en>Erinmhoey at 03:50, 12 November 2014

2014-11-12T03:50:39Z

en>Materialscientist: Reverted 1 edit by 103.27.8.43 identified as test/vandalism using STiki

2014-01-12T12:17:23Z

Reverted 1 edit by 103.27.8.43 identified as test/vandalism using STiki

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			{{About\|transmission through a ''medium''\|transmission or refraction through an ''interface'' (between two homogeneous media)\|Fresnel equations}}
			[[Image:Beer lambert1.png\|thumb\|240px\|Diagram of Beer-Lambert Law of transmittance of a beam of light as it travels through a [[cuvette]] of width ''l''.]]
			[[Image:Atmospheric.transmittance.IR.jpg\|thumb\|Earth's atmospheric transmittance. Because of the natural radiation of the hot atmosphere, the intensity of radiation is different from the transmitted part.]]

			[[Image:Ruby transmittance.svg\|thumb\|240px\|Transmittance of ruby in optical and near-IR spectra. Note the two broad blue and green absorption bands and one narrow absorption band on the wavelength of 694 nm, which is the wavelength of the [[ruby laser]].]]

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			A related terms is [[absorbance]],<ref>{{GoldBookRef\|title=Absorbance\|file=A00028}}</ref> or absorption factor,<ref>{{cite web\|url=http://www.crcpress.com/product/isbn/9780849328909\|title=CRC Dictionary of pure and applied physics, CRC Press, Editor: Dipak Basu (2001)}}</ref> which is the fraction of radiation absorbed by a sample at a specified wavelength.
			==Beer–Lambert law==
			{{main\|Beer–Lambert law}}
			In equation form,

			:<math>\mathcal{T}_\lambda = {I\over I_{0}} \qquad \mathcal{A}_\lambda = \frac{I_0-I}{I_0}</math>

			where <math>I_0</math> is the [[intensity (physics)\|intensity]] of the [[wiktionary:incident#Adjective\|incident]] radiation and I is the intensity of the radiation coming out of the sample and <math>\mathcal{T}_\lambda</math> and <math>\mathcal{A}_\lambda</math> are transmittance and absorptance respectively. In these equations, scattering and reflection are considered to be close to zero or otherwise accounted for. The transmittance of a sample is sometimes given as a percentage.

			For liquids, transmittance is related to [[absorbance]] ''A'' (not to be confused with absorptance) as

			:<math>A = - \log_{10}\mathcal{T}\ = - \log_{10}\left({I\over I_{0}}\right)</math>
			In the case of gases it is customary to use natural logarithms instead, making absorbance ''A'' for gases
			:<math>A = - \ln\mathcal{T}\ = - \ln\left({I\over I_{0}}\right)</math>

			From the above equation and the Beer-Lambert law, the transmittance for gases is thus given by

			:<math>\mathcal{T} = e^{-\alpha \, x}</math>,

			where <math>\alpha</math> is the [[attenuation coefficient]] and <math>x</math> is the path length. For liquids ''e'' is replaced by 10.

			Note that the term "[[Transmission coefficient\|transmission]]" refers to the physical process of radiation passing through a sample, whereas transmittance refers to the mathematical quantity.

			===Transmittance in the atmosphere===
			For [[atmospheric science]] applications, it is useful to introduce the quantity of [[optical depth]] <math>\tau</math>. Given a coefficient of extinction within an atmospheric column, <math>\beta_e</math>, optical depth is defined to be

			:<math>\tau = \int_{z_1}^{z_2} \beta_e(z) \mathrm{d}z</math>.

			With this, transmittance can be given as

			:<math>\mathcal{T} = e^{-\tau}</math>,

			or

			:<math>\mathcal{T} = e^{-\tau / \mu }</math>

			where, when the plane parallel assumption is invoked, <math>\mu=\|cos(\theta)\|</math> with <math>\theta</math> the angle of propagation of the ray from the normal of the surface.

			==See also==
			*[[Opacity (optics)]]

			Another equation that can be useful in solving for %T is the following: A = 2 - log(%T)
			Where A is a measure of absorbance. By manipulating the equation you can generate the more direct form of the equation: %T = 10^(2-A)

			==References==
			{{reflist}}

			[[Category:Optics]]
			[[Category:Spectroscopy]]

128.172.89.130 at 21:17, 14 August 2012

2012-08-14T21:17:10Z

New page

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Absorbance - Revision history

en>Erinmhoey at 03:50, 12 November 2014

en>Materialscientist: Reverted 1 edit by 103.27.8.43 identified as test/vandalism using STiki

128.172.89.130 at 21:17, 14 August 2012