446 Direct Vision Spectroscopes by Double Internal Reflection. 



equal to half the principal refracting angle of the corrected 

 prism, c. It is therefore evident that for spectroscopic pur- 

 poses the principal refracting angle, c, of a direct vision prism 

 cannot be made less than twice the " critical angle" of the 

 glass employed in its construction (unless the glass be silvered) 

 without involving a loss of light. The limiting form of such 

 prisms has a nearly constant angle a equal to 152°, and an 

 angle c varying from 67° to 90° for every kind of glass (see 

 Figs. 3, 4). In Table I. the angle of first internal reflection 

 is equal to the (< critical angle" of the glass. 



For spectroscopic purposes no advantage is gained by 

 diminishing the angles c and A in the manner now supposed. 

 The angles of incidence and emergence, as well as the original 

 uncorrected deviation, and the dispersive power of the prism 

 are all diminished at the same time. When on the contrary c 

 is increased A increases, and with it the dispersion of the 

 light. The angle of first internal reflection always remains 

 equal to the semi-vertical angle of the prism, or equal to 

 half c. When the latter angle, together with a, makes up 90 

 degrees the prism becomes isosceles, and the second internal 

 reflection no longer takes place (see Fig. 5) . A natural limit 

 is therefore placed to the 

 increase of the values of 

 these angles, however 

 desirable, and, therefore, to 

 the dispersive power of the 

 prism. 



Long before the na- 

 tural limit is reached the field of view becomes narrowed and 

 contracted. .Table II. exhibits the greatest possible angles 



Table II. 



Fig. 5. 



Index of 



refraction 



of the glass. 



Greatest 



angle (a) of 



the prism. 



1-4 

 1-5 

 1-6 

 1-7 



1-8 



24° 48' 

 26 43 



28 17 



29 37 



30 43 



Greatest angle 



(c) of the 



prism. 



130° 27' 

 126 34 

 123 26 

 120 46 

 118 34 



Extreme forms of prisms with greatest 

 possible angles A and c. 



Fig. 6. 



Fig. 7. 



Scale of angles for a direct vision prism, in which the second internal reflec- 

 tion disappears. The angles A and c have the greatest possible yaluea for double 

 internal reflection. 



