# Brewster’s law

A ray incident at a certain angle to a reflecting surface, when reflected, is completely polarized in a plane parallel to this surface.

Light, like any electromagnetic radiation, consists of propagating oscillations of electric and magnetic fields, which are oriented at right angles to each other. The direction of the electric field determines the direction in which the electric charge will move when the electromagnetic wave passes. Polarization waves are just called the direction of the electric field in the wave.

Light waves can have linear polarization (in this case, the oscillations of the electric field occur in a fixed plane), circular polarization (the electric field rotates like a clock hand) or elliptical polarization (the electric field rotates, while its absolute value depends on the direction). Brewster’s Law describes the linear polarization of light when a beam is reflected from a surface. According to this law, at a certain angle of incidence, light is completely polarized parallel to the reflecting surface, and the magnitude of this angle depends on the properties of the reflecting substance. The angle of incidence at which complete polarization of the reflected and refracted light occurs is called Brewster’s corner, and its tangent is equal to the refractive index of the reflecting substance. Even at angles of incidence that are noticeably different from the Brewster angle, the light is largely polarized, but in this case, both the refracted and the reflected beam are characterized by elliptical polarization.

Refractive index of light in matter is equal to the ratio of the speed of light in vacuum to the speed of light in matter. Ordinary glass, for example, has a refractive index of 1.5. This means that light traveling in a vacuum at a speed of about 300,000 km / s travels in glass at a speed of only about 200,000 km / s. Consequently, for glass, the Brewster angle at which complete polarization occurs is about 57 °.

You have probably encountered the phenomenon of polarization in everyday life. In particular, in our time, sunglasses are often made anti-glare, and this is achieved due to the fact that polarized lenses are inserted into them. In sunny weather, light reflected from shiny surfaces (glass, steel, water) turns out to be polarized mainly in the horizontal plane (according to Brewster’s law). And the lenses of anti-reflective sunglasses only allow vertically polarized light to pass through. Thanks to this, most of the glare reflected from objects around us is extinguished and does not blind us.

David BRUSTER
David Brewster, 1781-1868

Scottish physicist. Born in Jedborough. He studied theology at the University of Edinburgh, was ordained a priest and became one of the founders of the Free Scottish Church, but soon left this field for a career as a scientist and popularizer of science. He specialized in the study of optical phenomena, primarily spectral and polarization, discovered the law that bears his name. However, he earned a kind of immortal fame for himself by inventing a kaleidoscope in 1816. From 1859 until his death, Brewster was rector of the University of Edinburgh.