Brewster's Angle
tan θ_B = n₂/n₁. Reflected ray fully polarized perpendicular to plane.
Key Notes
Brewster's Law: When light strikes a transparent medium at the Brewster angle θ_B, the reflected ray is completely polarized with E perpendicular to the plane of incidence (s-polarization).
Brewster's law: tan θ_B = n₂/n₁. For light going from air (n=1) to glass (n=1.5): θ_B ≈ 56.3°.
At θ_B, the reflected and refracted rays are perpendicular to each other: θ_B + θ_t = 90°.
Only the s-component reflects; the p-component (E in the plane of incidence) is transmitted 100% into the denser medium.
Brewster's law is used to make polarizers (Brewster pile-of-plates) and in laser-tube end-windows to minimize reflection loss for one polarization.
Polarized sunglasses block horizontally polarized glare from horizontal surfaces (water, roads) reflected near the Brewster angle.
Reflected intensity at general angles is given by Fresnel equations; the p-component goes to zero exactly at θ_B.
Formulas
Brewster's Law
Angle at which reflected ray is completely polarized perpendicular to plane of incidence.
Refracted ray angle
Reflected and refracted rays are mutually perpendicular at θ_B.
Brewster for air → glass (n = 1.5)
Standard textbook value.
Fresnel reflectance, s-pol
Reflected intensity for E perpendicular to plane of incidence.
Fresnel reflectance, p-pol
Goes to zero exactly at the Brewster angle.
Important Points
Brewster's angle works in both directions: glass → air gives θ_B = arctan(1/n) ≈ 33.7°.
At Brewster's angle, reflected light contains NO p-polarization — only s. This is how to make perfectly polarized light by reflection.
Sunlight reflected off water near θ_B is horizontally polarized — that's why polarized sunglasses (vertical transmission axis) block it.
Brewster windows in lasers are tilted at θ_B so the p-polarization passes with zero reflection loss — boosts laser efficiency.
The two rays (reflected + refracted) make a right angle at θ_B — easy way to spot it geometrically.
Brewster's Angle notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.