Brewster's Angle Calculator
Calculate the angle at which reflected light becomes completely polarized
Common values: Air = 1.0, Water = 1.33, Glass = 1.5
The medium into which light is entering
How to Use This Calculator
Enter First Medium's Refractive Index
Input the refractive index of the medium from which light is coming (usually air, n = 1.0). Common values: air = 1.0, water = 1.33, glass = 1.5.
Enter Second Medium's Refractive Index
Input the refractive index of the medium into which light is entering (e.g., glass, water, or another material).
Calculate
Click the "Calculate Brewster's Angle" button to get the angle at which reflected light becomes completely polarized.
Formula
tan(θ_B) = n₂ / n₁
Where:
- θ_B = Brewster's angle (in degrees or radians)
- n₁ = Refractive index of the first medium (incident medium)
- n₂ = Refractive index of the second medium (transmitting medium)
Solving for θ_B:
θ_B = arctan(n₂ / n₁)
Example Calculation (Air to Glass):
Light traveling from air (n₁ = 1.0) to glass (n₂ = 1.5):
tan(θ_B) = 1.5 / 1.0 = 1.5
θ_B = arctan(1.5) = 56.31°
At this angle, the reflected light is completely polarized (only s-polarized component).
Another Example (Air to Water):
Light traveling from air (n₁ = 1.0) to water (n₂ = 1.33):
tan(θ_B) = 1.33 / 1.0 = 1.33
θ_B = arctan(1.33) = 53.06°
About Brewster's Angle Calculator
Brewster's angle (also known as the polarization angle) is the angle of incidence at which light with a particular polarization cannot be reflected from a surface. When unpolarized light strikes a surface at Brewster's angle, the reflected light becomes completely polarized perpendicular to the plane of incidence (s-polarized). This phenomenon was discovered by Scottish physicist David Brewster in 1815 and is fundamental to understanding polarization in optics.
When to Use This Calculator
- Optical Design: Design polarizers and optical filters using Brewster angle windows
- Photography: Understand and minimize reflections in photography using polarization
- Laser Systems: Design laser cavities and optical systems that use Brewster angle components
- Material Analysis: Determine refractive indices of materials using Brewster angle measurements
- Educational Purposes: Learn about polarization and the relationship between reflection and refraction
Why Use Our Calculator?
- ✅ Instant Results: Get accurate Brewster's angles immediately
- ✅ Easy to Use: Just enter the two refractive indices
- ✅ Multiple Units: Results displayed in both degrees and radians
- ✅ Educational: Includes formula explanations and worked examples
- ✅ 100% Free: No registration or payment required
- ✅ Mobile Friendly: Works perfectly on all devices
Common Applications
Laser Technology: Brewster angle windows are commonly used in laser cavities to minimize reflection losses. The windows are oriented at Brewster's angle so that light polarized in one direction passes through without reflection, while the other polarization is reflected.
Photography: Photographers use polarizing filters to reduce reflections from water, glass, and other surfaces. Understanding Brewster's angle helps predict when reflections will be most effectively eliminated.
Optical Polarizers: Brewster angle polarizers are used in scientific instruments to produce polarized light. They exploit the fact that at Brewster's angle, only one polarization component is reflected.
Tips for Best Results
- Refractive indices are typically between 1.0 (air) and 2.5 (dense materials)
- For air to glass (n = 1.5), Brewster's angle is approximately 56.3°
- At Brewster's angle, the reflected and refracted rays are perpendicular to each other
- The p-polarized component (parallel to plane of incidence) has zero reflection at Brewster's angle
- Brewster's angle depends on wavelength due to dispersion, so use the appropriate refractive index for your wavelength
Frequently Asked Questions
What happens at Brewster's angle?
At Brewster's angle, the reflected light becomes completely polarized perpendicular to the plane of incidence (s-polarized). The p-polarized component (parallel to the plane) has zero reflection, meaning all p-polarized light is transmitted.
Why is the reflected light polarized at Brewster's angle?
At Brewster's angle, the reflected and refracted rays are perpendicular to each other. Under this condition, the electric field component parallel to the plane of incidence (p-polarized) cannot oscillate in the direction of the reflected ray, so it cannot be reflected. Only the perpendicular component (s-polarized) is reflected.
Does Brewster's angle depend on wavelength?
Yes, because refractive indices vary with wavelength (dispersion), Brewster's angle also varies with wavelength. For accurate calculations, use the refractive index appropriate for your specific wavelength.
Can Brewster's angle be used for both directions?
Brewster's angle is specific to the direction of light travel. If light travels from medium 1 to medium 2, the angle is different from light traveling from medium 2 to medium 1. The formula tan(θ_B) = n₂/n₁ applies when light travels from medium 1 to medium 2.
What's the relationship between Brewster's angle and the critical angle?
Brewster's angle and the critical angle (for total internal reflection) are different phenomena. Brewster's angle is about polarization, while the critical angle is about total internal reflection. They occur at different angles and serve different purposes in optics.