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Brewster's Angle

When light hits a surface like water or glass at a particular angle, the reflected light becomes completely polarized. This angle is called Brewster's angle. It depends only on the refractive indices of the two materials. At this angle, the component of light vibrating parallel to the surface is perfectly transmitted and not reflected, so the reflected beam is purely polarized. For example, polaroid sunglasses exploit this effect to cut glare from water and roads. It is used in lasers and photography to control polarization.

Written by the Vorzep Team

Optics Geometric Optics Polarization

Brewster's Angle Calculator

At Brewster's angle, light polarized in the plane of incidence is not reflected at all, and the reflected beam is fully polarized. Enter any two of θB, n1 and n2 and the third is solved, with Fresnel reflectance curves.

θB = arctan(n2 / n1)θB + θt = 90°
Solve for
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Brewster angle from the normal
0°30°60°90°
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Step-by-step solution

Companion quantities

Ray diagram at Brewster's angle

Reflected and refracted rays are exactly 90° apart. Dots on the reflected ray show light polarized perpendicular to the plane of incidence (s-polarized).

Reflectance versus incidence angle

Reference data

MaterialnθB from air
Interface (n₁ → n₂)θBRs at θB

Refractive indices are typical values near 589 nm and vary with wavelength, so θB shifts slightly with colour. Your θB row is highlighted when it is within 0.5°.

FAQ

Why does p-polarized light vanish in the reflection?

At Brewster's angle the reflected and refracted rays are perpendicular. The charges in the second medium oscillate along the refracted ray's polarization direction, and an oscillating dipole does not radiate along its own axis. Since that axis points along the would-be reflected direction, no p-polarized light is reflected.

Where is Brewster's angle used?

Polarizing sunglasses and photographic filters cut glare from water and roads, which is mostly s-polarized near Brewster's angle. Laser tubes use Brewster windows for loss-free p-polarized transmission, and Brewster-angle microscopy images thin films at air-water interfaces.

Is there a Brewster angle when n₁ is larger than n₂?

Yes. Going from glass to air, θB = arctan(1/1.5) ≈ 33.7°. This is smaller than the critical angle, so it occurs before total internal reflection sets in.

Does reflection vanish completely at θB?

Only for p-polarization. The s-polarized component is still partly reflected, with Rs = cos²(2θB). For unpolarized light the reflectance drops to Rs/2 and the reflected beam is fully s-polarized.

Educational tool only. Results assume smooth, flat, lossless and non-magnetic dielectrics with real refractive indices. Metals, absorbing media, rough surfaces, coatings and anisotropic crystals behave differently and have no simple Brewster angle.

Variables

Symbol Quantity Unit
θB Brewster's angle degrees
n2 Refractive index of second medium
n1 Refractive index of first medium

What it means

Brewster’s angle is the angle of incidence at which light with a specific polarisation is perfectly transmitted, and the reflected light is completely polarised. It is used in polarising optics, laser cavities (to select polarisation), and to reduce reflections in windows (Brewster windows). The angle depends on the refractive indices of the two media. Understanding this is essential for optical engineers working on polarisation control and anti‑reflection coatings.

Worked example

Brewster's Angle – Two Detailed Examples

Real‑World
Scenario: A laser beam in air (n₁ = 1.0) strikes a glass surface (n₂ = 1.5). At Brewster's angle, the reflected light is perfectly polarised perpendicular to the plane of incidence. The physicist calculates θ_B = arctan(n₂/n₁) = arctan(1.5) ≈ 56.31°. By setting the laser to this angle, they can obtain a clean polarised beam with minimum reflection loss, which is useful in polarisation‑sensitive experiments.
ParameterValue
n₁1.0
n₂1.5
1θ_B = arctan(1.5/1.0) = arctan(1.5) ≈ 56.31°
Result 56.31° ✓ Brewster angle
Scenario: An underwater camera housing uses a glass window (n₂ = 1.5) in water (n₁ = 1.33). To reduce reflections from the window, the designer wants to know the Brewster angle. They compute θ_B = arctan(1.5/1.33) ≈ 48.44°. Orienting the window at this angle minimizes reflection of p‑polarised light, improving image clarity in aquatic photography.
ParameterValue
n₁1.33
n₂1.5
1θ_B = arctan(1.5/1.33) ≈ arctan(1.1278) ≈ 48.44°
Result 48.44° ✓ Brewster angle in water
Insight: At Brewster's angle, the reflected ray is completely polarised perpendicular to the plane of incidence, and the reflected and refracted rays are 90° apart. This is used in polarisers and anti‑reflection coatings.

Common mistakes

  • Brewster’s angle: θ_B = arctan(n₂/n₁) – the angle of incidence for which reflected light is perfectly polarised.
  • n₂/n₁: Ratio of indices of refraction – for a medium to air, n₂ is the medium, n₁=1.
  • Result: θ_B is measured from the normal.
  • Transmission: At Brewster’s angle, the reflected and refracted rays are perpendicular.
  • Units: Angle in degrees or radians – ensure arctan returns the correct unit.

Applications

Brewster's angle, θ_B = arctan(n₂/n₁), is the angle of incidence at which light with a specific polarisation is perfectly transmitted without reflection. This phenomenon is used to produce polarised light and to reduce reflections in optical systems. Engineers use it in designing polarising beamsplitters, laser optics, and anti‑reflection coatings. It is also applied in photography to reduce glare from surfaces. By setting the angle of incidence to Brewster's angle, they can eliminate p‑polarised reflections. Understanding this concept is important for managing polarisation in optical systems and for enhancing image quality.

  • Design of polarisers and polarising beam splitters
  • Anti‑reflection coatings for optical surfaces
  • Laser cavity design to minimise loss
  • Photography – reducing reflections from water or glass
  • Educational demonstration of polarisation

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  • Published July 13, 2026
  • Last updated September 13, 2026