Bouguer-Lambert-Beer Law

Bouguer-Lambert-Beer law

[bu̇′ger ¦läm·bert ¦ber ‚lȯ]
(analytical chemistry)
The intensity of a beam of monochromatic radiation in an absorbing medium decreases exponentially with penetration distance. Also known as Beer-Lambert-Bouguer law; Lambert-Beer law.

Bouguer-Lambert-Beer Law


a law defining the progressive weakening of a parallel monochromatic beam of light during its propagation in an absorptive substance. If the intensity of the beam entering a layer of matter of thickness l is equal to I0, then, according to the Bouguer-Lambert-Beer law, the intensity of the beam as it leaves the layer is

I(l) = I0e-kel

where k is the specific extinction coefficient of the light calculated per unit concentration c of the substance determining the absorption; k depends on the nature and state of the substance and on the wavelength of the radiation passing through it. The Bouguer-Lambert-Beer law was discovered by the French scientist P. Bouguer in 1729, treated in detail by the German scientist J. H. Lambert in 1760, and verified experimentally in regard to concentration c by the German scientist A. Beer in 1852.

The assertion that k is a constant is approximate. For large changes of concentration in gases and solutions, k usually begins to change owing to physicochemical interactions of the molecules. At the beginning of the 20th century, the Soviet scientist S. I. Vavilov experimentally verified the independence of the value kc of the light-beam intensity in a broad range of variation —from very large values (corresponding to direct solar beams collected by a lens) to negligible values (barely distinguishable to the dark-adapted eye). It was found that under all these conditions kc remains practically constant. However, as shown by Vavilov, the quantum nature of the light and the finite (although very small) duration of the excited state of the molecules must lead to the situation that for extremely high light-beam intensities, a significant fraction of all the molecules exist in an excited state, and the absorption of light diminishes. Vavilov’s prediction was confirmed by experiments on a large number of substances at emissive power densities created by optical quantum generators (lasers).


Bouguer, P. Opticheskii traktat o gradatsii sveta. Moscow, 1950. (Translated [from French].)
Vavilov, S. I. “O nezavisimosti koeffitsienta pogloshcheniia sveta ot iarkosti.” Sobr. soch., vol. 1. Moscow, 1954.
Vavilov, S. I. “Sledstviia nezavisimosti koeffitsienta pogloshcheniia sveta ot iarkosti.” Izv. fizicheskogo in-ta pri Moskovskom nauchno-issledovatel’skom in-te, 1920, part 1, no. 3.
Vavilov, S. I., and M. D. Galanin. “Izluchenie i pogloshchenie sveta v sisteme induktivno sviazannykh molekul.” Dokl. AN SSSR, 1949, vol. 67, part 5.