Brewster's Angle Calculator
Calculate Brewster's angle — the incidence angle at which reflected light is perfectly polarized — given two media's refractive indices. Essential for optics design, laser engineering, and polarization experiments.
About this calculator
When light strikes an interface between two transparent media at a specific angle called Brewster's angle (θ_B), the reflected beam contains only s-polarized (perpendicular) light — the p-polarized (parallel) component is entirely transmitted. This happens when the reflected and refracted rays are perpendicular to each other. Brewster's law states: θ_B = arctan(n₂ / n₁), where n₁ is the refractive index of the medium the light travels through and n₂ is the refractive index of the medium it strikes. At this angle, the p-polarized reflectance drops to zero, making it invaluable for designing anti-reflection windows in lasers (Brewster windows) and polarizing beam splitters. The formula used here is: θ_B = atan(n2 / n1) × (180 / π), converting the result from radians to degrees.
How to use
A laser beam travels through air (n₁ = 1.0) and strikes a glass surface (n₂ = 1.52). Step 1 — Enter 1.0 for First Medium Refractive Index. Step 2 — Enter 1.52 for Second Medium Refractive Index. Step 3 — The calculator computes: θ_B = atan(1.52 / 1.0) × (180 / π) = atan(1.52) × 57.296 ≈ 56.66°. If you tilt your glass plate to 56.7° from the normal, the reflected beam will be completely s-polarized and p-polarized light will pass through without reflection loss.
Frequently asked questions
Why is Brewster's angle important in laser design?
In laser cavities, even small reflection losses at optical surfaces reduce efficiency and can introduce unwanted feedback. By mounting optical elements such as windows and etalons at Brewster's angle, engineers ensure that p-polarized light passes through with zero reflection loss. This also forces the laser to emit linearly polarized light, which is essential for many scientific and industrial applications. Brewster windows are a standard feature in gas lasers like HeNe and CO₂ lasers precisely because they combine high transmission with automatic polarization selection.
What is the difference between Brewster's angle and the critical angle for total internal reflection?
Brewster's angle applies to light travelling in either direction across an interface and is the angle at which reflected light becomes fully s-polarized; it exists for all pairs of transparent media. The critical angle, by contrast, only exists when light travels from a denser medium to a less dense one (n₁ > n₂), and at angles beyond it, all light is totally internally reflected — none is transmitted. Brewster's angle is always less than 90° and typically lies between 50° and 60° for air-glass interfaces, while the critical angle for glass-to-air is around 42°. The two phenomena are governed by Fresnel equations but describe entirely different optical effects.
How does changing the refractive index of the second medium affect Brewster's angle?
Because θ_B = arctan(n₂ / n₁), a higher refractive index in the second medium increases the ratio n₂/n₁ and therefore increases Brewster's angle. For air (n₁ ≈ 1) striking diamond (n₂ ≈ 2.42), Brewster's angle is about 67.5°, noticeably steeper than the ~56.7° for ordinary glass. Conversely, a material with a refractive index close to air gives a Brewster angle near 45°. This relationship means that Brewster's angle can be used experimentally to measure the refractive index of unknown materials by finding the incidence angle at which reflected light is completely polarized.