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Unpolarised light is incident on a transparent sphere of refractive index sqrt(3) (see figure showing rays 1-4 from reflection/refraction). Identify the correct statement(s) about the polarisation of the rays.

1. Ray 1 is completely polarized.
2. Ray 2 is partially polarized.
3. Ray 4 is completely polarized.
4. Ray 3 is partially polarized.

Correct answer: Ray 1 is completely polarized.

Solution

Brewster's law gives tan(theta_B) = n = sqrt(3), so theta_B = 60 degrees. The figure is set up so the light strikes the sphere's surface at the Brewster angle; the ray reflected at that surface (ray 1) is completely plane polarised. The transmitted/refracted rays are only partially polarised. Therefore the completely polarised ray is ray 1.

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