Brewster Angle Calculator

About the Brewster Angle Calculator

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.

When This Page Helps

This calculator improves speed and consistency while reducing avoidable mistakes in practical workflows.

How to Use the Inputs

1. Select a preset material pair or enter custom refractive indices.
2. View the computed Brewster angle and related angles.
3. Enter a custom incidence angle to compare its reflectance to Brewster's angle.
4. Examine the angle comparison table to see how polarization varies.
5. Check the material reference table for Brewster angles of common materials.
6. Use the polarization bar visualization to compare s and p reflectance.

Example Calculation

Tips & Best Practices

• Keep angle units consistent; mixing degrees and radians is the most common source of wrong results.
• Use a simple known case or diagram to confirm the sign and scale of the answer.

When To Use This Calculator

Calculate Brewster Use it when you need a repeatable calculation in the physics / optics category and want the setup, result, and supporting values kept together. This is especially helpful when small input changes, unit choices, or rounding decisions can change the final number.

How To Check The Result

Start by confirming that the inputs match the formula shown on the page. Then compare the main output with the worked example and any secondary values shown by the calculator. If the result will be used in another calculation, keep extra precision until the final step and record the assumptions beside the number.

Practical Notes

Treat the result as a calculation aid rather than a substitute for context. For schoolwork, include the formula and substitution steps. For planning, technical, financial, or health-related decisions, verify important numbers against primary records, current rules, or a qualified professional before acting on them.

Frequently Asked Questions

• What is Brewster's angle used for?

  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.

• Why does p-polarized reflectance drop to zero?

  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.

• Does Brewster's angle depend on wavelength?

  Yes, because refractive indices vary with wavelength (dispersion). The effect is small for most visible-light applications but matters in precision optics.

• Is there a Brewster angle for metals?

  Metals have complex refractive indices (with absorption). A pseudo-Brewster angle exists where p-reflectance reaches a minimum but never truly reaches zero.

• How is Brewster's angle related to total internal reflection?

  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.

• Can Brewster's angle be used to measure refractive index?

  Yes, measuring the angle at which reflected light is fully polarized directly gives the refractive index ratio: n₂ = n₁ × tan(θ_B).