Answer to Question #187298 in Physics for Sael

Question

1. A ray of light (f = 5.09 X 1014 Hz) is traveling through the glycerol toward air. The angle of incidence of the ray is measured to be 10 degrees. Part of the ray is reflected and part of the ray is refracted.
2. Find the angle of reflection.
3. Find the angle of refraction.
4. Find the speed of light in glycerol
5. Find the wavelength of this ray in glycerol
6. Find the critical angle for light traveling from water to air.

Answer 1

2. Find the angle of reflection:

$$\theta_{ref}=\theta_i=10°.$$

3. Find the angle of refraction:

$$\frac{n_a}{n_g}=\frac{\sin\theta_i}{\sin\theta_r},\\\space\\ \theta_r=\arcsin\frac{n_g\sin\theta_i}{n_a}=\arcsin\frac{1.47\sin10°}{1}=14.8°.$$

4. Find the speed of light in glycerol

$$c_n=\frac cn=\frac{3·10^8}{1.47}=2.04·10^8\text{ m/s}.$$

5. Find the wavelength of this ray in glycerol

$$\lambda=\frac{c_n}{f}=4.01·10^{-9}\text{ m}.$$

6. Find the critical angle for light traveling from water to air.

$$\frac{n_a}{n_w}=\frac{\sin\theta_c}{\sin90°},\\\space\\ \theta_c=\arcsin\frac{1}{n_w}=\arcsin\frac{1}{1.33}=48.6°.$$