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Beer's Law

Excerpt from Field Guide to Spectroscopy

Beer's law (sometimes called the Beer-Lambert law) states that the absorbance is proportional to the path length, b, through the sample and the concentration of the absorbing species, c

A α b · c

The proportionality constant is sometimes given the symbol a, giving Beer's law an alphabetic look:

A = a · b · c

The constant a is called the absorptivity. More formally, the proportionality constant is represented by ε and is called the extinction coefficient:

A = ε · b · c

If ε has molar units, it is called the molar extinction coefficient, or the molar absorptivity. The molar absorptivity varies with wavelength, and Beer's law is more accurately written as a function of λ:

A(λ) = ε(λ) · b · c

Most substances follow Beer's law at low to moderate concentrations of absorbing species. Beer's law may not be followed very well due to saturation effects in highly concentrated samples, changes in the refractive index of the sample, solute-solvent interactions, stray light effects, or the polychromaticity of the spectrometer light.

The direct relationship between absorbance and concentration illustrated by Beer's law often makes absorbance a more useful mode for spectra than transmittance.


D. W. Ball, Field Guide to Spectroscopy, SPIE Press, Bellingham, WA (2006).

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