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Brewster's Angle Calculator

Find Brewster's angle for two media.

How it is calculated

Brewster's angle is θB = arctan(n2 ÷ n1). n1 is the refractive index of the medium the light travels in before it hits the surface (the incident side), and n2 is the index of the medium it meets. Both are plain numbers without units and must be greater than zero. The angle is given in degrees with two decimals and is measured from the surface normal (the line at 90° to the surface), not from the surface itself. Order matters: swapping n1 and n2 gives the complementary angle, because the two add up to 90°. The tool uses one refractive index per medium, so the small change of index with wavelength is not included.

Worked example

Light travels in air (n1 = 1) and strikes ordinary glass with n2 = 1.5. Divide: 1.5 ÷ 1 = 1.5. The arctangent of 1.5 is about 0.983 radians, which is 56.31° from the normal. At that angle of incidence the reflected light is fully polarized. If the light came from inside the glass towards air, the ratio would be 1 ÷ 1.5 = 0.667 and the angle 33.69°, and 56.31° + 33.69° = 90°.

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Common mistakes

  • Swapping the media. n1 is where the light comes from; putting glass first and air second gives 33.69° instead of 56.31°.
  • Measuring the answer from the surface instead of from the normal. The angle is from the perpendicular, so a camera or filter pointed 56.31° from the normal is only 33.69° above the surface.
  • Using the refractive index of a material at the wrong wavelength or leaving out air. Air is 1 (approximately), so for a surface in open air enter n1 = 1.
  • Expecting complete polarization from every reflection. Brewster's angle only applies to one specific incidence angle and to reflection from a transparent (dielectric) surface, and not to metal surfaces.
  • Entering the angle of the refracted ray or the critical angle. Only the two refractive indices are inputs here; neither angle is needed.

About this calculator

Brewster's angle is the specific angle of incidence at which light reflecting off a surface becomes completely polarized perpendicular to the plane of incidence, calculated as θ_B = atan(n₂/n₁), where n₁ and n₂ are the refractive indices of the first and second media. At this angle, derived from the Fresnel equations, the reflected and refracted rays end up exactly 90° apart, which is why the parallel-polarized component of reflected light drops to zero.

Optics engineers use Brewster's angle to design polarizers, laser windows, and anti-reflective components (Brewster windows in laser cavities minimize reflection loss for one polarization), photographers and cinematographers rely on the same physics — often intuitively — when using polarizing filters to cut glare off water or glass at the right angle, and physics students use it as a core application of Fresnel reflection and polarization theory.

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Comments (1)

  • Editorial team

    A practical case is glare off water. With n2 of 1.33, the angle comes out near 53.06 degrees from the normal, about 37 degrees above the surface. Light reflected at that angle is strongly polarised, which is why a polarising filter or sunglasses can cut the glare from a lake so effectively. The refractive indices must be for the same wavelength. Which materials are you working with?

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