# Brewster's Angle Calculator

Created by Dominik Czernia, PhD
Reviewed by Bogna Szyk and Adena Benn
Last updated: Jun 05, 2023

When the traveling light encounters a medium with a different refractive index, its direction of propagation changes. This light can both reflect, where the angle of reflected light equals the angle of the incident light, or refract, where the angle of refracted light can be estimated with Snell's law. Moreover, at a specific angle, called Brewster's angle, the reflected light will be perfectly polarized. In the text below, we explain:

• What light polarization is;
• How you can calculate Brewster's angle; and
• Where this effect finds an application.

## Light polarization

Light is an electromagnetic wave that consists of two oscillating fields: electric and magnetic. In general, those fields are always perpendicular to each other and can oscillate in all possible directions in space. This is the case of unpolarized light.

The light is polarized when its electric and magnetic fields can only oscillate in specific directions. There are three main types of polarization:

• Linear polarization - fields oscillate in only one direction;
• Circular polarization - directions of the fields rotate at the constant rate in the plane as light travels; and
• Elliptical polarization - directions of the fields form an ellipse in the plane as light travels.

## Polarization by reflection

When the angle of incident light equals Brewster's angle, the reflected light will be perfectly linearly polarized. The formula for this polarization angle can be easily derived, assuming that the sum of the angle of reflection and the angle of refraction is 90°. Using Snell's law, you can calculate Brewster's angle of polarization:

αB = arctan(n2 / n1)

where

• αB is Brewster's angle;
• n1 is the refractive index of the initial medium through which the light propagates;
• n2 is the refractive index of the medium that reflects light.

You can explore this idea further using our Snell's law calculator.

## Applications of polarized light

On bright days, the sunlight can reflect from water or road, making it difficult for us to see. The solution to this problem can be found in polarized sunglasses, which use Brewster's angle principle. Most of the reflected sunlight is linearly polarized and, therefore, can be blocked with appropriately polarized sunglasses.

We use the phenomenon of polarization by reflection in photography. Photographers can remove reflections from transparent surfaces (like water) to see objects beneath them by rotating the camera's polarizing filter.

Dominik Czernia, PhD
Refractive index 1
Refractive index 2
Brewster angle
deg
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