Ch. IX] INDEX OF REFRACTION AND VELOCITY 



279 



For crown glass the waves opposite the fixed hne B, if possessed of 

 a speed of i in the ether, would have a speed in the glass of 



I-S3I 



Opposite the E line, with the shorter waves, the speed would be ^ 



1.551 

 in crown glass. 



That is, then, just as in refraction (§ 445-446), if the velocity in 

 one medium and the index of refraction of the two media are known 

 the velocity in the second me- 

 dium can be determined; and 

 in general knowing any three 

 factors the fourth can be de- 

 termined. 



While for the discussion of 

 lenses the narrower view of re- 

 fraction, may sufl&ce, for optical 

 instruments generally it is of 

 fimdamental importance to real- 

 ize that there is just as much 

 effect on light waves striking 

 the surface of the refracting 

 body perpendicularly as ob- 

 liquely. In one case, that of the 

 obHque meeting, the ray is bent 

 due to the shortening of the 

 waves in passing from a rarer 

 to a denser medium. If the 

 waves meet the denser sub- 

 stance normally to its surface 

 the ray will not be bent, but the 

 shortening of the waves wiU be 

 the same leading to an optical 

 shortening of the path of the ray. 



Fig. 160. Criticai, Angle for Light 

 Passing trom Glass to Water, the 

 Angle ln the Water Being 90°. 



N_ Normal to the refracting surface. 

 sin i In this case sin 61° + or 0.8750 _ 

 sin r In this case sin 90° or i .0000 



-1^ in accordance with the general form- 

 1.52 



J sin i _ index r 

 sin r index i 

 b Light ray at the critical angle and 

 emerging into the water at an angle of 

 90° from the normal. 



d d' Ray of light at an angle greater 

 than the critical angle and hence reflected 

 back into the glass, the angle of incidence 

 and reflection being equal. 



This is of prime value when de- 

 signing optical apparatus where two optical paths must be made 

 equal, although the actual distance in millimeters may be unequal. 

 The binocular microscope is a striking example (fig. 53-54). The 



