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Light Ray
In optics a ray is an idealized geometrical model of light, obtained by choosing a curve that is perpendicular to the ''wavefronts'' of the actual light, and that points in the direction of energy flow. Rays are used to model the propagation of light through an optical system, by dividing the real light field up into discrete rays that can be computationally propagated through the system by the techniques of '' ray tracing''. This allows even very complex optical systems to be analyzed mathematically or simulated by computer. Ray tracing uses approximate solutions to Maxwell's equations that are valid as long as the light waves propagate through and around objects whose dimensions are much greater than the light's wavelength. ''Ray optics'' or ''geometrical optics'' does not describe phenomena such as diffraction, which require wave optics theory. Some wave phenomena such as interference can be modeled in limited circumstances by adding phase to the ray model. Definition ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Ray Optics
Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of '' rays''. The ray in geometrical optics is an abstraction useful for approximating the paths along which light propagates under certain circumstances. The simplifying assumptions of geometrical optics include that light rays: * propagate in straight-line paths as they travel in a homogeneous medium * bend, and in particular circumstances may split in two, at the interface between two dissimilar media * follow curved paths in a medium in which the refractive index changes * may be absorbed or reflected. Geometrical optics does not account for certain optical effects such as diffraction and interference. This simplification is useful in practice; it is an excellent approximation when the wavelength is small compared to the size of structures with which the light interacts. The techniques are particularly useful in describing geometrical aspects of imaging, including optical abe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Hamiltonian Optics-Rays And Wavefronts
Hamiltonian may refer to: * Hamiltonian mechanics, a function that represents the total energy of a system * Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system ** Dyall Hamiltonian, a modified Hamiltonian with two-electron nature ** Molecular Hamiltonian, the Hamiltonian operator representing the energy of the electrons and nuclei in a molecule * Hamiltonian (control theory), a function used to solve a problem of optimal control for a dynamical system * Hamiltonian path, a path in a graph that visits each vertex exactly once * Hamiltonian group, a non-abelian group the subgroups of which are all normal * Hamiltonian economic program, the economic policies advocated by Alexander Hamilton, the first United States Secretary of the Treasury See also * Alexander Hamilton (1755 or 1757–1804), American statesman and one of the Founding Fathers of the US * Hamilton (other) * List of things named after William Rowan Hamilton {{Sh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Straight Line
In geometry, a line is an infinitely long object with no width, depth, or curvature. Thus, lines are one-dimensional objects, though they may exist in two, three, or higher dimension spaces. The word ''line'' may also refer to a line segment in everyday life, which has two points to denote its ends. Lines can be referred by two points that lay on it (e.g., \overleftrightarrow) or by a single letter (e.g., \ell). Euclid described a line as "breadthless length" which "lies evenly with respect to the points on itself"; he introduced several postulates as basic unprovable properties from which he constructed all of geometry, which is now called Euclidean geometry to avoid confusion with other geometries which have been introduced since the end of the 19th century (such as non-Euclidean, projective and affine geometry). In modern mathematics, given the multitude of geometries, the concept of a line is closely tied to the way the geometry is described. For instance, in analytic ge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Arthur Schuster
Sir Franz Arthur Friedrich Schuster (12 September 1851 – 14 October 1934) was a German-born British physicist known for his work in spectroscopy, electrochemistry, optics, X-radiography and the application of harmonic analysis to physics. Schuster's integral is named after him. He contributed to making the University of Manchester a centre for the study of physics. Early years Arthur Schuster was born in Frankfurt am Main, Germany the son of Francis Joseph Schuster, a cotton merchant and banker, and his wife Marie Pfeiffer. Schuster's parents were married in 1849, converted from Judaism to Christianity, and brought up their children in that faith. In 1869, his father moved to Manchester where the family textile business was based. Arthur, who had been to school in Frankfurt and was studying in Geneva, joined his parents in 1870 and he and the other children became British citizens in 1875. Edgar Schuster (1897–1969) was his nephew. From his childhood, Schuster had bee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Fermat's Principle
Fermat's principle, also known as the principle of least time, is the link between ray optics and wave optics. In its original "strong" form, Fermat's principle states that the path taken by a ray between two given points is the path that can be traveled in the least time. In order to be true in all cases, this statement must be weakened by replacing the "least" time with a time that is "stationary" with respect to variations of the path — so that a deviation in the path causes, at most, a ''second-order'' change in the traversal time. To put it loosely, a ray path is surrounded by close paths that can be traversed in ''very'' close times. It can be shown that this technical definition corresponds to more intuitive notions of a ray, such as a line of sight or the path of a narrow beam. First proposed by the French mathematician Pierre de Fermat in 1662, as a means of explaining the ordinary law of refraction of light (Fig.1), Fermat's principle was initial ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Geometric Optics
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Refractive Index
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or refracted, when entering a material. This is described by Snell's law of refraction, , where ''θ''1 and ''θ''2 are the angle of incidence and angle of refraction, respectively, of a ray crossing the interface between two media with refractive indices ''n''1 and ''n''2. The refractive indices also determine the amount of light that is reflected when reaching the interface, as well as the critical angle for total internal reflection, their intensity (Fresnel's equations) and Brewster's angle. The refractive index can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is , and similarly the wavelength in that medium is , where ''� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Optical Medium
An optical medium is material through which light and other electromagnetic waves propagate. It is a form of transmission medium. The permittivity and permeability of the medium define how electromagnetic waves propagate in it. Properties The optical medium has an ''intrinsic impedance'', given by ::\eta = where E_x and H_y are the electric field and magnetic field, respectively. In a region with no electrical conductivity, the expression simplifies to: ::\eta = \sqrt\ . For example, in free space the intrinsic impedance is called the characteristic impedance of vacuum, denoted ''Z''0, and ::Z_0 = \sqrt\ . Waves propagate through a medium with velocity c_w = \nu \lambda , where \nu is the frequency and \lambda is the wavelength of the electromagnetic waves. This equation also may be put in the form : c_w = \ , where \omega is the angular frequency of the wave and k is the wavenumber of the wave. In electrical engineering, the symbol \beta, called the '' phase constant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Interface
Interface or interfacing may refer to: Academic journals * ''Interface'' (journal), by the Electrochemical Society * '' Interface, Journal of Applied Linguistics'', now merged with ''ITL International Journal of Applied Linguistics'' * '' Interface: A Journal for and About Social Movements'' * ''Interfaces'' (journal), now ''INFORMS Journal on Applied Analytics'' Arts and entertainment * ''Interface'' (album), by Dominion, 1996 * Interface (band), an American music group * ''Interface'' (film), a 1984 American film * ''Interface'' (novel), by Stephen Bury (a pseudonym), 1994 * "Interface" (''Star Trek: The Next Generation''), an episode of the TV series * ''Interface series'', a science fiction horror story in short installments on Reddit Science, social science and technology Computing and electronics * Interface (computing), a shared boundary between system components ** Interface (Java) ** Interface (object-oriented programming) ** Application binary interface, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Homogeneous Medium
In physics, a homogeneous material or system has the same properties at every point; it is uniform without irregularities. (accessed November 16, 2009). Tanton, James. "homogeneous." Encyclopedia of Mathematics. New York: Facts On File, Inc., 2005. Science Online. Facts On File, Inc. "A polynomial in several variables p(x,y,z,…) is called homogeneous ..more generally, a function of several variables f(x,y,z,…) is homogeneous ..Identifying homogeneous functions can be helpful in solving differential equations ndany formula that represents the mean of a set of numbers is required to be homogeneous. In physics, the term homogeneous describes a substance or an object whose properties do not vary with position. For example, an object of uniform density is sometimes described as homogeneous." James. homogeneous (math). (accessed: 2009-11-16) A uniform electric field (which has the same strength and the same direction at each point) would be compatible with homogeneity (all po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |