# Beer-Lambert law

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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.

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### Equations

The law states that there is a logarithmic dependence between the transmission (or transmissivity), 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 (i.e. the path length), . The absorption coefficient can, in turn, be written as a product of either a molar absorptivity (extinction coefficient) of the absorber, ε, and the concentration c of absorbing species in the material, or an absorption cross section, σ, and the (number) 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 difference between the use of base 10 and base e is purely conventional, requiring a multiplicative constant to convert between them.

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

This implies that the absorbance becomes linear with the concentration (or number density of absorbers) according to

and

for the two cases, respectively.

Thus, if the path length and the molar absorptivity (or the absorption cross section) are known and the absorbance is measured, the concentration of the substance (or the number density of absorbers) can be deduced.

Although several of the expressions above often are used as Beer–Lambert law, the name should strictly speaking only be associated with the latter two. The reason is that historically, the Lambert law states that absorption is proportional to the light path length, whereas the Beer law states that absorption is proportional to the concentration of absorbing species in the material.[1]