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| '''Opacity''' is the measure of impenetrability to [[electromagnetic radiation|electromagnetic]] or other kinds of [[radiation]], especially visible [[light]]. In [[radiative transfer]], it describes the absorption and scattering of radiation in a [[transmission medium|medium]], such as a [[plasma (physics)|plasma]], [[dielectric]], [[radiation shield|shielding material]], glass, etc. An '''opaque''' object is neither [[Transparency (optics)|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 reflection|diffuse]], for example light reflecting off a white wall, or [[specular reflection|specular]], for example light reflecting off a mirror. An opaque substance transmits no light, and therefore reflects, scatters, or absorbs all of it. Both [[mirror]]s 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 [[visible light|visual range]], are largely opaque to [[ultraviolet]] light. More extreme frequency-dependence is visible in the [[absorption line]]s of cold [[gas]]es. Opacity can be quantified in many ways; for example, see the article [[mathematical descriptions of opacity]].
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| For general information on what makes an object or medium opaque, see the articles on [[absorption (electromagnetic radiation)|absorption]], [[reflection (physics)|reflection]], and [[light scattering|scattering]]. These are the processes that lead to opacity.
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| ==Quantitative definition==
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| {{See also|Extinction (astronomy)|attenuation coefficient}}
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| 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.
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| In this use, "opacity" is another term for the [[mass attenuation coefficient]] (or, depending on context, [[mass absorption coefficient]], the difference is described [[Absorption coefficient#Attenuation versus absorption|here]]) <math>\kappa_\nu</math> at a particular frequency <math>\nu</math> of electromagnetic radiation.
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| More specifically, if a beam of light with frequency <math>\nu</math> travels through a medium with opacity <math>\kappa_\nu</math> and mass density <math>\rho</math>, both constant, then the intensity will be reduced with distance ''x'' according to the formula
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| :<math>I(x) = I_0 e^{-\kappa_\nu \rho x}</math>
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| where
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| * ''x'' is the distance the light has traveled through the medium
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| * <math>I(x)</math> is the intensity of light remaining at distance ''x''
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| * <math>I_0</math> is the initial intensity of light, at <math>x = 0</math>
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| 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<sup>2</sup>/mass. | |
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| ===Planck and Rosseland opacity===
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| It is customary to define the average opacity, calculated using a certain weighting scheme. '''Planck opacity''' uses normalized [[Planck's law of black body radiation|Planck black body radiation energy density distribution]] as the weighting function, and averages <math>\kappa_\nu</math> directly. '''Rosseland opacity''' (after [[Svein Rosseland]]), on the other hand, uses a temperature derivative of [[Planck's law of black body radiation|Planck distribution]] (normalized) as the weighting function, and averages <math>\kappa_\nu^{-1}</math>,
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| :<math>\frac{1}{\kappa} = \frac{\int_0^{\infty} \kappa_{\nu}^{-1} u(\nu, T) d\nu }{\int_0^{\infty} u(\nu,T) d\nu}</math>.
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| The photon mean free path is <math>\lambda_\nu = (\kappa_\nu \rho)^{-1}</math>. 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.
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| In practice, the mean opacity for [[Thomson scattering|Thomson electron scattering]] is:
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| :<math>\kappa_{\rm es} = 0.20(1+X) {\rm\, cm}^2{\rm \,g}^{-1}</math>
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| where <math> X </math> is the hydrogen mass fraction.
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| For [[Bremsstrahlung|nonrelativistic thermal bremsstrahlung]], or free-free transitions, it is:
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| :<math>\kappa_{\rm ff}(\rho, T) = 0.64 \times 10^{23} (\rho[ {\rm g}~ {\rm\, cm}^{-3}])(T[{\rm K}])^{-7/2} {\rm\, cm}^2 {\rm\, g}^{-1}</math>.<ref>Stuart L. Shapiro and [[Saul Teukolsky|Saul A. Teukolsky]], "Black Holes, White Dwarfs, and Neutron Stars" 1983, ISBN 0-471-87317-9.</ref> | |
| The Rosseland mean absorption coefficient including both scattering and absorption (also called the extinction coefficient) is:
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| :<math>\frac{1}{\kappa} = \frac{\int_0^{\infty} (\kappa_{\nu, {\rm es}} + \kappa_{\nu, {\rm ff}})^{-1} u(\nu, T) d\nu }{\int_0^{\infty} u(\nu,T) d\nu}</math>.<ref>George B. Rybicki and [[Alan Lightman|Alan P. Lightman]], "Radiative Processes in Astrophysics" 1979 ISBN 0-471-04815-1.</ref>
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| ==See also==
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| * [[Absorption (electromagnetic radiation)]]
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| * [[Mathematical descriptions of opacity]]
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| * [[Molar absorptivity]]
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| * [[Reflection (physics)]]
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| * [[Scattering theory]]
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| * [[Transparency and translucency]]
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| ==References==
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| {{reflist|1}}
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| [[Category:Optics]]
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| [[Category:Electromagnetic radiation]]
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| [[Category:Scattering, absorption and radiative transfer (optics)]]
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| [[Category:Spectroscopy]]
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| [[Category:Glass physics]]
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