176 



CRITICAL ANGLE AND TOTAL REFLECTION [Ch. IX 



(1) Critical angle 



. /sin i 

 water 1.33 whence 1 



of water and 



1 



i-33 



air: sin r (90°) is 1, index of 

 or sin i= 751+. This is the sine 



of 48 45', and whenever the ray in the water is at an angle of more 



than 48 45' it will not emerge 

 into the air, but be totally re- 

 flected back into the water. 



(2) Critical angle of glass and 



air: sin r (oo°) is 1. index for 



, . . sin i 1 

 glass is 1.52, whence = = 



1 1.52 

 sin 0.65789, which is the sine of 

 41 . Light having a greater 

 angle in glass than 41 is intern- 

 ally reflected as from a mirror 

 (fig. 152), and reflected back into 

 the glass. 



(3) Critical angle of glass 

 covered with water. 



Fig. 157. Displacement of a Ray 

 of Light in Traversing an Object 

 with Plane Faces. 



This figure is to show that while there 

 is no angular deviation of a ray of light 

 in traversing a dense medium with plane 

 faces, there is displacement; but the em- 

 erging ray (r) is parallel with the entering 

 ray (*). 



Air Glass The two media through 

 which the ray is traveling. 



i n Incident ray and normal at the 

 point of entrance into the glass. 



V Incident ray continued by dotted 

 lines to show the path which would have 

 been followed if no glass had intervened. 



n'r Normal and refracted ray on em- 

 ergence from the glass to the air again. 



r' Path of the refracted ray traced 

 backward. 



sin i 



sin r (sin 90 

 /index water (1.33) 

 \ index glass (1.52) 



i-52 



1) 



or 



(t-0 



whence sin i = .875 sine of critical 

 angle in glass covered with water. 

 The corresponding angle is ap- 

 proximately 6i°. 

 The last shows the advantage of water immersion when a large 



angle of light is desired. With homogeneous immersion there would 



be no critical angle for the glass. 



§ 449a. Critical angle. — As defined by some physicists the critical angle is the 

 least angle at which light undergoes total internal reflection at the surface of the 

 denser medium. 



