A ray of light is incident on the mid-point of a glass prism surface at an angle of 23.4° with the normal.For the glass,n = 1.60,and the prism apex angle is 51.8°.What is the angle of incidence at the glass-to-air surface on the side opposite where the ray exits the prism?
A)39.5°
B)14.4°
C)37.4°
D)28.4°
E)42.7°

Question

Quizplus · Accepted Answer

Using Snell's law, we can find the angle of refraction of the ray inside the prism:

sin(23.4°)/1.60 = sin(r)/sin(51.8°)
sin(r) = sin(51.8°)*(sin(23.4°)/1.60) = 0.416
r = arcsin(0.416) = 24.6°

Now, using the law of reflection, we know that the angle of incidence and the angle of reflection are equal:

i = r = 24.6°

Finally, using Snell's law again, we can find the angle of refraction of the ray as it exits the prism:

sin(i)/1.60 = sin(t)/sin(51.8°)
sin(t) = sin(51.8°)*(sin(i)/1.60) = 0.578
t = arcsin(0.578) = 37.4°

Therefore, the answer is (C).

A Ray of Light Is Incident on the Mid-Point of a Glass