${\dis$The Fresnel equations predict that light with the *p* polarization (electric field polarized in the same plane as the incident ray and the surface normal at the point of incidence) will not be reflected if the angle of incidence is

where *n*_{1} is the refractive index of the initial medium through which the light propagates (the "incident medium"), and *n*_{2} is the index of the other medium. This equation is known as **Brewster's law**, and the angle defined by it is Brewster's angle.

The physical mechanism for this can be qualitatively understood from the manner in which electric dipoles in the media respond to *p*-polarized light. One can imagine that light incident on the surface is absorbed, and then re-radiated by oscillating electric dipoles at the interface between the two media. The polarization of freely propagating light is always perpendicular to the direction in which the light is travelling. The dipoles that produce the transmitted (refracted) light oscillate in the polarization direction of that light. These same oscillating dipoles also generate the reflected light. However, dipoles do not radiate any energy in the direction of the dipole moment. If the refracted light is *p*-polarized and propagates exactly perpendicular to the direction in which the light is predicted to be specularly reflected, the dipoles point along the specular reflection direction and therefore no light can be reflected. (See diagram, above)

With simple geometry this condition can be expressed as

- $\theta}_{1}+{\theta}_{$
*p*-polarized light. One can imagine that light incident on the surface is absorbed, and then re-radiated by oscillating electric dipoles at the interface between the two media. The polarization of freely propagating light is always perpendicular to the direction in which the light is travelling. The dipoles that produce the transmitted (refracted) light oscillate in the polarization direction of that light. These same oscillating dipoles also generate the reflected light. However, dipoles do not radiate any energy in the direction of the dipole moment. If the refracted light is *p*-polarized and propagates exactly perpendicular to the direction in which the light is predicted to be specularly reflected, the dipoles point along the specular reflection direction and therefore no light can be reflected. (See diagram, above)
With simple geometry this condition can be expressed as

where *θ*_{1} is the angle of reflection (or incidence) and *θ*_{2} is the angle of refraction.

Using Snell's law,

- $n_{1}\sin \theta _{1}=n_{2}\sin \theta _{2},$
one can calculate the incident angle *θ*_{1} = *θ*_{B} at which no light is reflected:

- $\theta _{\mathrm {B} }=\arctan \!\left({\frac {n_{2}}{n_{1}}}\right)\!.$