Brewster Angle

\[\theta_B=\arctan\left(\frac{n_2}{n_1}\right)\]

Variables

thetaB[θB]Brewster angle (rad)

n1refractive index of the incident medium

n2refractive index of the refracting medium

Description

What is this formula?

The Brewster angle formula calculates the angle of incidence at which reflected light becomes completely polarized parallel to the interface. At this angle, the reflected and refracted rays are perpendicular to each other.

When to use it

Use this formula when studying polarization, optical reflection, dielectric interfaces, anti-reflective behavior, laser optics, and material optical properties.

Example

A light ray travels from air into glass.

Data:

n1 = 1.00

n2 = 1.50

Formula:

θB = atan(n2 / n1)

Substitution:

θB = atan(1.50 / 1.00)

Result:

θB ≈ 0.983 rad ≈ 56.3°

The Brewster angle for an air-glass interface is approximately 56.3°.

Applications

Polarizing filters, laser optics, glare reduction, optical coatings, photography, microscopy, material testing, and dielectric interface analysis.