Brewster Angle Calculator – Polarization Angle Calculator

Calculate Brewster's angle (polarization angle) for light passing between two media. At this angle, reflected light is completely polarized.

Medium 1 (n₁)

Medium 2 (n₂)

How to Use This Brewster Angle Calculator

Enter the refractive indices

Input n1 (first medium, usually air = 1.0003) and n2 (second medium like glass = 1.52, water = 1.33). Use the values for your specific materials.

Calculate the polarization angle

Click Calculate to find Brewster's angle — the angle where reflected light becomes completely polarized with the electric field parallel to the surface.

Review the angle results

The calculator shows Brewster's angle plus the reflected and refracted angles. At this angle, the reflected and refracted rays are exactly 90 degrees apart.

Refractive Indices Reference Table

Material	Refractive Index (n)	Brewster Angle (from air)
Air	1.0003	N/A
Water	1.33	53.1 degrees
Window Glass	1.52	56.7 degrees
Crown Glass	1.50-1.52	56.3-56.7 degrees
Flint Glass	1.62-1.75	58.3-60.3 degrees
Diamond	2.42	67.6 degrees
Silicon	3.42	73.7 degrees

Brewster's angle increases with higher refractive index. Values shown are for light traveling from air into the material. Actual values vary slightly with wavelength.

Understanding Brewster's Angle

What Is Brewster's Angle?

Brewster's angle (also called the polarization angle) is the angle of incidence where light reflecting off a surface becomes completely polarized. At this specific angle, the reflected ray and refracted ray are perpendicular to each other. Sir David Brewster discovered this phenomenon in 1815.

The Physics Behind Polarization

Light is an electromagnetic wave with electric fields oscillating in all directions perpendicular to propagation. When light hits a surface at Brewster's angle, the reflected light contains only waves oscillating parallel to the surface — it becomes linearly polarized. The perpendicular component is entirely transmitted.

Brewster's Law Formula

Brewster's law states: tan(theta_B) = n2/n1, where theta_B is Brewster's angle, n1 is the refractive index of the first medium, and n2 is the refractive index of the second medium. For air to glass (n = 1.52), this gives theta_B = arctan(1.52) = 56.7 degrees.

Why the 90 Degree Relationship Matters

At Brewster's angle, the reflected and refracted rays form exactly 90 degrees. This happens because the reflected ray contains only the component of light that cannot couple into the transmitted wave's oscillation direction. This geometric relationship is what makes the polarization complete.

Applications of Brewster's Angle

Polarizing Filters and Sunglasses

Polarized sunglasses block horizontally polarized light — the kind reflected from roads and water at Brewster's angle. This eliminates glare while allowing other light through.

Laser Physics

Laser tubes often have windows tilted at Brewster's angle. This allows one polarization to pass with zero reflection loss while the other polarization experiences loss, producing polarized laser output.

Photography and Imaging

Photographers use polarizing filters oriented to block reflections at Brewster's angle. This removes unwanted glare from water, glass, and shiny surfaces while enhancing sky contrast.

Material Science

Measuring Brewster's angle provides a precise way to determine a material's refractive index. This is useful for characterizing thin films, coatings, and unknown transparent materials.

Frequently Asked Questions

What happens if light travels from glass to air instead?

The formula still applies but n1 and n2 swap. For glass (n = 1.52) to air (n = 1.0003), Brewster's angle is arctan(1.0003/1.52) = 33.3 degrees. This is the complement of the air-to-glass angle (90 - 56.7 = 33.3 degrees).

Does Brewster's angle work for all wavelengths of light?

The principle applies to all wavelengths, but the exact angle varies slightly because refractive index depends on wavelength (dispersion). Blue light has a slightly different Brewster angle than red light for the same material.

Why is reflected light polarized at Brewster's angle?

At Brewster's angle, the reflected ray direction aligns with where the electric field of one polarization component would need to oscillate to radiate in that direction. Since electromagnetic waves cannot oscillate along their propagation direction, that component cannot be reflected.

Can Brewster's angle be greater than 45 degrees?

Yes, whenever n2 is greater than n1. For most materials viewed from air, Brewster's angle ranges from about 53 degrees (water) to 74 degrees (silicon). It only drops below 45 degrees when light travels from a higher-index to lower-index medium.

Is Brewster's angle the same as the critical angle?

No. The critical angle is for total internal reflection when light travels from high to low index. Brewster's angle is for polarization and exists for light traveling in either direction. They are different phenomena with different formulas.

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