Brewster's Angle: Polarization by Reflection

Incidence

Angle of incidence θᵢ 56°

Refractive index n₂ 1.50

Live readouts

Brewster angle θ_B

56.3°

Refraction angle θₜ

33.7°

R (s-pol, TE)

15.0%

R (p-pol, TM)

0.0%

Degree of polarization of reflected beam

100%

s-polarized (TE) — field ⟂ plane of incidence

p-polarized (TM) — field in plane of incidence

How it works

Unpolarized light striking a dielectric boundary splits into two independent polarization components, each with its own reflectance given by the Fresnel equations (non-magnetic media):

Snell's law:  n1 sin(θi) = n2 sin(θt)

r_s = [n1 cos(θi) - n2 cos(θt)] / [n1 cos(θi) + n2 cos(θt)]
r_p = [n2 cos(θi) - n1 cos(θt)] / [n2 cos(θi) + n1 cos(θt)]

R_s = r_s²   R_p = r_p²   (power reflectance)

r_p passes through exactly zero at one special angle — Brewster's angle — where the reflected and refracted rays would be perpendicular to each other:

tan(θ_B) = n2 / n1

At θ_B the reflected beam contains no p-component at all: it is perfectly linearly polarized in the s-direction, even though the incoming light was completely unpolarized. This is why polarized sunglasses cut glare from water and glass — most of that glare left the surface near Brewster's angle.

θᵢ slider — angle of incidence, measured from the surface normal.
n₂ slider / preset buttons — refractive index of the lower medium (upper medium is air, n₁ = 1.00).
Snap to Brewster angle — jumps θᵢ exactly to tan⁻¹(n₂/n₁) for the current material.

Watch the orange (p-pol) markers on the reflected beam shrink toward nothing as you approach θ_B, while the blue (s-pol) markers stay strong.

AT BREWSTER'S ANGLE — REFLECTED LIGHT FULLY POLARIZED

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