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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.
When an electromagnetic wave travels through a medium in which it gets attenuated (this is called an "opaque" or "attenuating" medium), it undergoes exponential decay as described by the Beer–Lambert law. However, there are many possible ways to characterize the wave and how quickly it is attenuated.
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.
The absorbance can be written as sum of absorbances of each species (Beer–Lambert law) = = (), where the concentration of species i, the optical path length. By definition, an isosbestic point can be interpreted as a fixed linear combination of species concentrations, L = ∑ i n b i c i , d L d t = 0 , {\displaystyle L=\sum _{i}^{n}b_{i}c_{i ...
whose solution is known as Beer–Lambert law and has the form = /, where x is the distance traveled by the beam through the target, and I 0 is the beam intensity before it entered the target; ℓ is called the mean free path because it equals the mean distance traveled by a beam particle before being stopped.
Beer continued to publish the results of his scientific labors, writing in 1854 Einleitung in die höhere Optik (Introduction to the Higher Optics). His findings, together with those of Johann Heinrich Lambert, make up the Beer–Lambert law. In 1855 he was appointed professor of mathematics at the University of Bonn. Beer also wrote "Einheit ...