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Fresnel's Equations & Brewster Angle

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Fresnel's Equations & Brewster Angle. See attached file for full problem description.

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Eor/Eoi = (1 - αβ)/(1 + αβ) -------------------- (1)
α = cos θt/ cos θi ---------------------------- (2)
Substituting for Alpha,

α = cos θt/ cos θi ---------------------------- (A)
β = n1/n2 ---------------------------- (B)

Eor/Eoi = (1 - β(cos θt/ cos θi))/(1 + β (cos θt/ cos θi))
Eor/Eoi = (cos θi - β cos θt )/ (cos θi + β cos θt )

But

n1 sin θi = n2 sin θt ----------------- (3)

Find cos θt in terms of cos θi using (3):

cos θt = sqrt (1 - sin2 θt) = sqrt [1 - (n12/ n22)sin2 θi] = sqrt [1 - (1/ β2)sin2 θi]

cos θt = sqrt [1 - (1/ β2)sin2 θi] = (1/ β)sqrt [β2 - sin2 θi]

cos θt = (1/ β)sqrt [β2 - sin2 θi] ------------------- (4)

Substituting this in Eor/Eoi,

Eor/Eoi = (cos θi - sqrt [β2 - sin2 θi] )/ (cos ...

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