#1 Free Brewster’s Angle Calculator 2025

How to Use This Calculator

This calculator determines Brewster's angle (θ_B), the angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection.

• Enter the refractive index of the initial medium (n₁) from which light is incident (e.g., Air ≈ 1.0003).
• Enter the refractive index of the second medium (n₂) into which light refracts (e.g., Water ≈ 1.333, Glass ≈ 1.5).
• Click the "Calculate Brewster's Angle" button.
• Results, including Brewster's angle, the angle of refraction, and a step-by-step solution, will be displayed.

Theory: Brewster's Angle & Polarization

When unpolarized light is incident on the interface between two dielectric media, the reflected and refracted light are generally partially polarized. Brewster's angle (θ_B), also known as the polarization angle, is a specific angle of incidence at which light with polarization parallel to the plane of incidence (p-polarized light) is perfectly transmitted, meaning there is no reflection of p-polarized light. The reflected light at this angle is therefore perfectly polarized perpendicular to the plane of incidence (s-polarized light).

This phenomenon was discovered by Scottish physicist Sir David Brewster in 1815. At Brewster's angle, the angle between the reflected ray and the refracted ray is 90°.

Brewster's angle is crucial in optics and electromagnetism for applications such as:

• Polarizing filters: Used in sunglasses and camera filters to reduce glare.
• Brewster windows: Used in lasers to allow light with a specific polarization to exit the laser tube with minimal loss.

Formulas Used

• 1. Brewster's Angle (θ_B):

  tan(θB) = n2 / n1

  θB = arctan(n2 / n1)

  • n1 = Refractive index of the initial medium
  • n2 = Refractive index of the second medium
• 2. Angle of Refraction (θ₂) at Brewster's Angle:

  When the angle of incidence is θ_B, the angle between the reflected and refracted ray is 90°. Therefore: θB + θ2 = 90° (or π/2 radians) θ2 = 90° - θB

  Alternatively, using Snell's Law: n1 sin(θB) = n2 sin(θ2)

Calculate Brewster's Angle

Calculation Results