A beam of light traveling in water (n = 1.33) encounters a boundary with another material. If the critical angle for total internal reflection is 81 degrees, what is the index of refraction of the other material?

the index of refraction of the other material = 1.31

Explanation:

Critical angle is given by the formula;

sin(θ_crit) = n_r/n_i

Where;

θ_crit is critical angle

n_r is index of refraction of the Refractive medium

n_i is index of refraction of incidence medium

We are given that θ_crit = 81° and n_i = 1.33

Thus;

sin 81 = n_r/1.33

n_r = 1.33 × sin 81

n_r = 1.33 × 0.9877

n_r ≈ 1.31

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denser than mercury would sink in it