Definition: The absorption coefficient of a medium,
![Rendered by QuickLaTeX.com mu_a](http://latamnirs.org/wp-content/ql-cache/quicklatex.com-c46cc90b31dab60c3f5a0ef147040bd7_l3.png)
is related to the probability of a photon to be absorbed by the medium after it travels some distance in the medium; more precisely, it is the rate of photon absorption per unit length in the medium. The absorption coefficient depends on medium composition and light wavelength. The inverse of the absorption coefficient, known as the absorption length,
![Rendered by QuickLaTeX.com l_a](http://latamnirs.org/wp-content/ql-cache/quicklatex.com-ad9cc1965de80b0d5e09b157f7ac7df4_l3.png)
can be understood as the distance traveled by a photon before its probability of not being absorbed in the medium has decreased by
![Rendered by QuickLaTeX.com e^{-1}](http://latamnirs.org/wp-content/ql-cache/quicklatex.com-928f18a9f120940a582ccd5417a1a5e8_l3.png)
. Quantitatively, the absorption coefficient can be related with the light intensity attenuation as it traverses the medium. Let
![Rendered by QuickLaTeX.com I](http://latamnirs.org/wp-content/ql-cache/quicklatex.com-18b5e45cb4a1ee02e81b9a980f828db8_l3.png)
represent the intensity at any point of the path, such that the differential intensity is
![Rendered by QuickLaTeX.com dI](http://latamnirs.org/wp-content/ql-cache/quicklatex.com-ded8c11f527708cbf74de93e862305e5_l3.png)
,
![Rendered by QuickLaTeX.com dl](http://latamnirs.org/wp-content/ql-cache/quicklatex.com-f509c8fa82447ad8e7b4263b83f6e4dc_l3.png)
a differential length along the path of the radiation. Then
![Rendered by QuickLaTeX.com frac{dI}{dl}=-mu_al](http://latamnirs.org/wp-content/ql-cache/quicklatex.com-dd810d27a75c63414f9855a5899424dd_l3.png)
, and the constant
![Rendered by QuickLaTeX.com mu_{a}](http://latamnirs.org/wp-content/ql-cache/quicklatex.com-00dc91109801f28ba97c704292f79221_l3.png)
is known as the absorption coefficient.
Alternative definition: At any given point in the path of radiation, the Absorption Coefficient determines the fractional reduction in intensity per unit length of the path.
Synonym:
References: https://doi.org/10.1036/1097-8542.001600
Related terms: Absorption