2 7 6 



CRITICAL ANGLE AND TOTAL REFLECTION [Cn. IX 



(i) Critical angle of water and air: sin r (90) is i, index of 



water 1.33 whence ( - -) = ( ) or sin i = 751+. This is the sine 



\ i ' M-33' 



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 (90) is i. index for 



, . sin i i 

 glass is i. 5 2, whence = - 



i 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. 



Air 



\ 



= i' 



sin r (sin 90 = i) 

 Andex water (1.33)^ /'sin i 

 >> index glass (1.52) ' 



r v- 



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 f Sin i 



faces, there is displacement; but the em- 

 erging ray (r) is parallel with the entering 

 ray (i). 



Air Glass The two media through 

 which the ray is traveling. 



/ n Incident ray and normal at the 

 point of entrance into the glass. 



i' Incident ray continued by dotted 

 lines to show the path which would have 

 been followed if no glass had intervened. wne nce sin / = .875 sine of critical 



n r Normal and refracted ray on em- 

 ergence from the glass to the air again, angle in glass covered with water. 



r' Path of the refracted ray traced The corresponding angle is ap- 

 backward. 



proximately 61 . 



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. 



44pa. 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. 



