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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 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.
molar absorption coefficient or molar extinction coefficient, also called molar absorptivity, is the attenuation coefficient divided by molarity (and usually multiplied by ln(10), i.e., decadic); see Beer-Lambert law and molar absorptivity for details;
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.
Mathematically, the probability of finding a particle at depth x into the material is calculated by the Beer–Lambert law: P ( x ) = e − x / λ {\displaystyle P(x)=e^{-x/\lambda }\!\,} . In general λ is material- and energy-dependent.
This may be related to other properties of the object through the Beer–Lambert law. Precise measurements of the absorbance at many wavelengths allow the identification of a substance via absorption spectroscopy, where a sample is illuminated from one side, and the intensity of the light that exits from the sample in every direction is measured.
According to Beer–Lambert law, the intensity of an electromagnetic wave inside a material falls off exponentially from the surface as =If denotes the penetration depth, we have
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.