The critical angle for a substance is measured at 53.7 degrees. Light enters from air at 45.0 degrees. At what angle it will continue to travel?

34.74

Explanation:

Critical angle is represented by the formula

θ(c) = sin^-1 (n2/n1)

And we have been given that the critical angle is 53.7, so we substitute

53.7 = sin^-1 (n2/n1), rearranging, we have

Sin 53.7 = n2/n1

0.8059 = n2/n1

Again, we know that the second medium is air, and the refractive index of air is 1, so

0.8059 = 1/n1, making n1 subject of formula

n1 = 1/0.8059

n1 = 1.24

Now, we have gotten both indices, using Snell's law of refraction, we then find the needed refraction

Sin θ(r) = n(i)/n(r) Sin θ(i)

Now, solving, we have

Sin θ(r) = 1/1.24 * sin 45

Sin θ(r) = 0.8059 * 0.7071

Sin θ(r) = 0.5699

θ(r) = Sin^-1 0.5699

θ(r) = 34.74

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