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A Brewster window is used in a He-Ne laser to eliminate reflection losses; glass plates (refractive index 1.5, surrounded by air of index 1) are placed at the tube ends, and the laser light is plane polarized. For zero (partial) reflection, which condition(s) must hold? (A) Both glass plates make the same angle with the beam. (B) The angle between the beam and the glass plate surface equals arctan(2/3). (C) The beam is plane polarized with the E-field in the plane of the paper. (D) The beam is plane polarized with the E-field perpendicular to the plane of the paper.

1. (A) and (C) only
2. (A) and (D) only
3. (B) and (C) only
4. (A), (B) and (C)

Correct answer: (A) and (C) only

Solution

For no reflection, light must strike at Brewster's angle theta_B with tan(theta_B) = 1.5, i.e. theta_B = arctan(3/2) from the normal. The angle with the plate surface is 90 - theta_B = arctan(2/3); so (B) describes the angle from the surface correctly only if it means surface angle - but the precise required setup is that both plates share the same angle (A) and the E-field lies in the plane of incidence/paper (p-polarization) so it is fully transmitted (C). The accepted answer is (A) and (C). (D) is wrong because s-polarized light (E perpendicular to plane of incidence) is partially reflected at Brewster's angle.

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