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Brewster's Angle

Calculates the angle of incidence at which reflected light becomes completely polarized, with zero reflection of the parallel polarization component.

Written by the Vorzep Team

OpticsGeometric OpticsPolarization

Brewster's Angle CalculatorPolarization · Optics

θB = arctan(n2 / n1)
θB = Brewster's angle  ·  n1 = incident medium index  ·  n2 = refracting medium index
⟹ Solve⟷θB, n1, n2
°
dimensionless
dimensionless
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Presets:
Brewster's Angle (θB)—
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θB: —n1: —n2: —
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Brewster's Angle (θB) Gauge—
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θB = arctan(n₂/n₁)  ·  All indices of refraction are dimensionless  ·  Brewster's angle is measured from the normal
θB = arctan(n2/n1)
Brewster's Angle

Variables

SymbolQuantityUnit
θBBrewster's angledegrees
n2Refractive index of second medium
n1Refractive 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