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Ewald–Oseen Extinction Theorem
In optics, the Ewald–Oseen extinction theorem, sometimes referred to as just the extinction theorem, is a theorem that underlies the common understanding of scattering (as well as refraction, reflection, and diffraction). It is named after Paul Peter Ewald and Carl Wilhelm Oseen, who proved the theorem in crystalline and isotropic media, respectively, in 1916 and 1915. Originally, the theorem applied to scattering by an isotropic dielectric objects in free space. The scope of the theorem was greatly extended to encompass a wide variety of bianisotropic media. Overview An important part of optical physics theory is starting with microscopic physics—the behavior of atoms and electrons—and using it to ''derive'' the familiar, macroscopic, laws of optics. In particular, there is a derivation of how the refractive index works and where it comes from, starting from microscopic physics. The Ewald–Oseen extinction theorem is one part of that derivation (as is the Lorentz–Lorenz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optics
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of optical instruments, instruments that use or Photodetector, detect it. Optics usually describes the behaviour of visible light, visible, ultraviolet, and infrared light. Light is a type of electromagnetic radiation, and other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties. Most optical phenomena can be accounted for by using the Classical electromagnetism, classical electromagnetic description of light, however complete electromagnetic descriptions of light are often difficult to apply in practice. Practical optics is usually done using simplified models. The most common of these, geometric optics, treats light as a collection of Ray (optics), rays that travel in straight lines and bend when they pass through or reflect from surfaces. Physical optics is a more comprehensive mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inhomogeneous Electromagnetic Wave Equation
In electromagnetism and applications, an inhomogeneous electromagnetic wave equation, or nonhomogeneous electromagnetic wave equation, is one of a set of wave equations describing the propagation of electromagnetic waves generated by nonzero source charges and currents. The source terms in the wave equations make the partial differential equations inhomogeneous, if the source terms are zero the equations reduce to the homogeneous electromagnetic wave equations, which follow from Maxwell's equations. Maxwell's equations For reference, Maxwell's equations are summarized below in SI units and Gaussian units. They govern the electric field E and magnetic field B due to a source charge density ''ρ'' and current density J: where ''ε''0 is the vacuum permittivity and ''μ''0 is the vacuum permeability. Throughout, the relation \varepsilon_0 \mu_0 = \dfrac is also used. SI units E and B fields Maxwell's equations can directly give inhomogeneous wave equations for the elec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Sitter Double Star Experiment
The de Sitter effect was described by Willem de Sitter in 1913 (as well as by Daniel Frost Comstock in 1910) and used to support the special theory of relativity against a competing 1908 emission theory by Walther Ritz that postulated a variable speed of light dependent on the velocity of the emitting object. De Sitter showed that Ritz's theory would have predicted that the orbits of binary stars would appear more eccentric than consistent with experiment and with the laws of mechanics, and would have been inconsistent with astronomical observations. This was confirmed by Kenneth Brecher in 1977 by observing x-ray spectra. For other experiments related to special relativity, see tests of special relativity. The effect According to simple emission theory, light thrown off by an object should move at a speed of c with respect to the emitting object. If there are no complicating dragging effects, the light would then be expected to move at this same speed until it eventually ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Special Relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between Spacetime, space and time. In Albert Einstein's 1905 paper, Annus Mirabilis papers#Special relativity, "On the Electrodynamics of Moving Bodies", the theory is presented as being based on just Postulates of special relativity, two postulates: # The laws of physics are Invariant (physics), invariant (identical) in all Inertial frame of reference, inertial frames of reference (that is, Frame of reference, frames of reference with no acceleration). This is known as the principle of relativity. # The speed of light in vacuum is the same for all observers, regardless of the motion of light source or observer. This is known as the principle of light constancy, or the principle of light speed invariance. The first postulate was first formulated by Galileo Galilei (see ''Galilean invariance''). Background Special relativity builds upon important physics ide ... [...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, 2 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 for whichever is in use. In the context of special relativity, a '' wave four-vector'' can be defined, combining the (angular) wave vector and (angular) frequency. Definition The terms ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Calculus Identities
The following are important identities involving derivatives and integrals in vector calculus. Operator notation Gradient For a function f(x, y, z) in three-dimensional Cartesian coordinate variables, the gradient is the vector field: : \operatorname(f) = \nabla f = \begin\displaystyle \frac,\ \frac,\ \frac \end f = \frac \mathbf + \frac \mathbf + \frac \mathbf where i, j, k are the standard unit vectors for the ''x'', ''y'', ''z''-axes. More generally, for a function of ''n'' variables \psi(x_1, \ldots, x_n), also called a scalar field, the gradient is the vector field: \nabla\psi = \begin\displaystyle\frac, \ldots, \frac \end\psi = \frac \mathbf_1 + \dots + \frac\mathbf_n where \mathbf_ \, (i=1,2,..., n) are mutually orthogonal unit vectors. As the name implies, the gradient is proportional to, and points in the direction of, the function's most rapid (positive) change. For a vector field \mathbf = \left(A_1, \ldots, A_n\right), also called a tensor fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cylindrical Coordinate System
A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions around a main axis (a chosen directed line) and an auxiliary axis (a reference ray). The three cylindrical coordinates are: the point perpendicular distance from the main axis; the point signed distance ''z'' along the main axis from a chosen origin; and the plane angle of the point projection on a reference plane (passing through the origin and perpendicular to the main axis) The main axis is variously called the ''cylindrical'' or ''longitudinal'' axis. The auxiliary axis is called the ''polar axis'', which lies in the reference plane, starting at the origin, and pointing in the reference direction. Other directions perpendicular to the longitudinal axis are called ''radial lines''. The distance from the axis may be called the ''radial distance'' or ''radius'', while the angular coordinate is sometimes referred to as the ''angular position'' or as the ''azimuth''. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Retarded Potential
In electrodynamics, the retarded potentials are the electromagnetic potentials for the electromagnetic field generated by time-varying electric current or charge distributions in the past. The fields propagate at the speed of light ''c'', so the delay of the fields connecting cause and effect at earlier and later times is an important factor: the signal takes a finite time to propagate from a point in the charge or current distribution (the point of cause) to another point in space (where the effect is measured), see figure below. In the Lorenz gauge The starting point is Maxwell's equations in the potential formulation using the Lorenz gauge: : \Box \varphi = \dfrac \,,\quad \Box \mathbf = \mu_0\mathbf where φ(r, ''t'') is the electric potential and A(r, ''t'') is the magnetic vector potential, for an arbitrary source of charge density ρ(r, ''t'') and current density J(r, ''t''), and \Box is the D'Alembert operator. Solving these gives the retarded potentials below ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Green's Function
In mathematics, a Green's function (or Green function) is the impulse response of an inhomogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions. This means that if L is a linear differential operator, then * the Green's function G is the solution of the equation where \delta is Dirac's delta function; * the solution of the initial-value problem L y = f is the convolution Through the superposition principle, given a linear ordinary differential equation (ODE), one can first solve for each , and realizing that, since the source is a sum of delta functions, the solution is a sum of Green's functions as well, by linearity of . Green's functions are named after the British mathematician George Green, who first developed the concept in the 1820s. In the modern study of linear partial differential equations, Green's functions are studied largely from the point of view of fundamental solutions instead. Under many ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plane Wave
In physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ..., a plane wave is a special case of a wave or field: a physical quantity whose value, at any given moment, is constant through any plane that is perpendicular to a fixed direction in space. For any position \vec x in space and any time t, the value of such a field can be written as F(\vec x,t) = G(\vec x \cdot \vec n, t), where \vec n is a unit-length vector, and G(d,t) is a function that gives the field's value as dependent on only two real parameters: the time t, and the scalar-valued displacement d = \vec x \cdot \vec n of the point \vec x along the direction \vec n. The displacement is constant over each plane perpendicular to \vec n. The values of the field F may be scalars, vectors, or any other physical or ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homogeneous Differential Equation
A differential equation can be homogeneous in either of two respects. A first order differential equation is said to be homogeneous if it may be written :f(x,y) \, dy = g(x,y) \, dx, where and are homogeneous functions of the same degree of and . In this case, the change of variable leads to an equation of the form :\frac = h(u) \, du, which is easy to solve by integration of the two members. Otherwise, a differential equation is homogeneous if it is a homogeneous function of the unknown function and its derivatives. In the case of linear differential equations, this means that there are no constant terms. The solutions of any linear ordinary differential equation of any order may be deduced by integration from the solution of the homogeneous equation obtained by removing the constant term. History The term ''homogeneous'' was first applied to differential equations by Johann Bernoulli in section 9 of his 1726 article ''De integraionibus aequationum differentialium'' (O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hertz Vector
The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), often described as being equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose formal expression in terms of SI base units is 1/s or s−1, meaning that one hertz is one per second or the reciprocal of one second. It is used only in the case of periodic events. It is named after Heinrich Rudolf Hertz (1857–1894), the first person to provide conclusive proof of the existence of electromagnetic waves. For high frequencies, the unit is commonly expressed in multiples: kilohertz (kHz), megahertz (MHz), gigahertz (GHz), terahertz (THz). Some of the unit's most common uses are in the description of periodic waveforms and musical tones, particularly those used in radio- and audio-related applications. It is also used to describe the clock speeds at which computers and other electronics are driven. The units are sometimes also used as a representation of the e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
