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Kirchhoff's Diffraction Formula
Kirchhoff's diffraction formula (also Fresnel–Kirchhoff diffraction formula) can be used to model the propagation of light in a wide range of configurations, either analytically or using numerical modelling. It gives an expression for the wave disturbance when a monochromatic spherical wave is the incoming wave of a situation under consideration. This formula is derived by applying the Kirchhoff integral theorem, which uses the Green's second identity to derive the solution to the homogeneous scalar wave equation, to a spherical wave with some approximations. The Huygens–Fresnel principle is derived by the Fresnel-Kirchhoff diffraction formula. Derivation of Kirchhoff's diffraction formula Kirchhoff's integral theorem, sometimes referred to as the Fresnel–Kirchhoff integral theorem, uses Green's second identity to derive the solution of the homogeneous scalar wave equation at an arbitrary spatial position P in terms of the solution of the wave equation and its first or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gustav Kirchhoff
Gustav Robert Kirchhoff (; 12 March 1824 – 17 October 1887) was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects. He coined the term black-body radiation in 1862. Several different sets of concepts are named "Kirchhoff's laws" after him, concerning such diverse subjects as black-body radiation and spectroscopy, electrical circuits, and thermochemistry. The Bunsen–Kirchhoff Award for spectroscopy is named after him and his colleague, Robert Bunsen. Life and work Gustav Kirchhoff was born on 12 March 1824 in Königsberg, Prussia, the son of Friedrich Kirchhoff, a lawyer, and Johanna Henriette Wittke. His family were Lutherans in the Evangelical Church of Prussia. He graduated from the Albertus University of Königsberg in 1847 where he attended the mathematico-physical seminar directed by Carl Gustav Jacob Jacobi, Franz Ernst Neumann and Fried ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kirchhoff 1
Kirchhoff, Kirchoff or Kirchhoffer is a German surname. Notable people with the surname include: * Adolf Kirchhoff (1826–1908), German classical scholar and epigrapher * Alfred Kirchhoff (1838–1907), German geographer and naturalist * Alphonse Kirchhoffer (1873–1913), French Olympic fencer * Charles William Henry Kirchhoff (1853-1916), American editor and metals expert * Detlef Kirchhoff (born 1967), German rower * Fritz Kirchhoff (1901–1953), German screenwriter, film producer and director * Gustav Kirchhoff (1824–1887), German physicist — Kirchhoff's laws in electricity, spectroscopy, thermochemistry * Gottlieb Kirchhoff (1764–1833), German chemist * Jan Kirchhoff (born 1990), German footballer * Mary Kirchoff (born 1959), American fantasy novelist * Paul Kirchhoff (1900–1972), German anthropologist and ethnologist of pre-Columbian Mesoamerican cultures * Robert Kirchhoff (born 1962), Slovak film director * Ulrich Kirchhoff (born 1967), German show jumper Se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Optics
In physics, physical optics, or wave optics, is the branch of optics that studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid. This usage tends not to include effects such as quantum noise in optical communication, which is studied in the sub-branch of coherence theory. Principle ''Physical optics'' is also the name of an approximation commonly used in optics, electrical engineering and applied physics. In this context, it is an intermediate method between geometric optics, which ignores wave effects, and full wave electromagnetism, which is a precise theory. The word "physical" means that it is more physical than geometric or ray optics and not that it is an exact physical theory. This approximation consists of using ray optics to estimate the field on a surface and then integrating that field over the surface to calculate the transmitted or scattered field. This resembles the Born app ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Waves
Waves most often refers to: *Waves, oscillations accompanied by a transfer of energy that travel through space or mass. *Wind waves, surface waves that occur on the free surface of bodies of water. Waves may also refer to: Music *Waves (band) Albums * Waves (Charles Lloyd album), ''Waves'' (Charles Lloyd album) * Waves (Jade Warrior album), ''Waves'' (Jade Warrior album) * Waves (Katrina and the Waves album), ''Waves'' (Katrina and the Waves album) * Waves (Moving Mountains album), ''Waves'' (Moving Mountains album) * Waves (Rachel Platten album), ''Waves'' (Rachel Platten album) * Waves (Rhydian Roberts album), ''Waves'' (Rhydian Roberts album) * Waves (Sam Rivers album), ''Waves'' (Sam Rivers album) * Waves (Story Untold album), ''Waves'' (Story Untold album) * Waves (Terje Rypdal album), ''Waves'' (Terje Rypdal album) * Waves (Waves album), ''Waves'' (Waves album) * ''Waves: Radio 1 Sessions 90–94'', a compilation album by Ride * Waves (EP), ''Waves'' (EP), by Mick Jenkin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oxford University Press
Oxford University Press (OUP) is the university press of the University of Oxford. It is the largest university press in the world, and its printing history dates back to the 1480s. Having been officially granted the legal right to print books by decree in 1586, it is the second oldest university press after Cambridge University Press. It is a department of the University of Oxford and is governed by a group of 15 academics known as the Delegates of the Press, who are appointed by the vice-chancellor of the University of Oxford. The Delegates of the Press are led by the Secretary to the Delegates, who serves as OUP's chief executive and as its major representative on other university bodies. Oxford University Press has had a similar governance structure since the 17th century. The press is located on Walton Street, Oxford, opposite Somerville College, in the inner suburb of Jericho. For the last 500 years, OUP has primarily focused on the publication of pedagogical texts an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Wiley & Sons
John Wiley & Sons, Inc., commonly known as Wiley (), is an American multinational publishing company founded in 1807 that focuses on academic publishing and instructional materials. The company produces books, journals, and encyclopedias, in print and electronically, as well as online products and services, training materials, and educational materials for undergraduate, graduate, and continuing education students. History The company was established in 1807 when Charles Wiley opened a print shop in Manhattan. The company was the publisher of 19th century American literary figures like James Fenimore Cooper, Washington Irving, Herman Melville, and Edgar Allan Poe, as well as of legal, religious, and other non-fiction titles. The firm took its current name in 1865. Wiley later shifted its focus to scientific, technical, and engineering subject areas, abandoning its literary interests. Wiley's son John (born in Flatbush, New York, October 4, 1808; died in East Orang ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wave Vector
In physics, a wave vector (or wavevector) is a vector used in describing a wave, with a typical unit being cycle per metre. It has a magnitude and direction. Its magnitude is the wavenumber of the wave (inversely proportional to the wavelength), and its direction is perpendicular to the wavefront. In isotropic media, this is also the direction of wave propagation. A closely related vector is the angular wave vector (or angular wavevector), with a typical unit being radian per metre. The wave vector and angular wave vector are related by a fixed constant of proportionality, 2π radians per cycle. It is common in several fields of physics to refer to the angular wave vector simply as the ''wave vector'', in contrast to, for example, crystallography. It is also common to use the symbol ''k'' for whichever is in use. In the context of special relativity, ''wave vector'' can refer to a four-vector, in which the (angular) wave vector and (angular) frequency are combined. Def ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Near And Far Field
The near field and far field are regions of the electromagnetic (EM) field around an object, such as a transmitting antenna, or the result of radiation scattering off an object. Non-radiative ''near-field'' behaviors dominate close to the antenna or scattering object, while electromagnetic radiation ''far-field'' behaviors dominate at greater distances. Far-field E (electric) and B (magnetic) field strength decreases as the distance from the source increases, resulting in an inverse-square law for the radiated ''power'' intensity of electromagnetic radiation. By contrast, near-field E and B strength decrease more rapidly with distance: the radiative field decreases by the inverse-distance squared, the reactive field by an inverse-cube law, resulting in a diminished power in the parts of the electric field by an inverse fourth-power and sixth-power, respectively. The rapid drop in power contained in the near-field ensures that effects due to the near-field essentially vanish a f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fraunhofer Diffraction
In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when plane waves are incident on a diffracting object, and the diffraction pattern is viewed at a sufficiently long distance (a distance satisfying Fraunhofer condition) from the object (in the far-field region), and also when it is viewed at the focal plane of an imaging lens. In contrast, the diffraction pattern created near the diffracting object (in the near field region) is given by the Fresnel diffraction equation. The equation was named in honor of Joseph von Fraunhofer although he was not actually involved in the development of the theory. This article explains where the Fraunhofer equation can be applied, and shows Fraunhofer diffraction patterns for various apertures. A detailed mathematical treatment of Fraunhofer diffraction is given in Fraunhofer diffraction equation. Equation When a beam of light is partly blocked by an obstacle, some of the light is scattered around the o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fresnel Diffraction
In optics, the Fresnel diffraction equation for near-field diffraction is an approximation of the Kirchhoff–Fresnel diffraction that can be applied to the propagation of waves in the near field. It is used to calculate the diffraction pattern created by waves passing through an aperture or around an object, when viewed from relatively close to the object. In contrast the diffraction pattern in the far field region is given by the Fraunhofer diffraction equation. The near field can be specified by the Fresnel number, , of the optical arrangement. When F \gg 1 the diffracted wave is considered to be in the near field. However, the validity of the Fresnel diffraction integral is deduced by the approximations derived below. Specifically, the phase terms of third order and higher must be negligible, a condition that may be written as \frac \ll 1, where \theta is the maximal angle described by \theta \approx a/L, and the same as in the definition of the Fresnel number. The m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kirchhoff 2
Kirchhoff, Kirchoff or Kirchhoffer is a German surname. Notable people with the surname include: * Adolf Kirchhoff (1826–1908), German classical scholar and epigrapher * Alfred Kirchhoff (1838–1907), German geographer and naturalist * Alphonse Kirchhoffer (1873–1913), French Olympic fencer * Charles William Henry Kirchhoff (1853-1916), American editor and metals expert * Detlef Kirchhoff (born 1967), German rower * Fritz Kirchhoff (1901–1953), German screenwriter, film producer and director * Gustav Kirchhoff (1824–1887), German physicist — Kirchhoff's laws in electricity, spectroscopy, thermochemistry * Gottlieb Kirchhoff (1764–1833), German chemist * Jan Kirchhoff (born 1990), German footballer * Mary Kirchoff (born 1959), American fantasy novelist * Paul Kirchhoff (1900–1972), German anthropologist and ethnologist of pre-Columbian Mesoamerican cultures * Robert Kirchhoff (born 1962), Slovak film director * Ulrich Kirchhoff (born 1967), German show jumper Se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Coordinate System
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the ''radial distance'' of that point from a fixed origin, its ''polar angle'' measured from a fixed zenith direction, and the ''azimuthal angle'' of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane. It can be seen as the three-dimensional version of the polar coordinate system. The radial distance is also called the ''radius'' or ''radial coordinate''. The polar angle may be called ''colatitude'', '' zenith angle'', '' normal angle'', or ''inclination angle''. When radius is fixed, the two angular coordinates make a coordinate system on the sphere sometimes called spherical polar coordinates. The use of symbols and the order of the coordinates differs among sources and disciplines. This article will ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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