Brewster’s Angle Calculator
Brewster’s angle — the angle of incidence at which reflected light is completely polarised — for any pair of refractive indices, with the critical angle for total internal reflection when it exists.
At Brewster’s angle the reflected and refracted rays are at right angles, and light polarised in the plane of incidence is not reflected at all: tan θ_B = n₂ ÷ n₁.
How the brewster’s angle calculator works
At Brewster’s angle the reflected and refracted rays are at right angles, and light polarised in the plane of incidence is not reflected at all: tan θ_B = n₂ ÷ n₁. It is why polarised sunglasses cut glare off water and roads. Going from a denser medium to a lighter one, there is also a critical angle beyond which everything reflects.
Formula: θ_B = arctan(n₂ ÷ n₁); θ_c = arcsin(n₂ ÷ n₁) when n₁ > n₂
Worked examples
| Inputs | Brewster’s angle (°) | Note |
|---|---|---|
| Air to glass (1.5) | 56.31 | 56.31° |
| Air to water (1.333) | 53.12 | 53.12° |
| Glass to air | 33.69 | 33.69°, critical angle 41.81° |
FAQFrequently asked questions
Why is the reflected light polarised at this angle?
At Brewster incidence the reflected and refracted rays are perpendicular. The molecules in the second medium oscillate along the refracted ray and cannot radiate along their own axis, so the component of light polarised in the plane of incidence has nothing to reflect it.
What is Brewster’s angle for water and glass?
About 53° for air to water (n = 1.33) and 56° for air to ordinary glass (n = 1.5). Low sun on water or a wet road sits near that angle, which is why polarised sunglasses work so well then.
What is the critical angle row?
When light travels from a denser medium to a lighter one, above the critical angle it is totally reflected — the principle of optical fibres. From a lighter into a denser medium there is no critical angle, and the row says so.
Does the angle depend on wavelength?
Slightly, because refractive index varies with wavelength (dispersion). For glass the difference across the visible spectrum is under a degree.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Measurement Institute — Australia's measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.