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 \(\alpha_2 = - \alpha_1 =\)
Refraction angle
\(\beta = \arcsin\left( \frac{n_1}{n_2} \sin(\alpha_1) \right) =\)
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