An electromagnetic wave in dielectric medium 1 (∈1 , μ0) impinges obliquely on a boundary...

An electromagnetic wave in dielectric medium 1 (∈1 , μ0) impinges obliquely on a boundary lane with dielectric medium 2 (∈2 , μ0). Let ϕi, and ϕt, denote the incident and refraction angles, respectively, and prove the following:

a) For perpendicular polarization:

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b) For parallel polarization:

(These four relations are known as Fresnel formulas)