Brewster's angle
θ_B = arctan(n₂/n₁), the angle at which reflected light from a dielectric interface is perfectly s-polarised because the p-polarised Fresnel reflection coefficient r_p vanishes. Brewster 1815.
Definition
Brewster's angle θ_B is the angle of incidence at which light reflected from a dielectric interface is purely s-polarised: the p-polarised component is fully transmitted with no reflection, because the Fresnel coefficient r_p = (n₂ cos θ₁ − n₁ cos θ₂)/(n₂ cos θ₁ + n₁ cos θ₂) passes through zero. Applying Snell's law to r_p = 0 gives tan θ_B = n₂/n₁. For air-to-glass, θ_B ≈ 56°; for air-to-water, θ_B ≈ 53°; for air-to-diamond, θ_B ≈ 67°.
The geometric origin of the effect is striking: at θ_B the reflected ray and the refracted ray are perpendicular to each other, so the dipoles induced in the second medium by the incident wave radiate along their own axis (which is suppressed by the dipole radiation pattern) for the p-polarised component but not for the s-polarised component. David Brewster discovered this in 1815 by systematic angle-and-polarisation measurements across dozens of materials. The effect is exploited in polarising sunglasses (which block horizontally-polarised glare from roads and water), in Brewster windows in laser cavities (where a window oriented at θ_B passes the laser-mode polarisation with zero reflection loss), and in Brewster-angle microscopes (which study molecular monolayers by viewing the sharp extinction at θ_B and the disruption of extinction caused by any change in the surface dielectric).