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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.

α1=α2\alpha_1 = - \alpha_2

with the angle of incidence α1\alpha_1 and the angle of reflection α2\alpha_2.

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


with the angle of incidence α\alpha, the angle of refraction β\beta, the refractive indices n1n_1 and n2n_2.

Reflection angle α2=α1=\alpha_2 = - \alpha_1 = -30 {}^\circ
Refraction angle β=arcsin(n1n2sin(α1))=\beta = \arcsin\left( \frac{n_1}{n_2} \sin(\alpha_1) \right) = -30 {}^\circ

The refractive index nn of a material

n=μrϵrn = \sqrt{\mu_r \epsilon_r}

with ϵr\epsilon_r is the material’s relative permittivity, and μr\mu_r is its relative permeability.

Total Internal Reflection

The total reflection will happen at the critical angle

αC=arcsin(n2n1)\alpha_C = \arcsin\left( \frac{n_2}{n_1} \right)

where αC\alpha_C is the critical angle, n1n_1 and n2n_2 are the refractive index.


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

Polarization Angle

Light that is reflected at Brewster’s angle

αG=arctan(n2n1)\alpha_G = \arctan\left( \frac{n_2}{n_1} \right)