Inclined plane - Revision history

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2015-01-11T00:14:31Z

Reverting possible vandalism by 67.243.149.53 to version by 197.32.163.69. False positive? Report it. Thanks, ClueBot NG. (2085382) (Bot)

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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]]

	~~'''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.~~

	~~==Formulations==~~

	~~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]]~~.
	If <~~math~~>~~I_0~~<~~/math~~> ~~is the [[intensity (physics)\|intensity]] of radiation at the source and <math>I</math>~~
	~~is the observed intensity after a given path, then optical depth <math>\tau</math> is defined by the~~
	~~following equation~~:~~<ref name="kitchin1987">{{cite book~~
	~~\| author=Kitchin, Christopher Robert~~
	~~\| year=1987~~
	~~\| title=Stars, Nebulae and the Interstellar Medium: Observational Physics and Astrophysics~~
	~~\| publisher=CRC Press~~
	~~\| location=~~
	~~\| id=}}</ref>~~

	~~:<math>I / I_0 = e^{-\tau}.\,</math>~~

	~~===Calculation from fundamental principles===~~
	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~~

	~~<math>\tau = \frac{d^2 \nu N} {2 c \hbar \epsilon_0 A \gamma}, </math>~~

	~~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.~~

	~~===Atmospheric science===~~
	~~{{See also\|Beer's law}}~~

	~~In [[atmospheric sciences]], one often refers to the optical depth of the atmosphere as corresponding to the~~
	~~vertical path from Earth's surface to outer space; at other times the optical path is from the observer's altitude to outer space.~~
	~~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~~
	~~atmosphere it is determined as ''m'' = sec θ, where θ is the~~
	~~[[celestial coordinate system\|zenith angle]] corresponding to the given path. Therefore~~

	~~:<math>I / I_0 = e^{-m \tau}.\, </math>~~

	~~The optical depth of the atmosphere can be divided into several components, ascribed to [[Rayleigh scattering]],~~
	~~[[particulate\|aerosols]], and gaseous [[absorption (electromagnetic radiation)\|absorption]].~~
	~~The optical depth of the atmosphere can be measured with a [[sun photometer]].~~

	~~===Stellar physics===~~

	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.

	~~Note that the optical depth of a given medium will be different for different colors ([[wavelength]]s) of light.~~

	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.

	~~==See also==~~
	*[[Absorbance]]
	*[[Actinometer]]
	*[[Aerosol]]
	*[[Angstrom exponent]]
	*[[Pyranometer]]
	*[[Radiative transfer]]
	*[[Transparency and translucency]]
	*[[Sun photometer]]

	~~==References==~~
	~~<references/>~~
	*{{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}}

	~~==External links==~~
	* [http://scienceworld.wolfram.com~~/physics/OpticalDepth.html optical depth equations]~~

	~~[[Category:Scattering, absorption and radiative transfer (optics)]]~~
	~~[[Category:Visibility~~]]

71.190.234.106 at 01:08, 28 January 2014

2014-01-28T01:08:57Z

← Older revision		Revision as of 03:08, 28 January 2014
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	~~<br><br>~~[~~http://toriwa~~.~~Mireene~~.co.~~kr/xe/?document_srl=298982 mireene~~.~~co.kr~~]~~We can find [https://gntl~~.~~zendesk.com/entries/43350285-Take-Good-Care-Of-Your-Body-It-Is-~~The~~-Only-Placed-You-Need-To-Live does~~ a ~~shot of vinegar clean system~~] a ~~safety, to~~ [~~http://Www~~.~~articlerun.com~~/~~22045~~/~~6-strange-facts-about-ginger-glass-jar~~/ ~~survive]~~ the ~~initial occurrences of nature. I invite one to come see this site~~ and ~~read my [http~~://~~165~~.~~132.39.93~~/~~xe/?document_srl~~=~~208805 free mini-course~~] ~~on " Top 10 Secrets To Healthy & Happy Finches”~~ by ~~clicking to.~~<br><br>~~They may also live in~~ the ~~sewage drains~~, ~~garbage cans~~, ~~watered house plants~~ and ~~canine bowls~~, ~~so that it~~ is ~~all~~ the ~~more challenging~~ to ~~get rid of them~~. ~~For people who chose~~ to ~~life~~ the ~~subsequent will be considered~~ a ~~start~~, ~~not~~ a ~~perfect nor a finish solution~~.<br><br>~~He or she will leave it~~ to the ~~people who are well versed~~ in the ~~technical information scriptwriting~~. ~~If you're~~ an ~~avid reader~~, ~~next~~ the ~~should not certainly~~ be ~~a problem to suit your needs~~. ~~Does peanut butter go bad if left out~~ [~~http://165~~.~~132~~.~~39.93/xe/?document_srl~~=~~208805 39.93~~][http://www.~~Bestpampers~~.~~com~~/~~groups~~/~~how~~-to-~~make-tea-shelf-life/ bad red] wine vinegar alcohol~~ [http://~~420nurses~~.com/~~profile-45436~~/~~info/ site web~~] ~~Com.ua/grafika/impact-health-care-legislation-hr-3962-outsourcing-industry">foods that last a long time</a> The people inside your novel must not always lead a peaceful~~ and ~~happy life otherwise readers will find your work boring. Choose the most important point for your essay and work out a strategy on the method that you could assemble it up within your essay.~~		{{Other uses\|Optical depth (astrophysics)}}

			'''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.

			==Formulations==

			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]].
			If <math>I_0</math> is the [[intensity (physics)\|intensity]] of radiation at the source and <math>I</math>
			is the observed intensity after a given path, then optical depth <math>\tau</math> is defined by the
			following equation:<ref name="kitchin1987">{{cite book
			\| author=Kitchin, Christopher Robert
			\| year=1987
			\| title=Stars, Nebulae and the Interstellar Medium: Observational Physics and Astrophysics
			\| publisher=CRC Press
			\| location=
			\| id=}}</ref>

			:<math>I / I_0 = e^{-\tau}.\,</math>

			===Calculation from fundamental principles===
			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

			<math>\tau = \frac{d^2 \nu N} {2 c \hbar \epsilon_0 A \gamma}, </math>

			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.

			===Atmospheric science===
			{{See also\|Beer's law}}

			In [[atmospheric sciences]], one often refers to the optical depth of the atmosphere as corresponding to the
			vertical path from Earth's surface to outer space; at other times the optical path is from the observer's altitude to outer space.
			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
			atmosphere it is determined as ''m'' = sec θ, where θ is the
			[[celestial coordinate system\|zenith angle]] corresponding to the given path. Therefore

			:<math>I / I_0 = e^{-m \tau}.\, </math>

			The optical depth of the atmosphere can be divided into several components, ascribed to [[Rayleigh scattering]],
			[[particulate\|aerosols]], and gaseous [[absorption (electromagnetic radiation)\|absorption]].
			The optical depth of the atmosphere can be measured with a [[sun photometer]].

			===Stellar physics===

			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.

			Note that the optical depth of a given medium will be different for different colors ([[wavelength]]s) of light.

			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.

			==See also==
			*[[Absorbance]]
			*[[Actinometer]]
			*[[Aerosol]]
			*[[Angstrom exponent]]
			*[[Pyranometer]]
			*[[Radiative transfer]]
			*[[Transparency and translucency]]
			*[[Sun photometer]]

			==References==
			<references/>
			*{{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}}

			==External links==
			* [http://scienceworld.wolfram.com/physics/OpticalDepth.html optical depth equations]

			[[Category:Scattering, absorption and radiative transfer (optics)]]
			[[Category:Visibility]]

en>Chetvorno: Undid revision 508571214 by 60.241.243.168 (talk) Edit left markup format in broken state so page would not display

2012-08-22T06:12:02Z

Undid revision 508571214 by 60.241.243.168 (talk) Edit left markup format in broken state so page would not display

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