Answer to Question #263670 in Physics for Karisa

Question

A ray of light impinges from air onto a block of ice (n = 1.309) at a 50.0⁰ angle of incidence. Assuming that this angle remains the same, find the radio of the angles of refraction (Ѳ_{2, ice} = Ѳ_{2, water}) when the ice turns to water (n = 1.333).

Answer 1

For ice the angle of refraction is

$$\theta_{ri}=\arcsin\frac{\sin\theta}{n_i}=\arcsin\frac{\sin50°}{1.309},\\\space\\ \theta_{ri}=36°.$$

For the molten ice:

$$\theta_{rw}=\arcsin\frac{\sin\theta}{n_w}=\arcsin\frac{\sin50°}{1.333},\\\space\\ \theta_{rw}=35°.$$

The ratio:

$$\frac{\theta_{ri}}{\theta_{rw}}=\frac{36°}{35°}=1.03.$$