Question

Which of the following statements must be true about this prism's critical angle for the violet light shown below?

A. The critical angle is exactly 47º.

B. The critical angle is greater than 47°.

C. The critical angle is less than 47°.

D. This question cannot be answered without knowing how light of other colors would behave.

Answer 1

B. The critical angle is greater than 47°.

Step-by-step explanation:

Explanation: Light is reflected back into a prism whenever the angle of incidence is greater than the critical angle. When the angle of incidence is less than the critical angle, the light refracts as it exits the prism. In this case, the violet light is refracted as it exits the prism, so the critical angle must be greater than 47°. Also, you can conclude that all other colors of visible light will be refracted as it exits the prism. Shorter wavelengths (at the violet end of the spectrum) are the "first" to be reflected. If violet light is not reflected, then no visible light will be reflected.

Answer 2

Answer: C. The critical angle is less than 47°.

Step-by-step explanation:

The critical angle is the angle such that the refracted beam is parallel to the surface of the prism, so we will have total internal refraction

This comes from the snell law:

n1*sen(a1) = n2*sen(a2)

where n1 is bigger than n2.

Then:

sen(a1) = (n2/n1)*sin(a2)

n2/n1 is smaller than 1, so the right side only can go up to (n2/n1)*1 (when a2 = 90°)

sen(a1) = n2/n1

this equation defines our critical angle.

If we use an angle bigger than the critical angle, we still have a total internal reflection, so we will no see a refracted beam.

In the image, we can see that the angle between the beam and the normal to the surface of the prism is 47°, and we also can see that we have a refracted beam, this means that 47° must be smaller than the critical angle.

So the correct option is C.