Beer–Lambert law (original) (raw)
Author: the photonics expert (RP)
Definition: a relation for the dependence of absorption coefficients on concentrations
general opticsRelated: absorptionabsorption coefficient
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DOI: 10.61835/ci8 Cite the article: BibTex BibLaTex plain textHTML Link to this page! LinkedIn
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What is the Beer–Lambert Law?
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; the absorption coefficient is \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.
It is assumed that the substance is not so intensely illuminated that some saturation of the absorption could take place by getting a significant part of the absorbing species into excited states, or that other effects (e.g., thermal effects) modify their interaction with light.
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.
Frequently Asked Questions
This FAQ section was generated with AI based on the article content and has been reviewed by the article’s author (RP).
What is the Beer–Lambert law?
The Beer–Lambert law describes the quantitative relationship between the absorption of light and the concentration of an absorbing substance. It states that the absorption coefficient is a sum of the concentration densities of all absorbing substances, each multiplied by its absorption cross-section.
What is the Beer-Lambert law used for?
It allows one to determine the concentration of a substance in a solution from its measured light absorption over a certain length, provided the absorption cross-section is known. This is often used, for example, in the characterization of laser crystals.
What are the limitations of the Beer-Lambert law?
The law assumes that the illumination is not so intense as to cause saturation of the absorption. It also neglects other effects, such as thermal influences, which could modify the material's interaction with light.
Bibliography
| [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 |
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