Brewster Angle Calculator

What Is Brewster's Angle?

Brewster's angle is the incidence angle at which light reflected from a dielectric surface is completely polarized. At this angle, reflected and refracted rays are perpendicular, so only the polarization perpendicular to the plane of incidence is reflected.

Brewster Angle Formula

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

$n_1$ is the refractive index of the incident medium and $n_2$ is the refractive index of the transmitted medium. The result is in radians; multiply by $180/\pi$ for degrees.

Example: light from air ($n_1 = 1$) into glass ($n_2 = 1.5$) gives $\theta_B = \arctan(1.5) \approx 56.31°$.

Frequently Asked Questions

What happens at Brewster's angle?

Reflected light is linearly polarized perpendicular to the plane of incidence. This is used in polarizing sunglasses and optical filters.

Can n₁ be larger than n₂?

Yes. The formula still applies. Light traveling from a denser to a rarer medium has a Brewster angle, but total internal reflection may occur at larger angles.

Why use refractive index instead of angle of refraction?

Brewster's law is defined in terms of refractive indices. Given $n_1$ and $n_2$, the Brewster angle is found directly without Snell's law.

Is Brewster's angle the same for all wavelengths?

No. Refractive index varies slightly with wavelength (dispersion), so Brewster's angle shifts a little across the visible spectrum.

What if one medium is air?

Use $n_1 = 1$ for air at standard conditions. For water to glass, use $n_1 \approx 1.33$ and the glass index for $n_2$.

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What Is Brewster's Angle?

Brewster Angle Formula

Frequently Asked Questions

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