Opacity (optics)


Opacity (optics)

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.

For general information on what makes an object or medium opaque, see the articles on absorption, reflection, and scattering. These are the processes that lead to opacity.

Contents

Quantitative definition

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) κν at a particular frequency ν of electromagnetic radiation.

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

I(x) = I_0 e^{-\kappa_\nu \rho x}

where

  • x is the distance the light has traveled through the medium
  • I(x) is the intensity of light remaining at distance x
  • I0 is the initial intensity of light, at x = 0

For a given medium at a given frequency, the opacity has a numerical value that may range between 0 and infinity, with units of length2/mass.

Planck and Rosseland opacity

It is customary to define the average opacity, calculated using a certain weighting scheme. Planck opacity uses normalized Planck black body radiation energy density distribution as the weighting function, and averages κν directly. Rosseland opacity (after Svein Rosseland), on the other hand, uses a temperature derivative of Planck distribution (normalized) as the weighting function, and averages \kappa_\nu^{-1},

\frac{1}{\kappa} = \frac{\int_0^{\infty} \kappa_{\nu}^{-1} u(\nu, T) d\nu }{\int_0^{\infty} u(\nu,T) d\nu}.

The photon mean free path is λν = (κνρ) − 1. 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:

κes = 0.20(1 + X)cm2g − 1

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

\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}.[1]

The Rosseland mean absorption coefficient including both scattering and absorption (also called the extinction coefficient) is:

\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}.[2]

See also

References

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

Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Opacity — may refer to: Opacity (optics), the degree to which light is not allowed to travel through Opaque context, a term to describe the linguistic context of co referential terms Phonological opacity, a term in phonology Opaque travel inventory, the… …   Wikipedia

  • optics — /op tiks/, n. (used with a sing. v.) the branch of physical science that deals with the properties and phenomena of both visible and invisible light and with vision. [1605 15; < ML optica < Gk optiká, n. use of neut. pl. of OPTIKÓS; see OPTIC,… …   Universalium

  • Mathematical descriptions of opacity — When an electromagnetic wave travels through a medium in which it gets absorbed (this is called an opaque or attenuating medium), it undergoes exponential decay as described by the Beer–Lambert law. However, there are many possible ways to… …   Wikipedia

  • Transparency (optics) — In optics, transparency (also called pellucidity) is the material property of allowing light to pass through. In mineralogy, another term for this property is diaphaneity. The opposite property is opacity. Transparent materials are clear: they… …   Wikipedia

  • Source function — 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… …   Wikipedia

  • Transmittance — In optics and spectroscopy, transmittance is the fraction of incident light at a specified wavelength that passes through a sample.:mathcal{T} = {Iover I {0where I 0 is the intensity of the light and I is the intensity of the light coming out of… …   Wikipedia

  • Refractive index — Refraction of light at the interface between two media. In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum… …   Wikipedia

  • Transparency and translucency — Diaphanes redirects here. For the genus of firefly, see Diaphanes (beetle). Translucence redirects here. For other uses, see Translucence (disambiguation). Translucent redirects here. For the Japanese manga series, see Translucent (manga).… …   Wikipedia

  • Absorption (electromagnetic radiation) — An overview of electromagnetic radiation absorption. This example discusses the general principle using visible light as specific example. A white beam source emitting light of multiple wavelengths is focused on a sample (the complementary color… …   Wikipedia

  • Cloak of invisibility — Alberich puts on the Tarnhelm and vanishes; illustration by Arthur Rackham to Richard Wagner s Das Rheingold Plot element from Folk lore and fairy tales First appearan …   Wikipedia


Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.