Question

Light travelling from water into a diamond, strikes the diamond at an angle of 42.0 degrees. What is the angle of refraction?

Answer 1

The angle of refraction (see Snell's law) is:

$$\sin\theta_r = \dfrac{n_1}{n_2}\sin\theta_i$$

where $n_2 = 2.417$ is the refractive index of diamond, $n_1 = 1.333$ is the refractive index of water, and $\theta_i = 42\degree$ is the incident angle. Thus, obtain:

$$\theta_r = \arcsin\left(\dfrac{1.333}{2.417}\sin42\degree\right) \approx 21.7\degree$$

Answer. $21.7\degree$.