Calculate Brewster's angle for any two media. Includes polarization reflectance, angle comparison tables, and material reference data.
Brewster's angle (also called the polarizing angle) is the angle of incidence at which light reflected from a surface is perfectly polarized. At this special angle, the reflected and refracted rays are perpendicular to each other, causing the p-polarized (parallel) component of reflected light to vanish completely. Only s-polarized (perpendicular) light is reflected.
Sir David Brewster discovered this relationship in 1815: tan(θ_B) = n₂/n₁, where n₁ and n₂ are the refractive indices of the two media. This elegant formula connects the polarization properties of light to the fundamental optical constants of materials. At Brewster's angle, all reflected light is linearly polarized, which has profound implications for optics design.
This calculator computes Brewster's angle for any pair of media, provides Fresnel reflectance coefficients at both Brewster's angle and a custom angle, includes a comprehensive angle-dependent reflectance table showing how s- and p-polarization evolve, and offers a material comparison table. It is indispensable for designing laser Brewster windows, anti-reflection coatings, polarizers, and understanding glare reduction in photography and everyday optics.
This calculator improves speed and consistency while reducing avoidable mistakes in practical workflows. This tool is designed for quick, accurate results without manual computation. Whether you are a student working through coursework, a professional verifying a result, or an educator preparing examples, accurate answers are always just a few keystrokes away.
Brewster's Angle: θ_B = arctan(n₂ / n₁). At Brewster's angle: θ_reflected + θ_refracted = 90°. Fresnel s-reflectance: R_s = ((n₁cosθ_i − n₂cosθ_t)/(n₁cosθ_i + n₂cosθ_t))².
Result: 56.66°
For air (n=1.0) to crown glass (n=1.52), Brewster's angle is arctan(1.52/1.0) = 56.66°. At this angle, reflected light is completely s-polarized.
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It is used in laser cavities (Brewster windows eliminate reflection losses for one polarization), anti-glare coatings, polarizing filters, and photography to reduce reflections from surfaces. Use this as a practical reminder before finalizing the result.
At Brewster's angle, the reflected and refracted rays are perpendicular. The oscillating dipoles induced in the refracting medium cannot emit radiation in the reflection direction for p-polarization.
Yes, because refractive indices vary with wavelength (dispersion). The effect is small for most visible-light applications but matters in precision optics.
Metals have complex refractive indices (with absorption). A pseudo-Brewster angle exists where p-reflectance reaches a minimum but never truly reaches zero.
Both phenomena arise from Snell's Law and Fresnel equations. The critical angle exists only when going from denser to less dense media, while Brewster's angle exists for any interface.
Yes, measuring the angle at which reflected light is fully polarized directly gives the refractive index ratio: n₂ = n₁ × tan(θ_B). Keep this note short and outcome-focused for reuse.