Fresnel equations

The Fresnel equations give the reflected and transmitted amplitudes of an electromagnetic wave at an interface, depending on polarization, incidence angle, and the media’s optical properties.

Fresnel reflection coefficients: Ratios describing reflected wave amplitudes relative to incident amplitudes at an interface. They are the equations’ direct predictions for reflected electric-field amplitudes.
Maxwell's equations: Four equations describing how electric and magnetic fields are generated and vary. They supply the field laws whose interface boundary conditions yield Fresnel relations.
Anti-reflective coating: A thin optical layer designed to reduce reflection from a surface. Its design uses interface reflection amplitudes and interference to suppress reflected light.
Fresnel equations for conductors: Fresnel relations applied to conducting media with complex optical constants. They extend the interface calculation to absorbing metals and other conductors.
Fresnel transmission coefficients: Ratios describing transmitted wave amplitudes relative to incident amplitudes at an interface. They quantify the transmitted fields paired with the reflected fields.
Electromagnetic boundary conditions: Rules governing field components across boundaries between electromagnetic media. Continuity conditions at the interface are the derivation’s essential constraints.
Thin-film interference: Interference between waves reflected or transmitted by the boundaries of a thin layer. Fresnel amplitudes at successive boundaries determine the resulting interference.
Fresnel equations for absorbing media: Fresnel relations for media in which propagating light loses energy through absorption. Complex refractive indices capture absorption absent from the simplest transparent-medium treatment.
s-polarization: Linear polarization with the electric field perpendicular to the plane of incidence. Its reflection coefficient is one of the two polarization-specific Fresnel results.
Refractive index: A dimensionless measure of how a medium changes light’s phase velocity. The indices of both media set reflection and transmission amplitudes.

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