What this calculator does
At one particular angle of incidence, light reflected from a surface comes off completely polarised. That angle is Brewster's angle, and it is why polarised sunglasses work so well against glare from water and roads.
The effect is strongest near that angle and falls away on either side, but reflections from horizontal surfaces are partially polarised across a wide range of angles, which is enough to make a filter useful in practice.
The formula
Take the arctangent of the second refractive index divided by the first. At that angle the reflected and refracted rays are exactly 90 degrees apart, which is the geometric condition behind the effect.
| Term | Meaning |
|---|---|
| Brewster's angle | The incidence angle at which reflected light is completely polarised parallel to the surface. |
| Refractive index (n) | How much a medium slows light. Air is about 1.00, water 1.33, glass 1.50. |
| p-polarisation | The component oscillating in the plane of incidence, which is entirely absent from the reflection at Brewster's angle. |
The inputs explained
| Field | What to enter |
|---|---|
| Refractive index of incident medium (air ≈ 1.00) | The refractive index of the medium the light starts in, usually air at 1.00. |
| Refractive index of second medium (glass ≈ 1.50) | The refractive index of the medium it reflects from. |
When to use it
Understanding polarised sunglasses
Glare from water peaks near Brewster's angle, and a filter oriented against it removes most of that reflection.
Photography through glass or water
A polarising filter turned to the right orientation near this angle can almost eliminate a reflection.
Designing laser optics
Brewster windows are set at exactly this angle so one polarisation passes with essentially no reflection loss.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What is Brewster's angle for common materials?
Reflection from a range of materials.
| Second medium | Brewster's angle | Refraction angle at this incidence |
|---|---|---|
| Water (1.33) | 53.06 ° | 36.94 ° |
| Glass (1.50) | 56.31 ° | 33.69 ° |
| Dense glass (1.70) | 59.53 ° | 30.47 ° |
| Diamond (2.42) | 67.55 ° | 22.45 ° |
Questions
Why does reflected light become polarised?
At this angle the reflected and refracted rays are perpendicular. The oscillation that would be needed to emit the reflected ray in the plane of incidence points directly along the reflected direction, and light cannot oscillate along its own direction of travel, so that component simply cannot be reflected.
Why are polarised sunglasses oriented vertically?
Because glare comes mostly off horizontal surfaces, which polarises it horizontally. A filter with a vertical transmission axis blocks that component while passing the rest of the scene.
Is all the light polarised at this angle?
Only the reflected portion. The transmitted light is partially polarised the other way, and most of the light energy goes into the transmitted beam rather than the reflection.
Does this work for any pair of materials?
Yes, for any two transparent media with different refractive indices. Going from glass into air gives a different angle, which is the complement of the air-to-glass one.
For light transmitted through a polariser, see the Malus's law calculator. For the refraction angle itself, see the Snell's law calculator.