Brewster’s law

Brewster’s law, relationship for light waves stating that the maximum polarization (vibration in one plane only) of a ray of light may be achieved by letting the ray fall on a surface of a transparent medium in such a way that the refracted ray makes an angle of 90° with the reflected ray. The law is named after a Scottish physicist, Sir David Brewster, who first proposed it in 1811.

The figure shows a ray of ordinary (nonpolarized) light of a given wavelength incident on a reflecting surface of a transparent medium (e.g., water or glass). Waves with the electric field component vibrating in the plane of the surface are indicated by short lines crossing the ray, and those vibrating at right angles to the surface are indicated by dots. The plane of incidence (AON) is the plane that contains the incident ray and the normal (ON, a line perpendicular to the surface) to the plane of the surface such that they intersect at the surface. Most of the waves of the incident ray will be transmitted across the boundary (the surface of the water or glass) as a refracted ray making an angle r with the normal, the rest being reflected. For a specific angle of incidence (p), called the polarizing angle or Brewster’s angle, all reflected waves will vibrate perpendicular to the plane of incidence (i.e., to the surface), and the reflected ray and the refracted ray will be separated by 90°. Brewster’s law also states that the tangent of the angle of polarization, p, for a wavelength of light passing from one substance to another is equal to the ratio of the refractive indices, n₁ and n₂, of the two contacting mediums: tan p = n₂/n₁.

For a light wave passing from air (n₁ = 1.00) to glass (n₂ = 1.50), the polarizing angle, p, is calculated to be 56°19′.