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| {{Other uses|Optical depth (astrophysics)}}
| | I am 30 years old and my name is Irene Whitford. I life in Furth (Germany).<br><br>Also visit my web site: home renovations ideas [[http://www.homeimprovementdaily.com homeimprovementdaily.com]] |
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| '''Optical depth''', or '''optical thickness''', is a measure of [[transparency (optics)|transparency]]. Optical depth is defined as the negative [[natural logarithm]] of the fraction of [[radiation]] (e.g., [[light]]) that is not scattered or absorbed on a path. Hence optical depth is [[Dimensionless quantity|dimensionless]], and in particular is not a length, though it is a monotonically increasing function of path length, and approaches zero as the path length approaches zero.
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| ==Formulations==
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| The optical depth expresses the quantity of light removed from a beam by [[scattering]] or [[absorption (electromagnetic radiation)|absorption]] during its path through a [[transmission medium|medium]].
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| If <math>I_0</math> is the [[intensity (physics)|intensity]] of radiation at the source and <math>I</math>
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| is the observed intensity after a given path, then optical depth <math>\tau</math> is defined by the
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| following equation:<ref name="kitchin1987">{{cite book
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| | author=Kitchin, Christopher Robert
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| | year=1987
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| | title=Stars, Nebulae and the Interstellar Medium: Observational Physics and Astrophysics
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| | publisher=CRC Press
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| | location=
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| | id=}}</ref>
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| :<math>I / I_0 = e^{-\tau}.\,</math>
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| ===Calculation from fundamental principles===
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| In [[atomic physics]], the optical depth of a cloud of atoms can be calculated from the quantum mechanical properties of the atoms. It is given by
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| <math>\tau = \frac{d^2 \nu N} {2 c \hbar \epsilon_0 A \gamma}, </math>
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| where ''d'' denotes the [[transition dipole moment]], γ the [[natural linewidth]] of the transition, ν the frequency, ''N'' the number of atoms, and ''A'' the cross-section of the beam.
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| ===Atmospheric science===
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| {{See also|Beer's law}}
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| In [[atmospheric sciences]], one often refers to the optical depth of the atmosphere as corresponding to the
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| vertical path from Earth's surface to outer space; at other times the optical path is from the observer's altitude to outer space.
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| Since τ refers to a vertical path, the optical depth for a slant path is τ′ = ''m'' τ, where ''m'' is called the [[airmass|relative airmass]], and for a plane-parallel
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| atmosphere it is determined as ''m'' = sec θ, where θ is the
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| [[celestial coordinate system|zenith angle]] corresponding to the given path. Therefore
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| :<math>I / I_0 = e^{-m \tau}.\, </math>
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| The optical depth of the atmosphere can be divided into several components, ascribed to [[Rayleigh scattering]],
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| [[particulate|aerosols]], and gaseous [[absorption (electromagnetic radiation)|absorption]].
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| The optical depth of the atmosphere can be measured with a [[sun photometer]].
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| ===Stellar physics===
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| Another example occurs in [[astronomy]] where the [[photosphere]] of a star is defined as the surface where its optical depth is 2/3. This means that each photon emitted at the photosphere suffers an average of less than one scattering before it reaches the observer. At the temperature at optical depth 2/3, the energy emitted by the star (the original derivation is for the sun) matches the observed total energy emitted.
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| Note that the optical depth of a given medium will be different for different colors ([[wavelength]]s) of light.
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| For [[planetary rings]], the optical depth is the proportion of light blocked by the ring when it lies between the source and the observer. This is usually obtained by observation of stellar occultations.
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| ==See also==
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| *[[Absorbance]]
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| *[[Actinometer]]
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| *[[Aerosol]]
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| *[[Angstrom exponent]]
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| *[[Pyranometer]]
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| *[[Radiative transfer]]
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| *[[Transparency and translucency]]
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| *[[Sun photometer]]
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| ==References==
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| <references/>
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| *{{anchor|drexel}}{{cite web |url=http://www.pages.drexel.edu/~brooksdr/DRB_web_page/papers/UsingTheSun/using.htm |title=Monitoring Solar Radiation and Its Transmission Through the Atmosphere |author=David R. Brooks |publisher=Drexel University |date=August 2006 |accessdate=2013-08-28}}
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| ==External links==
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| * [http://scienceworld.wolfram.com/physics/OpticalDepth.html optical depth equations]
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| [[Category:Scattering, absorption and radiative transfer (optics)]]
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| [[Category:Visibility]]
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I am 30 years old and my name is Irene Whitford. I life in Furth (Germany).
Also visit my web site: home renovations ideas [homeimprovementdaily.com]