定义：
描述两透明各向同性介质截面处透射系数和反射系数幅值的方程。

菲涅尔方程是描述两透明各向同性介质截面处透射系数和反射系数幅值的方程： 

图1：两介质截面处的折射过程 
其中n1 和n2 是两介质的折射率。对应的传播角度（与法线的夹角）为 θ1 和 θ2（见图1）。例如，s偏振（电场矢量与入射平面垂直）透射系数大小为ts。 
功率反射系数是对应反射系数大小的平方。而透射功率系数，考虑到不同的传播角度，需要在前面加一个系数(n2 cos θ2) / (n1 cos θ1)。 
 

 图2：s和p偏振的功率反射率，采用的折射率为1.45. 
图2给出了界面处功率反射率与入射角度和偏振态的关系。P偏振在入射角为布儒斯特角时（这里约为55.4°）反射系数变为0. 

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:

Figure 1: Refraction at an interface between two 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). n₁ and n₂ are the refractive indices of the two media. The corresponding propagation angles (measured against the normal direction) are θ₁ and θ₂ (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 (n₂ cos θ₂) / (n₁ cos θ₁) in order to take into account the different propagation angles.

Figure 2: Power reflectivity of the interface for s and p polarization, if a beam is incident from air onto a medium with refractive index 1.47 (e.g., silica at 1064 nm).

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°).

For the simplest case with normal incidence on the interface, the power reflectivity (which is the modulus squared of the amplitude reflectivity) can be calculated with the following equation:

Application to Absorbing Media

Fresnel equations can also be applied to absorbing media, including metals. In that case, a complex refractive index needs to be used; the imaginary part is related to the absorbance. The reflection and transmission coefficients are then generally no more real numbers.

A difficulty occurs concerning the calculation of power transmission in cases with non-normal incidence. The above mentioned correction factor for taking into account the different propagation angles will be complex, but the power transmission factor would of course have to be a real number. The problem is related to the fact that the optical intensity is no longer constant along the wavefronts.