PhysicsCalcs
Optics

Brewster’s Angle Calculator

Calculate Brewster’s angle, find refractive index, analyze polarization reflectance, and compare materials.

Interactive calculator

Brewster’s Angle Calculator

Calculate Brewster’s angle, find refractive index, analyze s/p-polarization reflectance, and compare materials.

Try an example

Incident medium (e.g., air = 1.0003)

Transmitting medium (e.g., glass = 1.52)

Your result will appear here.

Choose a calculation mode, fill in the known values, and click Calculate.

Quick Guide

  • Choose: find angle, find n, polarization info, material interface, or comparison table.
  • Enter refractive indices (e.g., air = 1.0003, glass = 1.52).
  • Results include s/p reflectance, critical angle, and TIR info.

Table of Contents

Key Takeaways

  • Brewster’s angle: θB = arctan(n₂/n₁).
  • At this angle, reflected light is 100% s-polarized (p-reflectance = 0).
  • The reflected and refracted rays are exactly 90° apart.
  • Air→Glass: θB ≈ 56.7°. Air→Water: θB ≈ 53.1°.
  • Used in laser optics, polarizing filters, and anti-glare coatings.
  • Higher refractive index difference = larger Brewster’s angle.

What Is Brewster’s Angle?

Brewster’s angle is the specific angle of incidence at which light reflected from a dielectric surface is completely linearly polarized. At this angle, the reflected and refracted rays are perpendicular (90° apart), and only s-polarized light is reflected.

Brewster’s Law

θB=arctan⁡(n2n1)\theta_B = \arctan\left(\frac{n_2}{n_1}\right)

Where n₁ is the refractive index of the incident medium and n₂ is the transmitting medium. At this angle, the p-polarization reflectance coefficient vanishes completely (Rp = 0).

Polarization at Brewster’s Angle

Light has two polarization components relative to the surface: s-polarization (perpendicular to the plane of incidence) and p-polarization (parallel). At Brewster’s angle, the oscillating dipoles in the transmitting medium cannot radiate in the direction of the reflected beam for p-polarization, so only s-polarized light reflects.

Real-World Applications

  • Laser optics — Brewster windows eliminate reflective losses for p-polarized laser beams.
  • Polarized sunglasses — reduce glare from surfaces near Brewster’s angle.
  • Measuring refractive index — determine n₂ by finding the polarization angle experimentally.
  • Photography — polarizing filters reduce reflections from glass and water.

How to Use

  1. Select a mode matching your problem.
  2. Enter refractive indices or angles.
  3. Click Calculate for Brewster’s angle, reflectance, and material comparison.

Examples

Air to Crown Glass

θB = arctan(1.52/1.0003) ≈ 56.66°

Air to Water

θB = arctan(1.333/1.0003) ≈ 53.10°

Air to Diamond

θB = arctan(2.42/1.0003) ≈ 67.53°

FAQ

What is Brewster’s angle?›

Brewster’s angle (also called the polarization angle) is the angle of incidence at which light reflected from a surface is completely polarized in the s-direction. The p-polarized component has zero reflectance.

How is Brewster’s angle calculated?›

θB = arctan(n₂/n₁), where n₁ is the refractive index of the incident medium and n₂ is that of the transmitting medium.

Why are polarized sunglasses effective?›

Glare from horizontal surfaces (water, road) is partially polarized. Polarized lenses block s-polarized light, reducing glare significantly, especially near Brewster’s angle.

What are s and p polarization?›

s-polarization oscillates perpendicular to the plane of incidence; p-polarization oscillates parallel to it. At Brewster’s angle, only s-polarized light is reflected.

Does Brewster’s angle depend on wavelength?›

Yes, because refractive index varies with wavelength (dispersion). But for most glass in the visible range, the variation is small (~1°).

Sources

  1. HyperPhysics – Brewster’s Angle
  2. OpenStax – Polarization
Manish Kumar

Author & technical reviewer

Manish Kumar

PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.

Learn more about Manish