A ray of light enters an equilateral prism made of material with n = 1.45 at an angle of incidence $\theta$.The internally refracted ray is parallel to the base of the prism.What is the angle of refraction for the ray leaving the prism?
A) 46.5$^{\circ}$
B) 30.0$^{\circ}$
C) 20.2$^{\circ}$
D) 15.7$^{\circ}$
E) the ray won't leave the prism

Question

A ray of light enters an equilateral prism made of material with n = 1.45 at an angle of incidence $\theta$.The internally refracted ray is parallel to the base of the prism.What is the angle of refraction for the ray leaving the prism? 
A) 46.5$^{\circ}$ 
B) 30.0$^{\circ}$ 
C) 20.2$^{\circ}$ 
D) 15.7$^{\circ}$ 
E) the ray won't leave the prism

Quizplus · Accepted Answer

Since the prism is equilateral, the angle of incidence is 60 degrees (F1F1F1S1F1F1F10). The angle of incidence is related to the angle of refraction by Snell's Law: n1sinθ1 = n2sinθ2. The angle of incidence in this case is 60 degrees, and the refractive index of the prism material is 1.45. Since the ray is internally refracted, it means that it hit the interface between the air and the prism material at an angle greater than the critical angle (which is around 41.8 degrees for this prism material-air interface). Therefore, the angle of refraction must be 90 degrees - the critical angle for the prism material-air interface, which is approximately 43.5 degrees. Finally, because the internally refracted ray is parallel to the base of the prism, it means that it must refract again when it exits the prism. The exit angle is easily found to be 90 - 60 = 30 degrees. The angle of refraction for the ray leaving the prism is therefore 30 degrees (choice A).

A Ray of Light Enters an Equilateral Prism Made of Material