Editing Fresnel equations (section)

== Overview ==
When light strikes the interface between a medium with [[refractive index]] {{math|''n''<sub>1</sub>}} and a second medium with refractive index {{math|''n''<sub>2</sub>}}, both [[reflection (physics)|reflection]] and [[refraction]] of the light may occur. The Fresnel equations give the ratio of the ''reflected'' wave's electric field to the incident wave's electric field, and the ratio of the ''transmitted'' wave's electric field to the incident wave's electric field, for each of two components of polarization. (The ''magnetic'' fields can also be related using similar coefficients.) These ratios are generally complex, describing not only the relative amplitudes but also the [[Reflection phase change|phase shifts]] at the interface.

The equations assume the interface between the media is flat and that the media are homogeneous and [[isotropy|isotropic]].<ref>Born & Wolf, 1970, p. 38.</ref> The incident light is assumed to be a [[plane wave]], which is sufficient to solve any problem since any incident light field can be decomposed into plane waves and polarizations.

=== S and P polarizations ===
{{Main|Plane of incidence}}
[[File:Plane of incidence.svg|thumb|425x425px|The plane of incidence is defined by the incoming radiation's propagation vector and the normal vector of the surface.]]
There are two sets of Fresnel coefficients for two different linear [[polarization (waves)|polarization]]  components of the incident wave. Since any [[Polarization (waves)#Polarization state|polarization state]] can be resolved into a combination of two orthogonal linear polarizations, this is sufficient for any problem. Likewise, [[Polarization (waves)#Unpolarized and partially polarized light|unpolarized]] (or "randomly polarized") light has an equal amount of power in each of two linear polarizations.

The s polarization refers to polarization of a wave's electric field ''[[Normal vector|normal]]'' to the [[plane of incidence]] (the {{mvar|z}} direction in the derivation below); then the magnetic field is ''in'' the plane of incidence. The p polarization refers to polarization of the electric field ''in'' the plane of incidence (the {{mvar|xy}} plane in the derivation below); then the magnetic field is ''normal'' to the plane of incidence. The names "s" and "p" for the polarization components refer to German "senkrecht" (perpendicular or normal) and "parallel" (parallel to the plane of incidence).

Although the reflection and transmission are dependent on polarization, at normal incidence ({{math|1=''θ'' = 0}}) there is no distinction between them so all polarization states are governed by a single set of Fresnel coefficients (and another special case is mentioned [[#Equal refractive indices|below]] in which that is true).