Brewster's angle (also known as the polarization angle) is an angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. When unpolarized light is incident at this angle, the light that is reflected from the surface is therefore perfectly polarized. This special angle of incidence is named after the Scottish physicist Sir David Brewster (1781–1868).
When light encounters a boundary between two media with different refractive indices, some of it is usually reflected as shown in the figure above. The fraction that is reflected is described by the Fresnel equations, and depends on the incoming light's polarization and angle of incidence.
The Fresnel equations predict that light with the p polarization (electric field polarized in the same plane as the incident ray and the surface normal at the point of incidence) will not be reflected if the angle of incidence is
where n1 is the refractive index of the initial medium through which the light propagates (the "incident medium"), and n2 is the index of the other medium. This equation is known as Brewster's law, and the angle defined by it is Brewster's angle.
The physical mechanism for this can be qualitatively understood from the manner in which electric dipoles in the media respond to p-polarized light. One can imagine that light incident on the surface is absorbed, and then re-radiated by oscillating electric dipoles at the interface between the two media. The polarization of freely propagating light is always perpendicular to the direction in which the light is travelling. The dipoles that produce the transmitted (refracted) light oscillate in the polarization direction of that light. These same oscillating dipoles also generate the reflected light. However, dipoles do not radiate any energy in the direction of the dipole moment. If the refracted light is p-polarized and propagates exactly perpendicular to the direction in which the light is predicted to be specularly reflected, the dipoles point along the specular reflection direction and therefore no light can be reflected.
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Polarization (also polarisation) is a property of transverse waves which specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. A simple example of a polarized transverse wave is vibrations traveling along a taut string (see image); for example, in a musical instrument like a guitar string. Depending on how the string is plucked, the vibrations can be in a vertical direction, horizontal direction, or at any angle perpendicular to the string.
Étienne-Louis Malus (ˈɛt.i.ɛn_ˈluː.i_məˈluːs; e.tjɛn.lwi ma.lys; 23 July 1775 – 23 February 1812) was a French officer, engineer, physicist, and mathematician. Malus was born in Paris, France. He participated in Napoleon's expedition into Egypt (1798 to 1801) and was a member of the mathematics section of the Institut d'Égypte. Malus became a member of the Académie des Sciences in 1810. In 1810 the Royal Society of London awarded him the Rumford Medal. His mathematical work was almost entirely concerned with the study of light.
Specular reflection, or regular reflection, is the mirror-like reflection of waves, such as light, from a surface. The law of reflection states that a reflected ray of light emerges from the reflecting surface at the same angle to the surface normal as the incident ray, but on the opposing side of the surface normal in the plane formed by the incident and reflected rays. This behavior was first described by Hero of Alexandria (AD c. 10–70). Later, Alhazen gave a complete statement of the law of reflection.
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