Brewster Angle
Calculate Brewster's angle of polarization using refractive indices of two optical media. Free online physics calculator for polarized light, reflection reduction, and optics applications with charts.
About This Calculator
The Brewster's Angle Calculator computes the angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface with zero reflection. Named after the Scottish physicist Sir David Brewster, this angle — also known as the polarization angle — is fundamental in optics, photonics, and the design of polarizing optical components.
Brewster's angle is calculated using the formula θB = arctan(n₂ / n₁), where n₁ is the refractive index of the incident medium (the medium the light travels through before hitting the surface) and n₂ is the refractive index of the refractive medium (the medium the light reflects from). At this specific angle, the reflected light becomes perfectly linearly polarized perpendicular to the plane of incidence.
Key Applications
- Polarized Sunglasses: Reduce glare from water, roads, and snow by blocking horizontally polarized reflected light at Brewster's angle.
- Photography: Camera polarizing filters rotate to eliminate reflections from water, glass, and other transparent surfaces, revealing objects beneath.
- Laser Optics: Brewster windows in gas lasers use Brewster's angle to allow p-polarized light to pass with zero reflective loss.
- Thin Film Analysis: Ellipsometry uses Brewster's angle measurements to determine thin film thicknesses and optical constants.
How It Works
When unpolarized light strikes a dielectric surface at Brewster's angle, the reflected light is completely polarized perpendicular to the plane of incidence (s-polarized). The transmitted (refracted) light becomes partially polarized parallel to the plane of incidence (p-polarized). This occurs because at Brewster's angle, the reflected and refracted rays are perpendicular to each other (90° apart), and the electric field oscillations parallel to the plane of incidence cannot be reflected.
Frequently Asked Questions
What is Brewster's angle?
Brewster's angle is the angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface with zero reflection. It is also known as the polarization angle.
How do I calculate Brewster's angle?
Brewster's angle is calculated using the formula θB = arctan(n₂/n₁), where n₁ is the refractive index of the incident medium and n₂ is the refractive index of the refractive medium. For example, for light traveling from air (n=1.0003) to glass (n=1.52), Brewster's angle is approximately 56.6°.
What is the Brewster angle for air to glass?
For light traveling from air (refractive index ≈ 1.0003) to standard window glass (refractive index ≈ 1.52), Brewster's angle is approximately 56.6 degrees.
How does Brewster's angle relate to polarized sunglasses?
Polarized sunglasses use Brewster's angle principle to block horizontally polarized reflected light from surfaces like water, roads, and snow. The lenses contain a polarizing filter that absorbs reflected light polarized at Brewster's angle, significantly reducing glare.
What is the Brewster angle for water?
For light traveling from air to water (refractive index ≈ 1.333), Brewster's angle is approximately 53.1 degrees. This is why polarized sunglasses are particularly effective near water surfaces.
Can Brewster's angle be greater than 90 degrees?
No, Brewster's angle is always between 0° and 90°. It approaches 90° only when the ratio n₂/n₁ approaches infinity, which does not occur in natural optical media.
What is the difference between Brewster angle and critical angle?
Brewster's angle is the polarization angle where reflected light is completely polarized (θB = arctan(n₂/n₁)). The critical angle is the angle of incidence above which total internal reflection occurs (θc = arcsin(n₂/n₁)). Brewster's angle is always smaller than the critical angle for the same media.