Brewster angle
The Brewster angle is the angle of incidence at which an ideal, smooth interface between two transparent, non-magnetic media does not reflect p-polarized light. For unpolarized light incident at that angle, the reflected beam is completely linearly polarized perpendicular to the plane of incidence. The angle depends on the refractive indices of the two media.
Polarization at an interface
When light reaches a boundary between transparent materials, part of it is generally reflected and part transmitted. The reflection depends on polarization: p-polarized light has its electric field in the plane of incidence, while s-polarized light has its electric field perpendicular to that plane. At one particular incidence angle, the reflected amplitude of the p component becomes zero in the ideal dielectric-interface model. This is the Brewster angle, also called the polarizing angle.
Brewster's law
For light traveling from a medium with refractive index n₁ into one with refractive index n₂, the Brewster angle θB satisfies tan θB = n₂/n₁. At this incidence, the reflected and refracted rays are at right angles to one another. For an air-to-glass interface with n₁ approximately 1.00 and n₂ approximately 1.50, the angle is about 56.3° measured from the normal. The formula presumes an ordinary interface between transparent, non-magnetic media; absorption, layered coatings, surface roughness and more complex materials can change the behavior.
Polarization of reflected light
Unpolarized light can be treated as a combination of s and p components. At the Brewster angle, the ideal interface reflects no p component, while some s-polarized light remains; consequently, the reflected beam is fully linearly polarized in the s direction. This does not mean that all incident light is reflected or that all light is transmitted: the two polarization components have different reflection and transmission coefficients.
Uses and practical limits
Brewster-angle geometry is used in some laser systems and optical arrangements to reduce reflection losses for p-polarized light without relying on an anti-reflection coating. It also helps explain why reflections from dielectric surfaces can be strongly polarized and underlies methods for measuring refractive index from reflected-light polarization. Real surfaces and beams are not perfectly ideal, so the p-polarized reflection may not vanish exactly. Polarized sunglasses can reduce glare from horizontal surfaces, but describing them as simply operating at the Brewster angle is an oversimplification: the filter axis, viewing geometry, surface, and incident angle all matter.
Key facts
- Definition
- Incidence angle at which an ideal dielectric interface has zero reflected p-polarized component.
- Brewster's law
- tan θB = n₂/n₁ for non-magnetic media, where θB is measured from the normal.
- Ray geometry
- At Brewster incidence, the reflected and refracted rays are perpendicular.
- Reflected polarization
- For unpolarized incident light, the ideal reflected beam at Brewster incidence is fully s-polarized.
- Air to glass example
- For refractive indices of approximately 1.00 and 1.50, θB is approximately 56.3°.
Ask about this article
Answers use only “Brewster angle” and its references, with citations.
References
- 1.Brewster's Angle – polarizing angle, p-polarized incident light, reflectivity, Fresnel equations
RP Photonics Encyclopedia · other · reliability: unverified · retrieved 27 October 2026
Supports: Defines the Brewster angle, Brewster's law, polarization of reflected light and laser-optics applications, with caveats for practical arrangements.
- 2.Brewster's Angle Tutorial: Polarized Light
Evident Scientific (Microscope Resource) · other · reliability: unverified · retrieved 27 October 2026
Supports: Explains polarization of reflection at Brewster incidence and gives illustrative angles for water, glass and diamond.
- 3.The Fresnel Equations and Brewster's Law
University of Oxford, Department of Physics (laboratory handout) · other · reliability: unverified · retrieved 27 October 2026
Supports: Derives Brewster's law from the Fresnel reflection coefficient and describes the orthogonality of reflected and refracted rays.
References are suggested by the research engine and may be incomplete. Unverified URLs are omitted rather than guessed.
Article history
- Version 127 October 2026 · EditorCreated by Zapia