Reflection and Transmission Coefficients

The power per unit area striking the interface = S. n
Here, n is the normal unit vector, in this case x.
The incident intensity is
        I1 = 1/2 ε1 v1 E²₀ I cos θ₁

The reflected intensity is
        IR = 1/2 ε₁ v1 E²₀R cos θR,

The transmitted intensity is
        IT = 1/2 ε² v₂ E²₀ T cos θT

The reflection and transmission coefficients for waves polarized parallel to the plane incidence are
        R = IR/I1 = (E₀R/E₀¹) = (α – β/α + β)2
        T = IT/I1 = ε₂ v₂/ε₁ v₁ (E₀T/E₀I) cos θT/ cos θI = αβ(2/α + β)2


R is the fraction of the incident energy that is reflected.
T is the fraction of the incident energy that is transmitted.
R + T = 1, in accordance with the law of conservation of energy.

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