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.

C. The critical angle is less than 47°.

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.

this means that the temperature of both substances will be equal

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)