Light enters a substance from air at 30.0° to the normal.It continues within the substance at 23.0° to the normal.What is the critical angle for this substance when it is surrounded by air?
A)53°
B)51.4°
C)36.7°
D)12.6°

Question

Quizplus · Accepted Answer

The critical angle is the angle of incidence at which the refracted angle becomes 90°. From Snell's law, we know that sin θ1/sin θ2 = n2/n1. We can rearrange this to solve for sin θ1: sin θ1 = (n1/n2) sin θ2. 
Using the given angles of 30.0° and 23.0°, we can find the refractive index of the substance: sin(30.0°)/sin(23.0°) = n2/1 (since air has a refractive index of 1). Solving for n2 = 1.51. 
Now we can solve for the critical angle: sin(θc) = (n2/n1) = 1.51/n1. When air is the incident medium (so n1 = 1), sin(θc) = 1.51. Taking the inverse sine of both sides, we find that θc = 51.4°. Therefore, the best choice is B.

Light Enters a Substance from Air at 30