Brewster's Angle Calculator

Calculate the polarization angle for any two media.

Enter the refractive indices of two different media to find the Brewster's angle, where reflected light is perfectly polarized.

Examples

See how Brewster's angle is calculated for different material pairs.

Air to Glass

Basic

Calculate Brewster's angle when light passes from air (n₁ = 1.00) to glass (n₂ = 1.50).

n₁ = 1

n₂ = 1.5

Air to Water

Basic

Find the polarization angle for air (n₁ = 1.00) to water (n₂ = 1.33).

n₁ = 1

n₂ = 1.33

Water to Glass

Basic

Calculate Brewster's angle from water (n₁ = 1.33) to glass (n₂ = 1.50).

n₁ = 1.33

n₂ = 1.5

Air to Diamond

Basic

Find Brewster's angle for air (n₁ = 1.00) to diamond (n₂ = 2.42).

n₁ = 1

n₂ = 2.42

Other Titles
Understanding Brewster's Angle Calculator: A Comprehensive Guide
Master the concept of polarization angle and its practical applications.

What is Brewster's Angle?

  • Definition and Physical Meaning
  • Mathematical Expression
  • Importance in Optics
Brewster's angle is the angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. At this angle, the reflected and refracted rays are perpendicular to each other.
Mathematical Formula
The formula for Brewster's angle (θB) is: θB = arctan(n₂/n₁), where n₁ and n₂ are the refractive indices of the two media.

Sample Calculations

  • Air to glass: θB = arctan(1.5/1.0) ≈ 56.31°
  • Air to water: θB = arctan(1.33/1.0) ≈ 53.06°

Step-by-Step Guide to Using the Calculator

  • Input Fields Explained
  • Calculation Process
  • Interpreting Results
To use the calculator, enter the refractive indices for both media. The tool will instantly compute the Brewster's angle in both degrees and radians.
How to Enter Data
Typical values: Air (1.00), Water (1.33), Glass (1.50), Diamond (2.42). Ensure both indices are positive and not equal for meaningful results.

Usage Examples

  • n₁ = 1.00, n₂ = 1.50 → θB ≈ 56.31°
  • n₁ = 1.33, n₂ = 1.50 → θB ≈ 48.75°

Real-World Applications of Brewster's Angle

  • Optical Coatings
  • Photography and Polarizing Filters
  • Laser Physics
Brewster's angle is crucial in designing anti-reflective coatings, polarizing sunglasses, and laser optics. It helps minimize unwanted reflections and maximize transmission.
Practical Uses
Engineers and scientists use Brewster's angle to optimize optical devices and experiments involving light polarization.

Application Scenarios

  • Designing camera lens coatings
  • Reducing glare in sunglasses

Common Misconceptions and Correct Methods

  • Misunderstanding the Formula
  • Incorrect Index Assignment
  • Ignoring Polarization Direction
A common mistake is swapping n₁ and n₂, which leads to incorrect angles. Always use n₁ for the incident medium and n₂ for the transmitting medium.
Correct Calculation Steps
Ensure the indices are entered correctly and the calculator is used as intended for accurate results.

Mistake Examples

  • Swapping air and glass indices gives wrong angle
  • Using negative or zero indices is invalid

Mathematical Derivation and Examples

  • Derivation from Snell's Law
  • Trigonometric Approach
  • Worked Examples
Brewster's angle can be derived from Snell's Law and the condition for zero reflection of p-polarized light. The tangent of the angle equals the ratio of refractive indices.
Example Calculation
For air (n₁ = 1.00) to diamond (n₂ = 2.42): θB = arctan(2.42/1.00) ≈ 67.38° (1.176 rad).

Derivation Examples

  • θB = arctan(1.33/1.00) ≈ 53.06°
  • θB = arctan(2.42/1.00) ≈ 67.38°