# Fresnel Equations

Definition: equations for the amplitude coefficients of transmission and reflection at the interface between two transparent homogeneous media

Fresnel equations specify the amplitude coefficients for transmission and reflection at the interface between two transparent homogeneous media:

For example, *t*_{s} is the amplitude transmission coefficient for s polarization; the transmitted amplitude is that factor times the incident amplitude in that case (disregarding any phase changes for transmission in the media). *n*_{1} and *n*_{2} are the refractive indices of the two media.
The corresponding propagation angles (measured against the normal direction) are θ_{1} and θ_{2} (see Figure 1).

For example, the amplitude transmission coefficient is *t*_{s} for s polarization, i.e., if the electric field vector is perpendicular to the plane of incidence.

The power reflection coefficients are obtained simply by taking the modulus squared of the corresponding amplitude coefficients.
For the transmission, one must add a factor (*n*_{2} cos θ_{2}) / (*n*_{1} cos θ_{1}) in order to take into account the different propagation angles.

Figure 2 shows in an example case how the reflectivity of the interface depends on the angle of incidence and the polarization. The reflection coefficient vanishes for p polarization if the angle of incidence is Brewster's angle (here: ≈55.4°).

See also: refraction, total internal reflection, Brewster's angle, refractive index

and other articles in the category general optics

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