CH. IX] INDEX OF REFRACTION AND VELOCITY 279 



For crown glass the waves opposite the fixed line J5, if possessed of 

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



Opposite the H line, with the shorter waves, the speed would be - 



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 suffice, for optical 

 instruments generally it is of 

 fundamental 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 

 oblique 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 will be 

 the same leading to an optical 

 shortening of the path of the ray. 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 



FIG. 1 60. CRITICAL ANGLE FOR LIGHT 

 PASSING FROM GLASS TO WATER, THE 

 ANGLE IN THE WATER BEING 90. 



N 

 sin i 



Normal to the refracting surface. 

 In this case sin 61 + or 0.8750 _ 

 sin r In this case sin 90 



or i.oooo 



^ in accordance with the general form- 

 index r 



1.52 



ula 



sin ^ 



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. 



