RP Photonics

Encyclopedia … combined with a great Buyer's Guide!

Sponsorship opportunity: support this popular resource, which serves the whole photonics community, and get recognition!

Beer–Lambert Law

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

German: Lambert-Beersches Gesetz

Category: general optics

How to cite the article; suggest additional literature

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:

Beer-Lambert law

where ni is the concentration density (number density, in units of m−3) of substance i and σi(λ) 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)

(Suggest additional literature!)

See also: absorption, absorption coefficient
and other articles in the category general optics

How do you rate this article?

Click here to send us your feedback!

Your general impression: don't know poor satisfactory good excellent
Technical quality: don't know poor satisfactory good excellent
Usefulness: don't know poor satisfactory good excellent
Readability: don't know poor satisfactory good excellent

Found any errors? Suggestions for improvements? Do you know a better web page on this topic?

Spam protection: (enter the value of 5 + 8 in this field!)

If you want a response, you may leave your e-mail address in the comments field, or directly send an e-mail.

If you enter any personal data, this implies that you agree with storing it; we will use it only for the purpose of improving our website and possibly giving you a response; see also our declaration of data privacy.

If you like our website, you may also want to get our newsletters!

If you like this article, share it with your friends and colleagues, e.g. via social media: