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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.
An electromagnetic wave propagating along a path C has the phase shift over C as if it was propagating a path in a vacuum, length of which, is equal to the optical path length of C. Thus, if a wave is traveling through several different media, then the optical path length of each medium can be added to find the total optical path length. The ...
Alternatively, if there is a beam of particles incident on the material, the attenuation length is the distance where the intensity of the beam has dropped to 1/e, or about 63% of the particles have been stopped. Mathematically, the probability of finding a particle at depth x into the material is calculated by the Beer–Lambert law:
A common expression of the Beer's law relates the attenuation of light in a material as: =, where is the absorbance; is the molar attenuation coefficient or absorptivity of the attenuating species; is the optical path length; and is the concentration of the attenuating species.
In many cases, attenuation is an exponential function of the path length through the medium. In optics and in chemical spectroscopy , this is known as the Beer–Lambert law . In engineering, attenuation is usually measured in units of decibels per unit length of medium (dB/cm, dB/km, etc.) and is represented by the attenuation coefficient of ...
Beer's law is commonly written in the form A = εcl, where A is the absorbance, c is the concentration in moles per liter, l is the path length in centimeters, and ε is a constant of proportionality known as the molar extinction coefficient. The law is accurate only for dilute solutions; deviations from the law occur in concentrated solutions ...