Brewster's Angle
Calculate the angle at which reflected light becomes fully polarized.
Used in laser design and glare reduction.
The Formula
θ_B = arctan(n₂ / n₁)
Brewster's angle is the specific angle of incidence at which reflected light is completely polarized. At this angle, the reflected and refracted rays are exactly 90° apart.
Variables
| Symbol | Meaning |
|---|---|
| θ_B | Brewster's angle (degrees) |
| n₁ | Refractive index of the first medium (where light comes from) |
| n₂ | Refractive index of the second medium (where light enters) |
Example 1
Find Brewster's angle for light going from air to glass (n=1.52)
θ_B = arctan(1.52 / 1.00)
θ_B = arctan(1.52) ≈ 56.7°
Example 2
Find Brewster's angle for light going from air to water (n=1.33)
θ_B = arctan(1.33 / 1.00)
θ_B = arctan(1.33) ≈ 53.1°
When to Use It
Use Brewster's angle when:
- Designing polarizing filters and anti-glare coatings
- Building laser cavities with minimal reflection loss
- Understanding why polarized sunglasses reduce glare
- Optimizing window angles in optical instruments