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Brewster's Angle Calculator (Polarizing Angle)

Find the angle of incidence at which reflected light becomes fully polarized, θB = arctan(n2 / n1), from the refractive indices of the two media.

Brewster's angle (θB)
56.31°
Angle of refraction at θB
33.69°

How it works

When light hits a boundary between two transparent media, the reflected beam is normally a mix of polarizations — except at one specific incidence angle, Brewster's angle, where the reflected ray comes out fully polarized parallel to the surface. That happens exactly when the reflected and refracted rays end up perpendicular to each other; combining that condition with Snell's law (n1·sin θ = n2·sin θt) and solving gives the closed form θB = arctan(n2 / n1). The refraction angle at that point is simply 90° − θB, since the reflected and refracted rays are perpendicular by construction.

For light going from air (n1 ≈ 1.0) into ordinary crown glass (n2 ≈ 1.5), θB works out to about 56.3° — the classic example used to explain why polarized sunglasses cut glare so effectively off glass, water, and other dielectric surfaces near that angle.

FAQ

Why do polarized sunglasses block glare using this angle?

Sunlight reflecting off a horizontal surface like water or a car hood near Brewster's angle is strongly polarized horizontally (parallel to the surface). Polarized lenses are made to block horizontally polarized light, so they cut that specific glare while still passing ordinary, unpolarized light through.

Does Brewster's angle depend on the light's wavelength?

Indirectly, yes — because a material's refractive index itself varies slightly with wavelength (dispersion), the exact Brewster's angle shifts by a small fraction of a degree across the visible spectrum for the same two materials. This calculator uses whatever single refractive index value you enter, so use the index for the wavelength you care about if the difference matters for your use case.

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