At Brewster’s angle, light polarised in the plane of incidence passes into the second medium without any reflection. Polarised sunglasses cut glare from water and roads for this reason, and laser windows are tilted at Brewster’s angle to avoid losses.
How to use the Brewster’s Angle Calculator
- First medium
- Refractive index n₁
- Second medium
- Refractive index n₂
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose or enter the refractive index of the medium the light comes from (n₁) and the one it enters (n₂).
Inputs explained
| Field | What to enter |
|---|---|
| First medium | Choose one: Vacuum, Air, Water at 20 °C, Ethanol … |
| Refractive index n₁ | A number |
| Second medium | Choose one: Vacuum, Air, Water at 20 °C, Ethanol … |
| Refractive index n₂ | A number |
What each result means
- Brewster angle θ_B = deg(atan([n2]÷[n1]))
- Refraction angle at θ_B = 90 – [Brewster angle θ_B]
Example values
How the main result changes when Refractive index n₁ changes and everything else stays at the example values above:
| Refractive index n₁ | Brewster angle θ_B (°) |
|---|---|
| 1 | 56.6516 |
| 1.25 | 56.6516 |
| 1.5 | 56.6516 |
| 2 | 56.6516 |
Formula
θ_B = arctan(n₂ / n₁)
Worked example
Inputs — First medium: Air; Second medium: Window glass.
Results — Brewster angle θ_B = 56.6516 °; Refraction angle at θ_B = 33.3484 °.
Key terms
- Polarisation
- The orientation of a light wave's electric field.
Frequently asked questions
What is Brewster's angle for air to glass?
About 56.7°.
Why are reflections at Brewster's angle polarised?
The p-polarised component has zero reflectance there.
How do polarised sunglasses use this?
They block the horizontally polarised glare from flat surfaces.
Do the reflected and refracted rays make a special angle?
Yes – they are perpendicular at Brewster's angle.