Opacity (optics) - Citizendia

Opacity is the measure of impenetrability to electromagnetic or other kinds of radiation, especially visible light. Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700 In radiative transfer, it describes the absorption and scattering of radiation in a medium, such as a plasma, dielectric, shielding material, glass, etc. The term radiative transfer refers to the physical phenomena of energy transfer in the form of electromagnetic radiation A dielectric is a nonconducting substance ie an insulator. The term was coined by William Whewell in response to a request from Michael Faraday. Radiation protection, sometimes known as radiological protection, is the science of protecting people and the environment from the harmful effects of Ionizing radiation An opaque object is neither transparent (allowing all light to pass through) nor translucent (allowing some light to pass through). In Optics, transparency (also called pellucidity) is the Material property of allowing In Optics, transparency (also called pellucidity) is the Material property of allowing 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). Refraction is the change in direction of a Wave due to a change in its Speed. An opaque substance transmits very little light, and therefore reflects, scatters, or absorbs most of it. Both mirrors and carbon black are opaque. A mirror is an object with a surface that has good Specular reflection; that is it is smooth enough to form an Image. Carbon black is a material produced by the incomplete Combustion of heavy Petroleum products such as FCC tar coal tar ethylene cracking tar and a small amount from Opacity depends on the frequency of the light being considered. Frequency is a measure of the number of occurrences of a repeating event per unit Time. For instance, some kinds of glass, while transparent in the visual range, are largely opaque to ultraviolet light. Glass in the common sense refers to a Hard, Brittle, transparent Solid, such as that used for Windows many Ultraviolet ( UV) light is Electromagnetic radiation with a Wavelength shorter than that of Visible light, but longer than X-rays More extreme frequency-dependence is visible in the absorption lines of cold gases. A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from an excess or deficiency of photons in a narrow frequency range compared This page is about the physical properties of gas as a state of matter In general, a material tends to emit light in the same proportions as it absorbs it.

1 Definition
2 Applications
3 Extinction coefficient
4 Physical definitions
5 See also
6 References

Definition

The opacity $κ ν$ gives the rate of absorption (or extinction), which is the fraction of the intensity $I ν$ , of the radiation that is absorbed or scattered per unit distance along a ray of propagation:

${\partial I_\nu\over\partial x}=-I_\nu\kappa_\nu$ . Extinction is a term used in Astronomy to describe the absorption and Scattering of Electromagnetic radiation emitted by Astronomical objects

For a given medium it has a numerical value that may range between 0 and infinity. It is also called the absorption coefficient (see also extinction coefficient). Opacity is the measure of impenetrability to electromagnetic or other kinds of radiation especially visible Light. In general $κ ν$ depends on the frequency $ν$ of the radiation, as well as the density, temperature, and composition of the medium. Frequency is a measure of the number of occurrences of a repeating event per unit Time. The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature The mean free path is the distance a photon travels in the medium before absorption or scattering is defined as $1 / (κ ν ρ)$ , where $ρ$ is the density of the material. In Physics the mean free path of a particle is the average distance covered by a particle ( Photon, Atom or Molecule) between subsequent impacts In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena The notation $κ λ$ is the opacity described as a function of wavelength $λ$ . In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency. While many materials are very opaque (steel in visible light having near-infinite opacity), and others very transparent (air in visible light having near-zero opacity), so that opacity often seems to be a boolean property, many others (such as water) have intermediate opacity. Steel is an Alloy consisting mostly of Iron, with a Carbon content between 0 Temperature and layers The temperature of the Earth's atmosphere varies with altitude the mathematical relationship between temperature and altitude varies among five Water is a common Chemical substance that is essential for the survival of all known forms of Life.

In astronomy and planetary imaging fields, tau, the optical depth, defines the opacity: zero indicates transparent and higher numbers indicate more and more opaque in an inverse exponential fashion, for example a tau of 1 indicates 36 percent of the light passes (e^-1 = 0. Astronomy (from the Greek words astron (ἄστρον "star" and nomos (νόμος "law" is the scientific study Tau (uppercase Τ, lowercase τ; Ταυ) is the 19th letter of the Greek alphabet. 36), and a Tau of 5 indicates less than 1 percent passes (e ^-5 = 0. 0067). ^[1]

In astrophysics and plasma physics "opacity", or absorption coefficient, $κ ν$ is defined so that $κ ν ρ I ν d ν d Ω$ gives the corresponding energy absorbed per unit volume per unit time from a beam of given intensity $I ν$ in a medium of density $ρ$ (thus $κ ν$ is measured in $cm 2 g - 1$ ). The optical depth $τ ν$ along the propagation direction is then $d τ ν = κ ν ρ d s$ , where $d s$ is the distance along this direction. 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 $κ ν$ directly. For a general introduction see Black body. In Physics, Planck's law describes the spectral radiance of Electromagnetic radiation Rosseland opacity, on the other hand, uses a temperature derivative of Planck distribution (normalized) as the weighting function, and averages $\kappa_\nu^{-1}$ ,

$\frac{1}{\kappa} = \frac{\int_0^{\infty} \kappa_{\nu}^{-1} u(\nu, T) d\nu }{\int_0^{\infty} u(\nu,T) d\nu}$ . For a general introduction see Black body. In Physics, Planck's law describes the spectral radiance of Electromagnetic radiation

The photon mean free path is $λ ν = (κ ν ρ) - 1$ . 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 $κ es = 0. In Physics, Thomson scattering is the scattering of Electromagnetic radiation by acharged particle 40cm 2 g - 1$ and for nonrelativistic thermal bremsstrahlung, or free-free transitions, it is $\kappa_{\rm ff}(\rho, T) = 0.64 \times 10^{23} (\rho[ {\rm g}~ {\rm cm}^{-3}])(T[{\rm K}])^{-7/2} {\rm cm}^2 {\rm g}^{-1}$ . Bremsstrahlung ( pronounced, from German de ''bremsen'' "to brake" and de ''Strahlung'' "radiation" i ^[2] The Rosseland mean absorption coefficient including both scattering and absorption (also called the extinction coefficient) is

$\frac{1}{\kappa} = \frac{\int_0^{\infty} (\kappa_{\nu, {\rm es}} + \kappa_{\nu, {\rm ff}})^{-1} u(\nu, T) d\nu }{\int_0^{\infty} u(\nu,T) d\nu}$ . ^[3]

Applications

In astrophysics, the variations in opacity within a star are important to the understanding of radiation transfer in stellar atmospheres and the spectra we observe. Astrophysics is the branch of Astronomy that deals with the Physics of the Universe, including the physical properties ( Luminosity, The term radiative transfer refers to the physical phenomena of energy transfer in the form of electromagnetic radiation A spectrum (plural spectra or spectrums) is a condition that is not limited to a specific set of values but can vary infinitely within a continuum.

In several types of chemical analysis, the concentration of a sample in a transparent medium (typically air or water) is determined via measuring its opacity or absorbance. Analytical chemistry is the study of the Chemical composition of natural and artificial Materials. In Spectroscopy, the absorbance A is defined as A_\lambda = -\log_{10}(I/I_0\ where I is the intensity of light In spectrophotometry the device identifies the sample's constituent substances from their absorbances. In Physics, spectrophotometry is the quantitative study of electromagnetic spectra.

Opacity is also used as a measurement of particulate emissions. Particulates, alternatively referred to as particulate matter (PM or fine particles, are tiny particles of solid or liquid suspended in a gas Emission standards are requirements that set specific limits to the amount of Pollutants that can be released into the environment

Extinction coefficient

The extinction coefficient for a particular substance is a measure of how well it scatters and absorbs electromagnetic radiation (EM waves). Scattering is a general physical process whereby some forms of Radiation, such as Light, Sound or moving particles for example are forced to deviate from In Physics, absorption of electromagnetic radiation is the process by which the Energy of a Photon is taken up by matter typically the electrons of an Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. If the EM wave can pass through very easily, the material has a low extinction coefficient. Conversely, if the radiation hardly penetrates the material, but rather quickly becomes "extinct" within it, the extinction coefficient is high.

A material can behave differently for different wavelengths of electromagnetic radiation. In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency. Glass is transparent to visible light, but many types of glass are opaque to ultra-violet wavelengths. Glass in the common sense refers to a Hard, Brittle, transparent Solid, such as that used for Windows many Ultraviolet ( UV) light is Electromagnetic radiation with a Wavelength shorter than that of Visible light, but longer than X-rays In general, the extinction coefficient for any material is a function of the incident wavelength. The extinction coefficient is used widely in ultraviolet-visible spectroscopy. Ultraviolet-visible spectroscopy or ultraviolet-visible spectrophotometry ( UV/ VIS) involves the Spectroscopy of Photons in the UV-visible

Physical definitions

The parameter used to describe the interaction of electromagnetic radiation with matter is the complex index of refraction, ñ, which is a combination of a real part and an imaginary part:

$\tilde{n}=n-ik.$

Here, n is also called the index of refraction, which sometimes leads to confusion. The refractive index (or index of Refraction) of a medium is a measure for how much the speed of light (or other waves such as sound waves is reduced inside the medium In Mathematics, the real numbers may be described informally in several different ways Geometric interpretation Geometrically imaginary numbers are found on the vertical axis of the complex number plane The refractive index (or index of Refraction) of a medium is a measure for how much the speed of light (or other waves such as sound waves is reduced inside the medium k is the extinction coefficient, which represents the damping of an EM wave inside the material. Both depend on the wavelength.

An EM wave travels in the material with velocity $v$ and angular frequency $ω$ . Do not confuse with Angular velocity In Physics (specifically Mechanics and Electrical engineering) angular frequency The time-varying electric field of the wave is described by

$\mathbf{E}(z,t) = \mathbf{E}_0 e^{i\omega(t - \frac{z}{v})},$

where only the real part of $\mathbf E$ has physical significance. In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can For simplicity, the radiation is assumed to be a plane wave, and its direction of propagation is denoted $z$ . In the Physics of Wave propagation (especially Electromagnetic waves, a plane wave (also spelled planewave) is a constant-frequency wave whose

The index of refraction is defined to be the ratio of the speed of light in a vacuum to the speed of the EM wave in the medium:

$\tilde{n} = \frac{c}{v}.$

Substituting for $\tilde{n}$ in the expression above gives

$\frac{1}{v} = \frac{n}{c} - i\frac{k}{c}.$

Substituting this in the expression for the EM wave's electric field gives

$\mathbf E(z, t) = \mathbf E_0 e^{i\omega(t - z(\frac{n}{c}))} e^{-(\frac{k \omega}{c})z}.$

This expression describes a propagating electromagnetic wave with an exponentially damped amplitude due to the $k$ term. This vacuum means "absence of matter" or "an empty area or space" for the cleaning appliance see Vacuum cleaner. Amplitude is the magnitude of change in the oscillating variable with each Oscillation, within an oscillating system This term causes the EM wave to "die out" as it travels further into the material. The intensity of the wave, which corresponds to the energy it carries with it, is simply the square of the magnitude of the wave's electric field. In Physics, intensity is a measure of the time-averaged Energy Flux. The magnitude of a mathematical object is its size a property by which it can be larger or smaller than other objects of the same kind in technical terms an Ordering The intensity of the wave is therefore

$I(z) = I_0 e^{-\frac{2\omega k}{c}z}.$

A law called the Beer-Lambert law states that in any medium that is absorbing light, the decrease in intensity $I$ per unit length $z$ is proportional to the instantaneous value of $I$ . In In mathematical form this is

$\frac{dI\left( z \right)}{dz}={-\alpha I\left(z\right)},$

where $α$ is the absorption coefficient of the material for that wavelength of EM radiation. The absorption coefficient α is a property of a material It defines the extent to which a material absorbs energy for example that of Sound waves or Electromagnetic This equation has the solution

${I\left(z \right)}={I_0 e^{-\alpha z}}$ ,

where $I 0$ is the intensity of the electromagnetic radiation at the surface of the absorbing medium. Comparing the two expressions for intensity obtained above gives

$\alpha = \frac{2\omega k}{c}.$

Since $c$ here denotes the speed of the EM wave in vacuum,

$c= \frac{\omega}{2\pi}\lambda$ .

Substituting this in the expression above and rearranging shows that the extinction coefficient and the absorption coefficient are related by

$k={\frac{\lambda}{4\pi}}\alpha$ ,

where λ is the vacuum wavelength (not the wavelength of the EM wave in the material). This vacuum means "absence of matter" or "an empty area or space" for the cleaning appliance see Vacuum cleaner.

References

^ Are The Mars Rovers Doomed? 'A tau of five means that less than one percent of direct sunlight is reaching the Mars surface'
^ Stuart L. In Mathematics and Physics, scattering theory is a framework for studying and understanding the Scattering of Waves and particles. The molar extinction coefficient, also known as molar absorptivity, is a measurement of how strongly a Chemical species absorbs light at a given 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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Contents

Definition

Applications

Extinction coefficient

Physical definitions

See also

References