In optics, the Beer–Lambert law, also known as Beer's law or the Lambert–Beer law or the Beer–Lambert–Bouguer law relates the absorption of light to the properties of the material through which the light is traveling.

The law states that there is a logarithmic dependence between the transmission, T, of light through a substance and the product of the absorption coefficient of the substance, α, and the distance the light travels through the material, ?. The absorption coefficient can, in turn, be written as a product of either a molar absorptivity of the absorber, ε, and the concentration c of absorbing species in the material, or an absorption cross section, σ, and the density N' of absorbers. For liquids, these relations are usually written as:

whereas for gases, and in particular among physicists and for spectroscopy and spectrophotometry, they are normally written

where I₀ and I are the intensity (or power) of the incident light and the transmitted light, respectively; σ is cross section of light absorption by a single particle and N is the density (number per unit volume) of absorbing particles.

The transmission (or transmissivity) is expressed in terms of an absorbance which, for liquids, is defined as

whereas, for gases, it is usually defined as

Beer's law can be applied to the analysis of a mixture by spectrophotometry, without the need for extensive pre-processing of the sample. An example is the determination of bilirubin in blood plasma samples. The spectrum of pure bilirubin is known, so the molar absorbance is known. Measurements are made at one wavelength that is nearly unique for bilirubin and at a second wavelength in order to correct for possible interferences. The law is used widely in infra-red spectroscopy for analysis of polymer degradation and oxidation. The carbonyl group absorption at about 6 micrometres can be detected quite easily, and degree of oxidation of the polymer calculated.