# Opacity (optics)

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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).

## Contents

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.

## 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) ${\displaystyle \kappa _{\nu }}$ at a particular frequency ${\displaystyle \nu }$ 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 cm2/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 ${\displaystyle \nu }$ travels through a medium with opacity ${\displaystyle \kappa _{\nu }}$ and mass density ${\displaystyle \rho }$, both constant, then the intensity will be reduced with distance x according to the formula

${\displaystyle I(x)=I_{0}e^{-\kappa _{\nu }\rho x}}$

where

• x is the distance the light has traveled through the medium
• ${\displaystyle I(x)}$ is the intensity of light remaining at distance x
• ${\displaystyle I_{0}}$ is the initial intensity of light, at ${\displaystyle x=0}$

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.

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:

${\displaystyle Opacity=100\%\left(1-{\frac {I(x)}{I_{0}}}\right)}$

### Planck and Rosseland opacities

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, ${\displaystyle B_{\nu }(T)}$, as the weighting function, and averages ${\displaystyle \kappa _{\nu }}$ directly:

${\displaystyle \kappa _{Pl}={\int _{0}^{\infty }\kappa _{\nu }B_{\nu }(T)d\nu \over \int _{0}^{\infty }B_{\nu }(T)d\nu }={\Big (}{\pi \over \sigma T^{4}}{\Big )}\int _{0}^{\infty }\kappa _{\nu }B_{\nu }(T)d\nu }$,

where ${\displaystyle \sigma }$ is the Stefan-Boltzmann constant.

Rosseland opacity (after Svein Rosseland), on the other hand, uses a temperature derivative of the Planck distribution, ${\displaystyle u(\nu ,T)=\partial B_{\nu }(T)/\partial T}$, as the weighting function, and averages ${\displaystyle \kappa _{\nu }^{-1}}$,

${\displaystyle {\frac {1}{\kappa }}={\frac {\int _{0}^{\infty }\kappa _{\nu }^{-1}u(\nu ,T)d\nu }{\int _{0}^{\infty }u(\nu ,T)d\nu }}}$.

The photon mean free path is ${\displaystyle \lambda _{\nu }=(\kappa _{\nu }\rho )^{-1}}$. 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:

${\displaystyle \kappa _{\rm {es}}=0.20(1+X){\rm {\,cm}}^{2}{\rm {\,g}}^{-1}}$

where ${\displaystyle X}$ is the hydrogen mass fraction. For nonrelativistic thermal bremsstrahlung, or free-free transitions, assuming solar metallicity, it is:

${\displaystyle \kappa _{\rm {ff}}(\rho ,T)=0.64\times 10^{23}(\rho [{\rm {g}}~{\rm {\,cm}}^{-3}])(T[{\rm {K}}])^{-7/2}{\rm {\,cm}}^{2}{\rm {\,g}}^{-1}}$. [2]

The Rosseland mean attenuation coefficient is:

${\displaystyle {\frac {1}{\kappa }}={\frac {\int _{0}^{\infty }(\kappa _{\nu ,{\rm {es}}}+\kappa _{\nu ,{\rm {ff}}})^{-1}u(\nu ,T)d\nu }{\int _{0}^{\infty }u(\nu ,T)d\nu }}}$. [3]

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## References

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