refract- 

 ing angle of the corrected prism.* 

 It is essential for distinct spec- 

 troscopic vision that these angles i 

 and e, of incidence and emergence, 

 should be equal to one another, 

 and the deviation of the ray (in the 

 uncorrected prism) a minimum; 

 for otherwise the image of the 

 spectrum is blurred, and the dark 

 and bright lines are undistinguish- 

 able. In that case our last equa- 



c 

 tion becomes i=e=~. It will be 



CI 



found on examination of the figure 

 that the angle of first internal re- 

 flection also becomes equal to either 

 of the three angles named in this Fla - 2 - 



equation. The angle of first internal reflection is therefore 



Table I. 



Index of 



refraction 



of tbe glass. 



Least angle 



(a) of the 



prism. 



15° 



5' 



15 



26 



15 



41 



15 



46 



15 



45 



Least angle 



(c) of the 



prism. 



91° 16' 



83 36 



77 20 



72 4 



67 30 



Extreme forms of prisms with least 

 possible angles A and C. 



Fig. 3. 



Fig. 4. 



Scale of angles for a direct vision prism, in which first internal refiVction 

 takes place at the " critical " angle of the glass. The angles A and have their 

 least possible values consistently with no loss of light. 



* General formulae of calculation are given by M. Eadau in the number of the 

 Moniteur Scientijique for March 15th (Vol. vi. p. 259). 



