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**Opacity** is the measure of impenetrability to electromagnetic or other kinds of radiation, especially visible light. In radiative transfer, it describes the absorption and scattering of radiation in a medium, such as a plasma, dielectric, shielding material, glass, etc. An **opaque** object is neither transparent (allowing all light to pass through) nor translucent (allowing some light to pass through). When light strikes an interface between two substances, in general some may be reflected, some absorbed, some scattered, and the rest transmitted (also see refraction). Reflection can be diffuse, for example light reflecting off a white wall, or specular, for example light reflecting off a mirror. An opaque substance transmits no light, and therefore reflects, scatters, or absorbs all of it. Both mirrors and carbon black are opaque. Opacity depends on the frequency of the light being considered. For instance, some kinds of glass, while transparent in the visual range, are largely opaque to ultraviolet light. More extreme frequency-dependence is visible in the absorption lines of cold gases. Opacity can be quantified in many ways; for example, see the article mathematical descriptions of opacity.

In physics, **electromagnetic radiation** refers to the waves of the electromagnetic field, propagating (radiating) through space, carrying electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) light, ultraviolet, X-rays, and gamma rays.

In physics, **radiation** is the emission or transmission of energy in the form of waves or particles through space or through a material medium. This includes:

**Light** is electromagnetic radiation within a certain portion of the electromagnetic spectrum. The word usually refers to **visible light**, which is the visible spectrum that is visible to the human eye and is responsible for the sense of sight. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), or 4.00 × 10^{−7} to 7.00 × 10^{−7} m, between the infrared and the ultraviolet. This wavelength means a frequency range of roughly 430–750 terahertz (THz).

Different processes can lead to opacity including absorption, reflection, and scattering.

In physics, **absorption** of electromagnetic radiation is how matter takes up a photon's energy — and so transforms electromagnetic energy into internal energy of the absorber. A notable effect (attenuation) is to gradually reduce the intensity of light waves as they propagate through a medium. Although the absorption of waves does not usually depend on their intensity, in certain conditions (optics) the medium's transparency changes by a factor that varies as a function of wave intensity, and saturable absorption occurs.

**Reflection** is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The *law of reflection* says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected. Mirrors exhibit specular reflection.

*Radiopacity* is preferentially used to describe opacity of X-rays. In modern medicine, radiodense substances are those that will not allow X-rays or similar radiation to pass. Radiographic imaging has been revolutionized by radiodense contrast media, which can be passed through the bloodstream, the gastrointestinal tract, or into the cerebral spinal fluid and utilized to highlight CT scan or X-ray images. Radiopacity is one of the key considerations in the design of various devices such as guidewires or stents that are used during radiological intervention. The radiopacity of a given endovascular device is important since it allows the device to be tracked during the interventional procedure.

**Radiography** is an imaging technique using X-rays, gamma rays, or similar radiation to view the internal form of an object. To create the image, a beam of X-rays or other form of electromagnetic radiation is produced by an X-ray generator and is projected toward the object. A certain amount of the X-rays or other radiation is absorbed by the object, dependent on the object's density and structural composition. The X-rays that pass through the object are captured behind the object by a detector. The generation of flat two dimensional images by this technique is called projectional radiography. In computed tomography an X-ray source and its associated detectors rotate around the subject which itself moves through the conical X-ray beam produced. Any given point within the subject is crossed from many directions by many different beams at different times. Information regarding attenuation of these beams is collated and subjected to computation to generate two dimensional images in three planes which can be further processed to produce a three dimensional image.

The **gastrointestinal tract** is an organ system within humans and other animals which takes in food, digests it to extract and absorb energy and nutrients, and expels the remaining waste as feces. The mouth, esophagus, stomach and intestines are part of the gastrointestinal tract. *Gastrointestinal* is an adjective meaning of or pertaining to the stomach and intestines. A tract is a collection of related anatomic structures or a series of connected body organs.

In medicine, a **stent** is a metal or plastic tube inserted into the lumen of an anatomic vessel or duct to keep the passageway open, and **stenting** is the placement of a stent. There is a wide variety of stents used for different purposes, from expandable coronary, vascular and biliary stents, to simple plastic stents used to allow the flow of urine between kidney and bladder. "Stent" is also used as a verb to describe the placement of such a device, particularly when a disease such as atherosclerosis has pathologically narrowed a structure such as an artery.

The words "opacity" and "opaque" are often used as colloquial terms for objects or media with the properties described above. However, there is also a specific, quantitative definition of "opacity", used in astronomy, plasma physics, and other fields, given here.

In this use, "opacity" is another term for the mass attenuation coefficient (or, depending on context, mass absorption coefficient, the difference is described here) at a particular frequency of electromagnetic radiation.

The **mass attenuation coefficient**, **mass extinction coefficient**, or **mass narrow beam attenuation coefficient** of the volume of a material characterizes how easily it can be penetrated by a beam of light, sound, particles, or other energy or matter. In addition to visible light, mass attenuation coefficients can be defined for other electromagnetic radiation, sound, or any other beam that attenuates. The SI unit of mass attenuation coefficient is the square metre per kilogram. Other common units include cm^{2}/g and mL⋅g^{−1}⋅cm^{−1}. "Mass extinction coefficient" is an old term for this quantity.

More specifically, if a beam of light with frequency travels through a medium with opacity and mass density , both constant, then the intensity will be reduced with distance *x* according to the formula

where

*x*is the distance the light has traveled through the medium- is the intensity of light remaining at distance
*x* - is the initial intensity of light, at

For a given medium at a given frequency, the opacity has a numerical value that may range between 0 and infinity, with units of length^{2}/mass.

Opacity in air pollution work refers to the percentage of light blocked instead of the attenuation coefficient (aka extinction coefficient) and varies from 0% light blocked to 100% light blocked:

It is customary to define the average opacity, calculated using a certain weighting scheme. **Planck opacity** (also known as Planck-Mean-Absorption-Coefficient^{ [1] }) uses the normalized Planck black body radiation energy density distribution, , as the weighting function, and averages directly:

- ,

where is the Stefan-Boltzmann constant.

**Rosseland opacity** (after Svein Rosseland), on the other hand, uses a temperature derivative of the Planck distribution, , as the weighting function, and averages ,

- .

The photon mean free path is . The Rosseland opacity is derived in the diffusion approximation to the radiative transport equation. It is valid whenever the radiation field is isotropic over distances comparable to or less than a radiation mean free path, such as in local thermal equilibrium. In practice, the mean opacity for Thomson electron scattering is:

where is the hydrogen mass fraction. For nonrelativistic thermal bremsstrahlung, or free-free transitions, assuming solar metallicity, it is:

- .
^{ [2] }

The Rosseland mean attenuation coefficient is:

- .
^{ [3] }

Look up in Wiktionary, the free dictionary. opacity (optics) |

In physics, **optical depth** or **optical thickness**, is the *natural logarithm* of the ratio of incident to *transmitted* radiant power through a material, and **spectral optical depth** or **spectral optical thickness** is the natural logarithm of the ratio of incident to *transmitted* spectral radiant power through a material. Optical depth is dimensionless, and in particular is not a length, though it is a monotonically increasing function of optical path length, and approaches zero as the path length approaches zero. The use of the term "optical density" for optical depth is discouraged.

The **Eddington luminosity**, also referred to as the **Eddington limit,** is the maximum luminosity a body can achieve when there is balance between the force of radiation acting outward and the gravitational force acting inward. The state of balance is called hydrostatic equilibrium. When a star exceeds the Eddington luminosity, it will initiate a very intense radiation-driven stellar wind from its outer layers. Since most massive stars have luminosities far below the Eddington luminosity, their winds are mostly driven by the less intense line absorption. The Eddington limit is invoked to explain the observed luminosity of accreting black holes such as quasars.

**Yang–Mills theory** is a gauge theory based on the SU(*N*) group, or more generally any compact, reductive Lie algebra. Yang–Mills theory seeks to describe the behavior of elementary particles using these non-abelian Lie groups and is at the core of the unification of the electromagnetic force and weak forces as well as quantum chromodynamics, the theory of the strong force. Thus it forms the basis of our understanding of the Standard Model of particle physics.

The **Einstein–Hilbert action** in general relativity is the action that yields the Einstein field equations through the principle of least action. With the (− + + +) metric signature, the gravitational part of the action is given as

A **radiation zone**, or **radiative region** is a layer of a star's interior where energy is primarily transported toward the exterior by means of radiative diffusion and thermal conduction, rather than by convection. Energy travels through the radiation zone in the form of electromagnetic radiation as photons.

**Einstein's constant** or **Einstein's gravitational constant**, denoted κ (kappa), is the coupling constant appearing in the Einstein field equation which can be written:

**Einstein coefficients** are mathematical quantities which are a measure of the probability of absorption or emission of light by an atom or molecule. The Einstein A coefficient is related to the rate of spontaneous emission of light and the Einstein B coefficients are related to the absorption and stimulated emission of light.

**Radiative transfer** is the physical phenomenon of energy transfer in the form of electromagnetic radiation. The propagation of radiation through a medium is affected by absorption, emission, and scattering processes. The **equation of radiative transfer** describes these interactions mathematically. Equations of radiative transfer have application in a wide variety of subjects including optics, astrophysics, atmospheric science, and remote sensing. Analytic solutions to the radiative transfer equation (RTE) exist for simple cases but for more realistic media, with complex multiple scattering effects, numerical methods are required. The present article is largely focused on the condition of radiative equilibrium.

The **source function** is a characteristic of a stellar atmosphere, and in the case of no scattering of photons, describes the ratio of the emission coefficient to the absorption coefficient. It is a measure of how photons in a light beam are removed and replaced by new photons by the material it passes through. Its units in the cgs-system are erg s^{−1} cm^{−2} sr^{−1} Hz^{−1} and in SI are W m^{−2} sr^{−1} Hz^{−1}. The *source function* can be written

The **Newman–Penrose** (**NP**) **formalism** is a set of notation developed by Ezra T. Newman and Roger Penrose for general relativity (GR). Their notation is an effort to treat general relativity in terms of spinor notation, which introduces complex forms of the usual variables used in GR. The NP formalism is itself a special case of the tetrad formalism, where the tensors of the theory are projected onto a complete vector basis at each point in spacetime. Usually this vector basis is chosen to reflect some symmetry of the space-time, leading to simplified expressions for physical observables. In the case of the NP formalism, the vector basis chosen is a null tetrad: a set of four null vectors—two real, and a complex-conjugate pair. The two real members asymptotically point radially inward and radially outward, and the formalism is well adapted to treatment of the propagation of radiation in curved spacetime. The most often-used variables in the formalism are the Weyl scalars, derived from the Weyl tensor. In particular, it can be shown that one of these scalars-- in the appropriate frame—encodes the outgoing gravitational radiation of an asymptotically flat system.

In the Newman–Penrose (NP) formalism of general relativity, **Weyl scalars** refer to a set of five complex scalars which encode the ten independent components of the Weyl tensors of a four-dimensional spacetime.

The **attenuation coefficient** or **narrow-beam attenuation coefficient** characterizes how easily a volume of material can be penetrated by a beam of light, sound, particles, or other energy or matter. A large attenuation coefficient means that the beam is quickly "attenuated" (weakened) as it passes through the medium, and a small attenuation coefficient means that the medium is relatively transparent to the beam. The SI unit of attenuation coefficient is the reciprocal metre (m^{−1}). **Extinction coefficient** is an old term for this quantity but is still used in meteorology and climatology. Most commonly, the quantity measures the number of downward *e*-foldings of the original intensity that will be had as the energy passes through a unit thickness of material, so that an attenuation coefficient of 1 m^{-1} means that after passing through 1 metre, the radiation will be reduced by a factor of *e*, and for material with a coefficient of 2 m^{-1}, it will be reduced twice by *e*, or *e*^{2}. Other measures may use a different factor than *e*, such as the *decadic attenuation coefficient* below.

** f(R)** is a type of modified gravity theory which generalizes Einstein's general relativity.

The **Grey atmosphere** is a useful set of approximations made for radiative transfer applications in studies of stellar atmospheres based on the simplification that the absorption coefficient of matter within the atmosphere is constant for all frequencies of incident radiation.

**Kramers' opacity law** describes the opacity of a medium in terms of the ambient density and temperature, assuming that the opacity is dominated by bound-free absorption or free-free absorption. It is often used to model radiative transfer, particularly in stellar atmospheres. The relation is named after the Dutch physicist Hendrik Kramers, who first derived the form in 1923.

In mathematical physics, the **Belinfante–Rosenfeld tensor** is a modification of the energy–momentum tensor that is constructed from the canonical energy–momentum tensor and the spin current so as to be symmetric yet still conserved.

In fluid dynamics, the **Falkner–Skan boundary layer** describes the steady two-dimensional laminar boundary layer that forms on a wedge, i.e. flows in which the plate is not parallel to the flow. It is a generalization of the Blasius boundary layer.

**Gauge vector–tensor gravity** (**GVT**) is a relativistic generalization of Mordehai Milgrom's modified Newtonian dynamics (MOND) paradigm where gauge fields cause the MOND behavior. The former covariant realizations of MOND such as the Bekenestein's tensor–vector–scalar gravity and the Moffat's scalar–tensor–vector gravity attribute MONDian behavior to some scalar fields. GVT is the first example wherein the MONDian behavior is mapped to the gauge vector fields. The main features of GVT can be summarized as follows:

**Quantum stochastic calculus** is a generalization of stochastic calculus to noncommuting variables. The tools provided by quantum stochastic calculus are of great use for modeling the random evolution of systems undergoing measurement, as in quantum trajectories. Just as the Lindblad master equation provides a quantum generalization to the Fokker-Planck equation, quantum stochastic calculus allows for the derivation of quantum stochastic differential equations (QSDE) that are analogous to classical Langevin equations.

- ↑ Modest, Radiative Heat Transfer, ISBN 978-0-12386944-9
- ↑ Stuart L. Shapiro and Saul A. Teukolsky, "Black Holes, White Dwarfs, and Neutron Stars" 1983, ISBN 0-471-87317-9.
- ↑ George B. Rybicki and Alan P. Lightman, "Radiative Processes in Astrophysics" 1979 ISBN 0-471-04815-1.

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