Question

The critical angle for an air-glass interface is 25.3°. When a light ray in air is incident on the interface, the reflected ray is 100% polarized. What is the angle of refraction of that ray?

Answer 1

First, consider the case of total internal reflection.
n2 * sinc = n1 * sin(90)
Where n1 is the refractive index of air, c is the critical angle, and n2 is the refractive index of the glass.
n2 * sin(25.3) = 1 * 1
n2 = 1 / sin(25.3)
= 2.34
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The incident angle for 100% polarization is Brewster's angle. Brewster's angle can be written as,
B = tan^-1(n2 / n1)
B = tan^-1(2.34 / 1)
= 66.86 degrees.

Using Snell's law,
n1 * sinB = n2 * sinr
Where r is the angle of refraction.
1 * sin(66.86) = 2.34 * sinr
sinr = 0.393
r = sin^-1(0.393)
= 23.14 degree