Brewster's law, the relation between the refractive index n of a dielectric and the angle of incidence φ of natural (unpolarised) light on it at which the light reflected from the surface of the dielectric is completely polarised. Only the component Es of the electric vector of the light wave that is perpendicular to the plane of incidence, that is, parallel to the interface, is reflected, while the component Ep, which lies in the plane of incidence, is not reflected but refracted (Fig. ).
This happens when tan φ = n. The angle φ is called the Brewster angle. Since, by the law of refraction, sin φ/sin r = n (r is the angle of refraction), it follows from Brewster's law that cos φ = sin r, or φ+r=90°, that is, the angle between the reflected and the refracted ray is 90°. Brewster's law was established by the English physicist D. Brewster in 1815. Brewster's law can be obtained from the Fresnel formulas for the passage of light through the boundary between two dielectrics. The simplest physical interpretation of Brewster's law is the following: the electric field of the incident wave sets up oscillations of the electrons in the dielectric whose direction coincides with the direction of the electric vector of the refracted wave Erefr. These oscillations excite at the interface the reflected wave Erefl, which travels away from the dielectric. But an electron oscillating linearly does not radiate along the direction of its oscillations. Thus, in the reflected wave the oscillations of the electric field (Es)refl take place only in the plane perpendicular to the plane of incidence. As special experiments have shown, Brewster's law does not hold strictly enough: when light falls at the angle φ, the reflected light shows a weak elliptical polarisation, which means that the electric field of the reflected wave also contains the component (Ep)refl in the plane of incidence. The small departure from Brewster's law is explained by the existence of a very thin transition layer at the reflecting interface between the two media, where n1 passes into n2 by a rapid continuous change rather than by a jump.