Brewster's Angle
Reflection at Brewster angle. Builds on Snell's Law & Refraction and Polarization.
Unpolarized sunlight hits the surface of a calm lake. You put on polarizing sunglasses and look at the glare from the water at various angles.
At one specific angle, the reflected glare almost completely disappears through your polarizing sunglasses. Why?
At Brewster’s angle, reflected light becomes 100% polarized! When the reflected and refracted rays are exactly 90° apart, the parallel (p) polarization component cannot reflect — it would need to oscillate along the ray direction, which EM waves can’t do. Only the perpendicular (s) polarization reflects. Your sunglasses are oriented to block s-polarization, eliminating the glare completely. For water (n ≈ 1.33), Brewster’s angle is about 53°.
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Adjust the angle of incidence and watch the reflected ray’s polarization. At Brewster’s angle, the reflected ray becomes 100% s-polarized (shown in blue). Notice that the reflected and refracted rays are exactly 90° apart at this point.
tan θ_B = n₂/n₁
At Brewster’s angle, the reflected and refracted rays are perpendicular. P-polarized light ‘tries’ to oscillate along the reflected ray — but transverse waves can’t do that. So p-polarized reflection drops to zero.
Glare from water, roads, and car hoods is partially polarized (strongest near Brewster’s angle). Polarizing lenses block the s-polarization, dramatically reducing glare while preserving overall brightness.
Photographers use polarizing filters to cut reflections from glass and water. Rotating the filter at the right angle eliminates window reflections, revealing what’s behind the glass.
Gas laser tubes use Brewster windows tilted at θ_B. P-polarized light passes with zero reflection loss at each window. This is why HeNe lasers produce polarized light — the windows select the p-polarization.
High-end displays use anti-reflection coatings engineered with Fresnel equation principles. By controlling the film thickness, reflections at the display’s viewing angles are minimized.
“At one magic angle, reflected light becomes perfectly polarized. A transverse wave simply cannot oscillate along its own direction of travel — and that geometric impossibility is the key to glare-free sunglasses.”
Brewster’s Angle Lab
Explore the Fresnel equations interactively. Adjust the angle of incidence and watch how s- and p-polarization reflectivities change. Find Brewster’s angle for different materials.
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Start with air-to-glass (n=1.5). Sweep the angle and watch the p-reflection curve dip to zero at Brewster’s angle (~56°). The s-reflection increases monotonically. Now try different materials: water (53°), diamond (67°). Toggle the 3D view to see why p-polarization can’t reflect — the reflected and refracted rays are perpendicular at θ_B. Try angles near 90° where both polarizations approach 100% reflection.
The Fresnel equations describe how much of each polarization reflects at any angle. Brewster’s angle is where p-reflectivity hits zero because the reflected ray can’t carry a longitudinal oscillation. This one geometric constraint gives us polarized light, glare-free sunglasses, and low-loss laser windows.