Mastering Physics Solutions: Exercise 22.20

Exercise 22.20

Part A = 54 degrees Click to use the calculator/solver for this part of the problem

Solution Below:

Assume all angles to be exact.
A beam of light is incident from air onto a flat piece of polystyrene at an angle of 60° relative to a normal to the surface.

Part A

What angle does the refracted ray make with the plane of the surface?
Express your answer using two significant figures.

We can use Snell’s law to find the angle. But first we need the index of refraction for polystyrene. Mastering Physics should give it to you, but it doesn’t, so I will. Different sources will give you different numbers (usually around 1.57), but for this problem, I had to use use 1.49. I don’t know exactly which index Mastering Physics will want for you, so you can change the value in the calculator. Mastering Physics might not, but I try to help you.

Note: This problem gives the angle of incidence that you need to use for Snell’s law. But it asks for the angle of refraction relative to the plane of the surface. In other words, you need to take 90 – θ2 to get the answer this problem wants.

n1 * sin(θ1) = n2 * sin(θ2)
1.00 * sin(60) = 1.49 * sin(θ2)
0.8660 = 1.49 * sin(θ2)
0.5812 = sin(θ2)
θ2 = 35.53°

So to get the answer, just subtract θ2 from 90:

90 – 35.53 = 54.47 degrees

Round to 2 significant figures and you get 54 degrees (the answer).

54 degrees

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