Abeles Matrix Formalism The transfer-matrix method is a method used in optics and acoustics to analyze the propagation of electromagnetic wave, electromagnetic or acoustic waves through a stratified medium. This is for example relevant for the design of anti-reflective coatings and dielectric mirrors. The Reflection (physics), reflection of light from a single interface between two medium (optics), media is described by the Fresnel equations. However, when there are multiple Wiktionary:interface, interfaces, such as in the figure, the reflections themselves are also partially transmitted and then partially reflected. Depending on the exact path length, these reflections can Interference (wave propagation), interfere destructively or constructively. The overall reflection of a layer structure is the sum of an infinite number of reflections. The transfer-matrix method is based on the fact that, according to Maxwell's equations, there are simple continuity conditions for the electric field across boundari ... [...More Info...]       [...Related Items...] picture info Ray Transfer Matrix Analysis Ray transfer matrix analysis (also known as ABCD matrix analysis) is a mathematical form for performing Ray tracing (physics), ray tracing calculations in sufficiently simple problems which can be solved considering only paraxial rays. Each optical element (surface, interface, mirror, or beam travel) is described by a 2×2 ''ray transfer matrix (math), matrix'' which operates on a vector space, vector describing an incoming ray (optics), light ray to calculate the outgoing ray. Multiplication of the successive matrices thus yields a concise ray transfer matrix describing the entire optical system. The same mathematics is also used in accelerator physics to track particles through the magnet installations of a particle accelerator, see electron optics. This technique, as described below, is derived using the ''paraxial approximation'', which requires that all ray directions (directions normal to the wavefronts) are at small angles ''θ'' relative to the optical axis of the system, s ... [...More Info...]       [...Related Items...] picture info Maxwell's Equations Maxwell's equations are a set of coupled partial differential equation In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). I ...s that, together with the Lorentz force In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Ph ... law, form the foundation of classical electromagnetism Classical electromagnetism or classical electrodynamics is a branch of theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and ..., classical optics Optics is the branch of physics Phys ... [...More Info...]       [...Related Items...] picture info Transmittance Transmittance of the surface of a material is its effectiveness in transmitting radiant energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succ .... It is the fraction of incident electromagnetic power that is transmitted through a sample, in contrast to the transmission coefficient The transmission coefficient is used in physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the ..., which is the ratio of the transmitted to incident electric field An electric field (sometimes E-field) is the physical field that surrounds electrically-charged particle In physics Physics (from grc, φυσική (ἐπιστήμη), phys ... [...More Info...]       [...Related Items...] picture info Reflectance The reflectance of the surface of a material is its effectiveness in reflecting radiant energy. It is the fraction of incident electromagnetic power that is reflected at the boundary. Reflectance is a component of the response of the electronic structure of the material to the electromagnetic field of light, and is in general a function of the frequency, or wavelength, of the light, its polarization, and the angle of incidence (optics), angle of incidence. The dependence of reflectance on the wavelength is called a ''reflectance spectrum'' or ''spectral reflectance curve''. Mathematical definitions Hemispherical reflectance The ''hemispherical reflectance'' of a surface, denoted ''R'', is defined as :R = \frac, where Φer is the radiant flux ''reflected'' by that surface and Φei is the radiant flux ''received'' by that surface. Spectral hemispherical reflectance The ''spectral hemispherical reflectance in frequency'' and ''spectral hemispherical reflectance in wavelength'' of a ... [...More Info...]       [...Related Items...] picture info Special Linear Group In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ..., the special linear group of degree ''n'' over a field Field may refer to: Expanses of open ground * Field (agriculture), an area of land used for agricultural purposes * Airfield, an aerodrome that lacks the infrastructure of an airport * Battlefield * Lawn, an area of mowed grass * Meadow, a grassl ... ''F'' is the set of matrices Matrix or MATRIX may refer to: Science and mathematics * Matrix (mathematics) In mathematics, a matrix (plural matrices) is a rectangle, rectangular ''wikt:array, array'' or ''table'' of numbers, symbol (formal), symbols, or expression (mathema ... with determinant In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (numb ... [...More Info...]       [...Related Items...] picture info Maxwell's Equation Maxwell's equations are a set of coupled partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be sol ...s that, together with the Lorentz force In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. " ... law, form the foundation of classical electromagnetism Classical electromagnetism or classical electrodynamics is a branch of theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and ..., classical optics Optics is the branch of physics that studies ... [...More Info...]       [...Related Items...] picture info Wave Number In the physical science Physical science is a branch of natural science that studies abiotic component, non-living systems, in contrast to life science. It in turn has many branches, each referred to as a "physical science", together called the "physical sciences". D ...s, the wavenumber (also wave number or repetency) is the spatial frequency In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ... of a wave In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular su ..., measured in cycles per unit distance or radians per unit distance. Whereas temporal frequency Frequency is the number of ... [...More Info...]       [...Related Items...] picture info Permeability (electromagnetism) In electromagnetism Electromagnetism is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in ..., permeability is the measure of magnetization In classical electromagnetism Classical electromagnetism or classical electrodynamics is a branch of theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and s ... that a material obtains in response to an applied magnetic field A magnetic field is a vector field In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space. For instance, a vector field in the plane can be visualised as a collection of arrows with .... Permeability is typically represented by the (italicized) Greek letter ''μ''. The term was coined ... [...More Info...]       [...Related Items...] Absorption (electromagnetic Radiation) Absorption may refer to: Chemistry and biology *Absorption (chemistry), diffusion of particles of gas or liquid into liquid or solid materials *Absorption (skin), a route by which substances enter the body through the skin *Absorption (pharmacology), absorption of drugs into the body *Absorption (biology), digestion **Absorption (small intestine) *Carbon dioxide scrubber, CO2 scrubber, the absorbent (of carbon dioxide) in a rebreather Physics and chemical engineering *Absorption (electromagnetic radiation), absorption of light or other electromagnetic radiation by a material *Absorption (acoustics), absorption of sound waves by a material *Absorption refrigerator, a refrigerator that runs on surplus heat rather than electricity *Absorption air conditioning, a type of solar air conditioning *Dielectric absorption, the inability of a charged capacitor to completely discharge when briefly discharged Mathematics and economics *Absorption (logic), one of the rules of inference *Absor ... [...More Info...]       [...Related Items...] picture info Surface Normal In geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position of figures. A mat ..., a normal is an object such as a line Line, lines, The Line, or LINE may refer to: Arts, entertainment, and media Films * ''Lines'' (film), a 2016 Greek film * ''The Line'' (2017 film) * ''The Line'' (2009 film) * ''The Line'', a 2009 independent film by Nancy Schwartzman Lite ..., ray Ray may refer to: Science and mathematics * Ray (geometry), half of a line proceeding from an initial point * Ray (graph theory), an infinite sequence of vertices such that each vertex appears at most once in the sequence and each two consecutive ..., or vector Vector may refer to: Biology *Vector (epidemiology) In epidemiology Epidemiology is the study and analysis of the distribution (who, when, and where), pat ... [...More Info...]       [...Related Items...] picture info Frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparently irreversible process, irreversible succession from the past, through the presen .... It is also occasionally referred to as temporal frequency to emphasize the contrast to spatial frequency In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ..., and ordinary frequency to emphasize the contrast to angular frequency In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, t ... [...More Info...]       [...Related Items...] picture info Electromagnetic Waves In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical scie ..., electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, propagating through space, carrying electromagnetic radiant energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succ .... It includes radio wave Radio waves are a type of electromagnetic radiation In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies ma ...s, microwave Microwave is a form of ele ... [...More Info...]       [...Related Items...]