The Bouguer-Lambert-Beer law, determines the attenuation of a beam of monochromatic light as it passes through an absorbing substance. If the intensity of the beam incident on a layer of the substance of thickness l is I0, then, according to the Bouguer-Lambert-Beer law, the intensity of the beam leaving the layer is I(l)=I0e-kλl, where kλ is the absorption coefficient, which differs for different wavelengths K but does not depend on the light intensity I. For solutions kλ can be written as the product of the concentration C of the absorbing substance and the specific absorption coefficient η, which characterises the attenuation of a light beam in a solution of unit concentration and depends on the nature and the state of the substance and on λ. The Bouguer-Lambert-Beer law is then written as I(l)=I0e-ηCl. The Bouguer-Lambert-Beer law was discovered experimentally by the French scientist P. Bouguer in 1729, derived theoretically by the German scientist J. H. Lambert in 1760, and formulated for solutions by the German scientist A. Beer in 1852. (see Absorption of light).
The independence of η from the concentration of the solution and the nature of the solvent that the Bouguer-Lambert-Beer law assumes is only approximate. At high values of C in gases and solutions η is no longer a constant quantity, but changes appreciably because of interactions between the molecules of the absorbing substance. Where η may be taken to be independent of concentration, the Bouguer-Lambert-Beer law is used to determine the concentration of the absorbing substance by measuring the absorption, which can be done very accurately. By increasing the thickness l of the layer, vanishingly small concentrations of a substance can be determined.
The physical meaning of the Bouguer-Lambert-Beer law lies in the assertion that the process by which photons are lost is independent of their density in the light beam, that is, of the intensity of the light passing through the substance. This assertion holds over wide limits; however, when the intensity of the light is very great (for example, in the focused beams of pulsed lasers), kλ becomes dependent on the intensity (see Bleaching effect, Nonlinear optics) and the Bouguer-Lambert-Beer law ceases to be applicable.