The Fresnel equations give reflection and transmission amplitudes for both transverse-electric and transverse-magnetic polarization of an electromagnetic wave at a planar interface. They follow by applying interface conditions for electromagnetic fields to incident, reflected and refracted plane electromagnetic waves.
When the permeabilities agree, the signed reflected-to-incident electric-field ratio for polarization normal to the plane of incidence isFor incidence from lower to higher refractive index it never vanishes.
For equal permeabilities on the two sides of an interface, tangential-field continuity and Snell law for electromagnetic waves givefor consistently signed electric amplitudes normal to the plane of incidence.
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The Fresnel equations describe how light is reflected and refracted at the interface between two different media. They are derived from the wave nature of light and provide a mathematical framework for understanding how the intensity and polarization of light change when it encounters a boundary, such as the surface of a prism, water, or glass.
