Brewster Angle Calculator
Brewster's angle is the angle of incidence at a dielectric interface at which the reflected beam is completely s-polarized (no p-polarized component). It is given by theta_B = arctan(n2/n1), where n1 is the refractive index of the incident medium and n2 is the refractive index of the transmitted medium. At this angle, the reflected and refracted rays are perpendicular to each other (they form a 90-degree angle). Brewster windows in gas lasers are aligned to this angle to minimize reflection losses. Polarizing filters in photography use the same principle to eliminate glare from non-metallic surfaces such as water and glass. Enter the refractive indices of the two media to find the Brewster angle in degrees.
Brewster angle formula
theta_B = arctan(n2 / n1)
Where n1 is the refractive index of the incident medium and n2 is the refractive index of the second medium. At this angle the reflected beam is completely polarized (s-polarized only).
Common Brewster angles
- Air to water (n=1.333): about 53.1 degrees.
- Air to crown glass (n=1.52): about 56.7 degrees.
- Air to diamond (n=2.42): about 67.5 degrees.
- Water to glass (n1=1.333, n2=1.52): about 48.8 degrees.
- The complementary angle (90 minus Brewster angle) equals the refraction angle at Brewster incidence, confirming the 90-degree angle between reflected and refracted rays.
Brewster angle: frequently asked questions
What is Brewster's angle?
Brewster's angle (also called the polarization angle) is the angle of incidence at which light striking an interface between two media is reflected with complete linear polarization (the s-polarized component reflects while the p-polarized component does not reflect at all). It is named after Sir David Brewster who described the relationship in 1815.
What is the Brewster angle formula?
The Brewster angle is theta_B = arctan(n2/n1), where n1 is the refractive index of the medium in which the incident ray travels and n2 is the refractive index of the second medium. At this angle, the reflected and transmitted rays are perpendicular to each other.
What are typical refractive indices?
Common values: air or vacuum = 1.000, water = 1.333, crown glass = 1.52, flint glass = 1.62, diamond = 2.42. For an air-glass interface (n1=1, n2=1.52), Brewster's angle is about 56.7 degrees.
Why does Brewster's angle matter in practice?
Brewster's angle is used in photography (polarizing filters to reduce glare from water or glass), laser design (Brewster windows in laser cavities to minimize reflection losses for p-polarized light), and optical coatings. Polarized sunglasses exploit this principle to cut glare from horizontal surfaces.
What happens to the transmitted ray at Brewster's angle?
At Brewster's angle, the transmitted (refracted) ray is only partially polarized because both s- and p-polarization components are transmitted, but the reflected beam is 100% s-polarized. The transmitted ray is enriched in p-polarization but not completely polarized.
Official sources
- OpenStax University Physics Volume 3, Chapter 1: The Nature of Light. openstax.org.
- NIST Physical Measurement Laboratory, Refractive index data. physics.nist.gov.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.