When light in air strikes the flat surface of a certain glass at 31.2° with the normal, the reflected ray is 100 percent polarized. What is the critical angle for the air-glass interface of this glass?
A) $21.4 ^ { \circ }$
B) $68.6 ^ { \circ }$
C) $58.8 ^ { \circ }$
D) $52.7 ^ { \circ }$
E) $37.3 ^ { \circ }$

Question

When light in air strikes the flat surface of a certain glass at 31.2° with the normal, the reflected ray is 100 percent polarized. What is the critical angle for the air-glass interface of this glass? 
A) $21.4 ^ { \circ }$
B) $68.6 ^ { \circ }$
C) $58.8 ^ { \circ }$
D) $52.7 ^ { \circ }$
E) $37.3 ^ { \circ }$

Quizplus · Accepted Answer

The reflected ray is 100% polarized at Brewster's angle, where the angle of incidence plus the angle of refraction equals 90°. Using Brewster's law, $ n = \tan(\theta_i) $, where $ \theta_i = 31.2^\circ $. Solving for the critical angle using $ \sin(\theta_c) = 1/n $, we find it to be approximately $ 37.3^\circ $.

When Light in Air Strikes the Flat Surface of a Certain