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What is Brewster's Angle?
Brewster's angle, named after Scottish physicist Sir David Brewster, is the angle of incidence at which light reflected from a surface is completely polarized in the plane parallel to the surface. At this special angle, the reflected and refracted rays are perpendicular to each other. The p-polarized component (polarized in the plane of incidence) has zero reflectance, while only s-polarized light is reflected.
This phenomenon occurs because at Brewster's angle, the refracted light would need to oscillate along its direction of propagation to produce a reflected p-polarized wave, which is impossible for a transverse wave. Brewster's angle has important applications in laser optics, photography, and the design of anti-reflection coatings and polarizing elements.
The Formula
Where θB is Brewster's angle, n1 and n2 are the refractive indices of the two media, and θr is the refraction angle. At Brewster's angle, the reflected and refracted rays are perpendicular.
Common Materials
| Interface | n1 | n2 | Brewster Angle |
|---|---|---|---|
| Air/Glass | 1.000 | 1.500 | 56.31° |
| Air/Water | 1.000 | 1.333 | 53.06° |
| Air/Diamond | 1.000 | 2.417 | 67.52° |
| Water/Glass | 1.333 | 1.500 | 48.36° |
Frequently Asked Questions
How is Brewster's angle used in lasers?
Laser cavities use Brewster windows at the ends of the gain medium to minimize reflection losses without coatings. Windows tilted at Brewster's angle have zero reflection loss for p-polarized light, so the laser output naturally becomes linearly polarized. This is more efficient and more durable than anti-reflection coatings, which can be damaged by high laser power. Most gas lasers and many solid-state lasers use Brewster-angle windows.
Why do polarizing sunglasses reduce glare?
Light reflected from horizontal surfaces (roads, water) at angles near Brewster's angle is predominantly s-polarized (horizontally polarized). Polarizing sunglasses have a vertical transmission axis that blocks this horizontally polarized glare. Since Brewster's angle for water is about 53 degrees, the glare from water at typical viewing angles is strongly polarized and effectively blocked by polarizing lenses.
Can Brewster's angle exist for total internal reflection?
No, Brewster's angle and total internal reflection are distinct phenomena. Brewster's angle occurs at any interface and always exists. Total internal reflection occurs only when light travels from a denser to a rarer medium (n1 > n2) and only at angles above the critical angle. However, even in total internal reflection geometry, a Brewster's angle exists at a lower angle where the p-polarized reflectance passes through zero.