Questions: Brewster's Angle and Polarization by Reflection

Question 1

A glass plate is tilted to Brewster's angle (≈56° for glass). A beam of randomly polarized light hits the plate. Which of the following correctly describes what happens to the reflected beam?

• A. The reflected beam contains both s- and p-polarized light in equal proportions
• B. The reflected beam is completely s-polarized — no p-polarized component is reflected
• C. The reflected beam is completely p-polarized — no s-polarized component is reflected
• D. The reflected beam is unpolarized but reduced in intensity by exactly half

Answer: (B)

At Brewster's angle, the reflected and refracted rays are perpendicular. The oscillating dipoles responsible for re-radiating p-polarized light cannot radiate along their own axis (the direction of the reflected ray), so zero p-polarized light is reflected. Only s-polarized light is reflected. Option C has it backwards — p-polarized light is fully *transmitted*, not reflected. Option A is the intuitive-but-wrong guess that both polarizations behave the same.

Question 2

Polarized sunglasses dramatically reduce glare from wet roads and water surfaces. This works because glare from horizontal surfaces is predominantly which type, and the lenses block which orientation?

• A. Glare is p-polarized (vertical oscillation); lenses block vertical polarization
• B. Glare is s-polarized (horizontal oscillation); lenses block horizontal polarization
• C. Glare is circularly polarized; lenses convert it to linear polarization
• D. Glare is p-polarized (horizontal oscillation); lenses block horizontal polarization

Answer: (B)

Glare from near-horizontal surfaces like roads and water is reflected near Brewster's angle, making it predominantly s-polarized — the electric field oscillates horizontally (perpendicular to the plane of incidence, which is vertical for a horizontal surface). Polarized sunglass lenses have a vertical transmission axis, blocking this horizontal s-polarization. Option A confuses the s/p labeling: s-polarization on a horizontal surface means horizontal oscillation, not vertical.

Question 3

At Brewster's angle, both s-polarized and p-polarized components of incident light are partially reflected.

• T. True
• F. False

Answer: False

At Brewster's angle, p-polarized light has zero reflectance — it is entirely transmitted. Only s-polarized light is reflected. This is the defining feature of Brewster's angle: complete polarization of the reflected beam by eliminating one polarization component entirely from reflection.

Question 4

Brewster windows in laser cavities are tilted at Brewster's angle so that p-polarized light passes through with essentially zero reflection loss.

• T. True
• F. False

Answer: True

This is the direct application of Brewster's angle in optics engineering. At normal incidence, each glass surface reflects about 4% of the light due to Fresnel reflection. Tilting the window to Brewster's angle makes the reflectance for p-polarized light exactly zero, eliminating cavity losses for that polarization component. It simultaneously selects and preserves p-polarized light inside the laser resonator.

Question 5

Why does p-polarized light experience zero reflection at Brewster's angle? Explain in terms of the geometry of the reflected and refracted rays and the physics of dipole radiation.

Model answer: At Brewster's angle, the reflected ray and the refracted ray are exactly perpendicular to each other (separated by 90°). The p-polarized component's electric field oscillates in the plane of incidence, driving dipole oscillations along that axis. A dipole does not radiate along its own oscillation axis — it radiates perpendicular to it. Because the 'would-be' reflected ray direction coincides with the dipole's oscillation axis, no p-polarized light can be re-radiated into that direction. The result is complete cancellation of p-polarized reflection.

This is the physical mechanism behind Brewster's angle. The condition θB + θr = 90° (reflected and refracted rays perpendicular) combined with Snell's law yields tan(θB) = n₂/n₁. The zero-reflection result is not a coincidence or just a mathematical result — it follows directly from the dipole radiation pattern, which has a null along the oscillation axis.