Question

A laser beam is incident on a 45º-45º-90º prism perpendicular to one of its faces, as shown in Figure P22.20. The transmitted beam that exits the hypotenuse of the prism makes an angle of 15º with the direction of the incident beam. Find the index of refraction of the prism.

Answer 1

To find the index of refraction of the prism, use the formula n = sin((a+b)/2) / sin(a/2), where a is the angle of incidence and b is the angle of refraction.

Step-by-step explanation:

To find the index of refraction of the prism, we can use the formula provided in the question: n = sin((a+b)/2) / sin(a/2). In this formula, a is the angle of incidence and b is the angle of refraction. We are given that the angle of incidence is 45 degrees and the angle of refraction is 15 degrees. Plugging these values into the formula, we get:

n = sin((45+15)/2) / sin(45/2) = sin(30) / sin(22.5)

Now we can use a calculator to find the value of n.