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Ref legal event code : CD. Ref country code : SE. Payment date : Year of fee payment : Ref country code : IT. Log In. The red solid and blue dashed lines correspond to Eq.
The media parameters are the same as in Fig. Sign up to receive regular email alerts from Physical Review B. Journal: Phys. A Phys. B Phys. C Phys. D Phys. E Phys. 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. See diagram, above.
Using Snell's law ,. Since the refractive index for a given medium changes depending on the wavelength of light, Brewster's angle will also vary with wavelength. In , Brewster experimented with higher-quality materials and showed that this angle was a function of the refractive index, defining Brewster's law.
Brewster's angle is often referred to as the "polarizing angle", because light that reflects from a surface at this angle is entirely polarized perpendicular to the plane of incidence " s -polarized". A glass plate or a stack of plates placed at Brewster's angle in a light beam can, thus, be used as a polarizer. The concept of a polarizing angle can be extended to the concept of a Brewster wavenumber to cover planar interfaces between two linear bianisotropic materials.
In the case of reflection at Brewster's angle, the reflected and refracted rays are mutually perpendicular. For magnetic materials, Brewster's angle can exist for only one of the incident wave polarizations, as determined by the relative strengths of the dielectric permittivity and magnetic permeability.
Thus reflected light from horizontal surfaces such as the surface of a road at a distance much greater than ones height so that the incidence angle of specularly reflected light is near, or usually well beyond the Brewster angle is strongly s -polarized. Polarized sunglasses use a sheet of polarizing material to block horizontally-polarized light and thus reduce glare in such situations.
These are most effective with smooth surfaces where specular reflection thus from light whose angle of incidence is the same as the angle of reflection defined by the angle observed from is dominant, but even diffuse reflections from roads for instance, are also significantly reduced.
Photographers also use polarizing filters to remove reflections from water so that they can photograph objects beneath the surface. Using a polarizing camera attachment which can be rotated, such a filter can be adjusted to reduce reflections from objects other than horizontal surfaces, such as seen in the accompanying photograph right where the s polarization approximately vertical has been eliminated using such a filter.
When recording a classical hologram , the bright reference beam is typically arranged to strike the film in the p polarization at Brewster's angle. By thus eliminating reflection of the reference beam at the transparent back surface of the holographic film, unwanted interference effects in the resulting hologram are avoided. Entrance windows or prisms with their surfaces at the Brewster angle are commonly used in optics and laser physics in particular.
The polarized laser light enters the prism at Brewster's angle without any reflective losses. In surface science, Brewster angle microscopes are used to image layers of particles or molecules at air-liquid interfaces.
Using illumination by a laser at Brewster's angle to the interface and observation at the angle of reflection, the uniform liquid does not reflect, appearing black in the image. However any molecular layers or artifacts at the surface, whose refractive index or physical structure contrasts with the liquid, allows for some reflection against that black background which is captured by a camera.
Only the reflected light at Brewster's angle is polarized. Here you can submit questions and comments. The author will decide on acceptance based on certain criteria. Essentially, the issue must be of sufficiently broad interest. Please do not enter personal data here; we would otherwise delete it soon. See also our privacy declaration. If you wish to receive personal feedback or consultancy from the author, please contact him e.
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