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When an electromagnetic wave encounters an interface between two dielectric media with different ε (permittivity) and μ (permeability), the wave undergoes reflection and transmission.

The following Fresnel Coefficients mathematically describe the reflection and transmission at oblique incidence, assuming the wave is propagating from region 1 to region 2. As the boundary conditions at the interface must be taken into consideration, parallel polarization E|| (electric field parallel to the plane of incidence) and perpendicular polarization E (electric field parallel to the plane of incidence) will be considered separately.

For both polarizations, Snell's Law of reflection and refraction is:

    Θi = Θr angle of incidence equals angle of reflection, yo
    β1 sin Θi = β2 sin Θt
where Θi and Θr and Θt are the angles of incidence, reflection, and transmission, and β1 and β2 are the wavenumbers in dielectric 1 and 2, respectively.


The Reflection coefficients R and T are:

    R = (η2 cos Θi - η1 cos Θt) / (η2 cos Θi + η1 cos Θt)

    T = 2 η2 cos Θi / (η2 cos Θi + η1 cos Θt)

where η is the characteristic impedance of the dielectric, η = sqrt(μ/ε).


The Reflection coefficients R|| and T|| are:

    R|| = (-η1 cos Θi + η2 cos Θt) / (η1 cos Θi + η2 cos Θt)

    T|| = 2 η2 cos Θi / (η1 cos Θi + η2 cos Θt)

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