Question

Light travels through a medium with an index of refraction of 1.04. It comes to the surface of another medium at an angle of 83°. If the index of refraction for this medium is 2.11, what angle does the refracted light make with respect to the surface?

Answer 1

Given:

$n_i=1.04$

$n_r=2.11$

$\theta_i=90^\circ-83^\circ=7^\circ$

$$n_i\sin\theta_i=n_r\sin\theta_r$$

$$\theta_r=\sin^{-1}\frac{n_i\sin\theta_i}{n_r}=\sin^{-1}\frac{1.04\sin7^\circ}{2.11}\\ =3.44^\circ$$

The angle that refracted light makes with respect to the surface

$$90^\circ-3.44^\circ=86.6^\circ$$