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An electromagnetic wave incident on the common surface between two isotropic dielectrics must satisfy Maxwell's boundary conditions at the surface. The existence of these boundary conditions results in a reflected wave and a transmitted wave into the second medium. The ratio of the amplitudes of the electric vectors of the reflected and transmitted waves to that of the incident wave is given by Fresnel's equations. In order to derive these equations from the boundary conditions one generally takes two separate idealized cases. For the first case the electric vector of the incident wave is taken to be perpendicular to the plane of incidence and for the second case the incident vector is considered to lie in the plane of incidence. The general case when the electric vector makes an arbitrary angle with the plane of incidence is then treated by resolving the incident vector into parallel and normal components.

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