# Reflection and Refraction#

Reflection and Refraction are two wave phenomena that cause a change in direction of a wavefront at an interface between two different media. In general, a light wave is partially refracted and partially reflected when it passes from one medium to another at any angle other than 0° from the normal.

Reflection: The angle at which the wave is incident on the surface equals the angle at which it is reflected.

$\alpha_1 = - \alpha_2$

with the angle of incidence $$\alpha_1$$ and the angle of reflection $$\alpha_2$$.

Refraction: The direction of the propagating wave changes according to the refractive indices.

$\frac{\sin(\alpha)}{\sin(\beta)}=\frac{n_2}{n_1}=\frac{c_1}{c_2}=\frac{\lambda_1}{\lambda_2}$

with the angle of incidence $$\alpha$$, the angle of refraction $$\beta$$, the refractive indices $$n_1$$ and $$n_2$$.

Reflection angle $$\alpha_2 = - \alpha_1 =$$ -30 $${}^\circ$$
Refraction angle $$\beta = \arcsin\left( \frac{n_1}{n_2} \sin(\alpha_1) \right) =$$ -30 $${}^\circ$$

The refractive index $$n$$ of a material

$n = \sqrt{\mu_r \epsilon_r}$

with $$\epsilon_r$$ is the material's relative permittivity, and $$\mu_r$$ is its relative permeability.

### Total Internal Reflection#

The total reflection will happen at the critical angle

$\alpha_C = \arcsin\left( \frac{n_2}{n_1} \right)$

where $$\alpha_C$$ is the critical angle, $$n_1$$ and $$n_2$$ are the refractive index.

#### Explanation#

• If $$\alpha \le \alpha_C$$, the ray will split; some of the ray will reflect
• If $$\alpha \gt \alpha_C$$, the entire ray reflects from the boundary.

### Polarization Angle#

Light that is reflected at Brewster's angle

$\alpha_G = \arctan\left( \frac{n_2}{n_1} \right)$