Beer–Lambert law
The Beer–Lambert law, also known as Beer's law, the Lambert–Beer law, or the Beer–Lambert–Bouguer law relates the attenuation of light to the properties of the material through which the light is traveling. The law is commonly applied to chemical analysis measurements and used in understanding attenuation in physical optics, for photons, neutrons or rarefied gases. In mathematical physics, this law arises as a solution of the BGK equation.
The law was discovered by Pierre Bouguer before 1729. It is often attributed to Johann Heinrich Lambert, who cited Bouguer's Essai d'optique sur la gradation de la lumière (Claude Jombert, Paris, 1729)—and even quoted from it—in his Photometria in 1760. Lambert's law stated that absorbance of a material sample is directly proportional to its thickness (path length). Much later, August Beer discovered another attenuation relation in 1852. Beer's law stated that absorbance is proportional to the concentrations of the attenuating species in the material sample. The modern derivation of the Beer–Lambert law combines the two laws and correlates the absorbance to both the concentrations of the attenuating species as well as the thickness of the material sample.
By definition, the transmittance of material sample is related to its optical depth τ and to its absorbance A as
where
The Beer–Lambert law states that, for N attenuating species in the material sample,
or equivalently that
where
Attenuation cross section and molar attenuation coefficient are related by
and number density and amount concentration by
where NA is the Avogadro constant.
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