Brewster's Angle Calculator

Created by Krishna Nelaturu
Last updated: Sep 20, 2022

Our Brewster's angle calculator is here to help you determine the exact angle of incidence at which the reflected light is perfectly polarized. We shall briefly discuss light polarization in the following article before examining polarization by reflection and the Brewster angle formula. So join us below to learn how to calculate the Brewster angle.

If you only want to investigate the reflected light, our mirror equation calculator is a perfect place to start!

Light polarization

Light is an electromagnetic wave comprised of oscillating electric and magnetic fields. These fields are perpendicular to each other and the direction of light propagation. In unpolarised light, the electric field can be oriented in any random direction. Light is said to be polarised when the electric fields are oriented in a specific direction. For example, in vertically polarised light, all the light rays contain electric fields oscillating vertically. Any other direction of oscillation (say, diagonal or horizontal) is not allowed.

Brewster angle formula

Light incident on a boundary between two media of different refractive indices will refract as it enters the second medium, according to Snell's law. However, a portion of incident light is also reflected back into the first medium. When light is incident at a certain angle (see figure below), the reflected light is polarised. We call this incident angle Brewster's angle (or polarisation angle.)

Brewster angle depiction.
Light ray incident at Brewster angle θB\theta_B on the boundary between two media reflecting some portion of polarised light. (Source: Wikimedia.)

The formula for Brewster angle is:

θB=arctan(n2n1)\theta_B = \arctan\left( \frac{n_2}{n_1}\right)

Where:

  • θB\theta_B - Brewster's angle;
  • n2n_2 - Refractive index of the medium which reflects the light (and through which light refracts); and
  • n1n_1 - Refractive index of the medium from which light initially propagated.

🔎 Polarization by reflection: Say you go to the lake to enjoy your summer vacation. However, you find that the glare from the water's surface is too much to bear! This glare is due to the water surface reflecting the sunlight. But you know that the reflected light is partially polarised since some of the light will eventually be incident at Brewster's angle, whose corresponding reflection would be perfectly polarised. So you wear polarised glasses which protect you from glare. This works because the polariser in the glasses blocks light polarised in undesirable orientations!

You can calculate the decrease in light intensity when it passes through a polariser using our Malus law calculator.

How to use this Brewster's angle calculator

Our Brewster's angle calculator is easy to use:

  • Enter the refractive index of the initial medium from which the light is incident on the interface.
  • Provide the refractive index of the second medium, which reflects perfectly polarised light.
  • Using the Brewster angle formula, the calculator will automatically calculate Brewster's angle.
Krishna Nelaturu
Refractive index 1
Refractive index 2
Brewster angle
deg
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