Brewster's Angle Calculator

Brewster's angle (also called the polarization angle) is the specific angle of incidence at which light striking a surface between two media with different refractive indices produces a perfectly polarized reflected beam. At this angle, the reflected and refracted rays are perpendicular to each other, and the reflected light oscillates in only one plane.

Brewster's angle (θB) is calculated using the formula θB = arctan(n₂ / n₁), where n₁ is the refractive index of the incident medium and n₂ is the refractive index of the refracted medium. Simply divide n₂ by n₁ and take the arctangent to get the angle in radians, then convert to degrees if needed.

The Brewster angle formula is θB = arctan(n₂ / n₁). This was derived by Sir David Brewster in 1815 and describes the unique angle at which the reflected light from a dielectric surface is completely s-polarized (transverse electric polarization). At this angle, no p-polarized light is reflected.

For light traveling from air (n₁ ≈ 1.0003) into standard glass (n₂ ≈ 1.5), Brewster's angle is approximately arctan(1.5 / 1.0003) ≈ 56.3°. This is a commonly cited example in optics and is why polarized sunglasses are effective at reducing glare from glass surfaces.

Brewster's angle and the critical angle are different phenomena. Brewster's angle applies to any two media and is where reflected light becomes fully polarized, calculated as arctan(n₂/n₁). The critical angle applies only when light travels from a denser to a less dense medium and is where total internal reflection begins, calculated as arcsin(n₂/n₁). Both depend on the refractive indices, but they describe distinct optical effects.

At Brewster's angle, the reflected and refracted rays are exactly 90° apart. Because of the way electromagnetic waves interact with a surface, the p-polarized component (parallel to the plane of incidence) cannot reflect when this 90° condition is met — its oscillation direction would require it to radiate back along the refracted beam, which is physically impossible. Only the s-polarized component (perpendicular to the plane of incidence) reflects, making the reflected beam completely polarized.

Brewster's angle has many real-world applications. Polarized sunglasses use this principle to block glare reflected from flat surfaces like roads and water. In laser technology, Brewster windows are used to produce polarized laser light with minimal reflection loss. Photography polarizing filters exploit the same effect to reduce glare and enhance contrast. Anti-reflective coatings in optics are also designed with Brewster's angle in mind.

Yes. When light travels in the reverse direction (from glass to air), the formula becomes θB = arctan(n_air / n_glass) ≈ arctan(1/1.5) ≈ 33.7°. This is the complement of the original 56.3°, which makes sense because the two Brewster angles for a given interface always add up to 90°.