Mastering Physics Solutions: Exercise 22.46

Exercise 22.46

Part A = red

Solution Below:

White light passes through a piece of crown glass and strikes an interface with air at an angle of 41.15°. The index of refraction of crown glass is 1.515 for red light and 1.523 for blue light.

Part A

Which color(s) of light will be refracted out into the air?

  • both red and blue
  • red
  • blue

This is a total internal reflection problem. Use Snell’s law to find out which colors can be refracted out

For red:

n1 * sin(θ1) = n2 * sin(θ2)
1.515 * sin(41.15) = 1.515 * sin(θ2)
0.9969 = sin(θ2)
θ2 = 85.5°

So red light will be refracted out. You didn’t actually have to find the angle because the sin θ2 is less than 1. This is a valid sin, so you know the light will be refracted out.

For blue light:

n1 * sin(θ1) = n2 * sin(θ2)
1.523 * sin(41.15) = 1.515 * sin(θ2)
1.00218 = sin(θ2)

Since the sin of θ2 is greater than 1, this isn’t a valid angle, so light won’t be refracted out.

red

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