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Beer–Lambert Law

Definition: a relation for the dependence of absorption coefficients on concentrations

German: Lambert-Beersches Gesetz

Category: general optics


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When an absorbing substance is dissolved in some liquid, the resulting absorption for light depends on the concentration of the substance. The Beer–Lambert law describes that quantitatively, more generally for solutions containing multiple absorbing species:

$$\alpha(\lambda) = \sum\limits_i n_i \: \sigma_i(\lambda) $$

where <$n_i$> is the concentration density (number density, in units of m−3) of substance <$i$> and <$\sigma_i(\lambda )$> its absorption cross-section.

With that equation, one can determine the concentration of a substance in a solution from the measured absorbance over some length, if the absorption cross-section is known. If the number density is known, one may determine the absorption cross-section.

This technique is often applied to the characterization of laser crystals, for example. Unfortunately, the doping concentration is not always exactly known, and this can result in corresponding uncertainties of the transition cross-sections.


[1]J. H. Lambert, “Photometria sive de mensura et gradibus luminis, colorum et umbrae”, Eberhardt Klett (1760)
[2]A. Beer, “Bestimmung der Absorption des rothen Lichts in farbigen Flüssigkeiten”, Annalen der Physik und Chemie 86: 78 (1852), DOI:10.1002/andp.18521620505

See also: absorption, absorption coefficient

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