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The extinction law's primary application is in chemical analysis, where it underlies the Beer–Lambert law, commonly called Beer's law. Beer's law states that a beam of visible light passing through a chemical solution of fixed geometry experiences absorption proportional to the solute concentration .
The Beer–Lambert 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), ℓ.
The absorbance of a material that has only one absorbing species also depends on the pathlength and the concentration of the species, according to the Beer–Lambert law =, where ε is the molar absorption coefficient of that material; c is the molar concentration of those species; ℓ is the path length.
The product logarithm Lambert W function plotted in the complex plane from −2 − 2i to 2 + 2i The graph of y = W(x) for real x < 6 and y > −4. The upper branch (blue) with y ≥ −1 is the graph of the function W 0 (principal branch), the lower branch (magenta) with y ≤ −1 is the graph of the function W −1. The minimum value of x is ...
The roots of the term absorbance are in the Beer–Lambert law.As light moves through a medium, it will become dimmer as it is being "extinguished". Bouguer recognized that this extinction (now often called attenuation) was not linear with distance traveled through the medium, but related by what we now refer to as an exponential function.
A surface which obeys Lambert's law is said to be Lambertian, and exhibits Lambertian reflectance. Such a surface has a constant radiance / luminance , regardless of the angle from which it is observed; a single human eye perceives such a surface as having a constant brightness, regardless of the angle from which the eye observes the surface.
When using spectrophotometric analysis to determine the concentration of DNA or RNA, the Beer–Lambert law is used to determine unknown concentrations without the need for standard curves. In essence, the Beer Lambert Law makes it possible to relate the amount of light absorbed to the concentration of the absorbing molecule.
This can be modeled based on the Beer–Lambert law, which states = / where is the IMFP and is the axis perpendicular to the sample. In fact it is generally the case that the IMFP is only weakly material dependent, but rather strongly dependent on the photoelectron kinetic energy.