A ray of light is normally incident on face ab of a plastic prism with an index of refraction n = 1.20 as shown.

-Determine the largest value of the angle so that the ray is totally reflected at the face ac if the prism is immersed in air.
A)28°
B)34°
C)45°
D)56°
E)Total internal reflection will not occur for any value of

Question

A ray of light is normally incident on face ab of a plastic prism with an index of refraction n = 1.20 as shown.
 
-Determine the largest value of the angle so that the ray is totally reflected at the face ac if the prism is immersed in air.
A)28° 
B)34° 
C)45° 
D)56° 
E)Total internal reflection will not occur for any value of

Quizplus · Accepted Answer

Using Snell's law, we can find that the angle of refraction at face ac is:

sin(theta)/1.20 = sin(90° - theta)/1

sin(theta) = 1.20 sin(90° - theta)

sin(theta) = 1.20 cos(theta)

tan(theta) = 1.20

theta = tan^-1(1.20) ≈ 50.5°

For total internal reflection to occur, the angle of incidence must be greater than the critical angle, which is given by:

sin(critical angle) = 1/1.20

critical angle = sin^-1(1/1.20) ≈ 49.2°

Therefore, the largest angle 11ec9dff_6c98_d7c0_8d20_9d547df2ed5a_TB6393_11 that allows for total internal reflection is slightly larger than the critical angle, which is approximately 49.2°. The only answer choice that fits this is B (34°).

A Ray of Light Is Normally Incident on Face Ab