Brewster angle

At an interface between two transparent media of refractive indices $n_1$ (incident side) and $n_2$, the Brewster angle is

At $\theta_B$, the reflectivity for p-polarized light (electric field in the plane of incidence) is exactly zero. The reflectivity for s-polarized light (electric field perpendicular to the plane of incidence) is nonzero and substantial. Light reflected from a surface near the Brewster angle is therefore strongly s-polarized, even from unpolarized incident light — this is the principle behind polarizing sunglasses and dielectric pile-of-plates polarizers.

Geometric origin: at $\theta_B$, the reflected and refracted beams are exactly perpendicular ($\theta_B + \theta_r = 90°$). The dipoles in the second medium oriented along the refracted beam cannot radiate in the perpendicular direction, eliminating the p-polarized reflected beam.

Typical Brewster angles (from air, $n_1 = 1$):

Applications in laser systems:

• Brewster windows in gas lasers (HeNe, argon-ion, dye lasers): glass plates tilted at Brewster angle inside the cavity transmit p-polarized light with zero loss while reflecting s-polarization out of the cavity. The intracavity field is forced to oscillate purely p-polarized.
• Edge facets of solid-state lasers sometimes use Brewster-cut geometry to eliminate one polarization mode and enforce single-polarization output.
• Polarizing prisms (Glan-Thompson, Wollaston) exploit the difference between Brewster transmission and total internal reflection at different angles.

Brewster transmission applies only to dielectric interfaces. Metals do not have a true Brewster angle; instead they have a pseudo-Brewster angle where p-reflection reaches a minimum (but nonzero) value. See Fresnel equations for the full reflectivity expressions.