Question

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?

Answer 1

the index of refraction of the other material = 1.31

Step-by-step 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