# Brewster's Angle Calculator

By Dominik Czernia, PhD candidate
Last updated: Jul 07, 2018

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 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 which 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 the unpolarized light.

The light is polarized when its fields, electric and magnetic, 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,
• 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 which reflects light.

## Applications of polarized light

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

Phenomenon of polarization by reflection is also used in photography. Photographers can remove reflections from transparent surfaces (like water) to see objects beneath it by simply rotating the polarizing filter in the camera.

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