A common and practical expression of the Beer–Lambert law relates the optical attenuation of a physical material containing a single attenuating species of uniform concentration to the optical path length through the sample and absorptivity of the species. This expression is:where
* is the absorbance
* is the molar attenuation coefficient or absorptivity of the attenuating species
* is the optical path length
* is the concentration of the attenuating species
A more general form of the Beer–Lambert law states that, for  attenuating species in the material sample,or equivalently thatwhere
* is the attenuation cross section of the attenuating species  in the material sample;
* is the number density of the attenuating species  in the material sample;
* is the molar attenuation coefficient or absorptivity of the attenuating species  in the material sample;
* is the amount concentration of the attenuating species  in the material sample;
* is the path length of the beam of light through the material sample.
In the above equations, the transmittance  of material sample is related to its optical depth  and to its absorbance  by the following definitionwhere
* is the radiant flux transmitted by that material sample;
* is the radiant flux received by that material sample.
Attenuation cross section and molar attenuation coefficient are related byand number density and amount concentration byor equivalentlyCases of non-uniform attenuation occur in atmospheric science applications and radiation shielding theory for instance.
The law tends to break down at very high concentrations, especially if the material is highly scattering. Absorbance within range of 0.2 to 0.5 is ideal to maintain linearity in the Beer–Lambert law. If the radiation is especially intense, nonlinear optical processes can also cause variances. The main reason, however, is that the concentration dependence is in general non-linear and Beer's law is valid only under certain conditions as shown by derivation below. For strong oscillators and at high concentrations the deviations are stronger. If the molecules are closer to each other interactions can set in. These interactions can be roughly divided into physical and chemical interactions. Physical interaction do not alter the polarizability of the molecules as long as the interaction is not so strong that light and molecular quantum state intermix (strong coupling), but cause the attenuation cross sections to be non-additive via electromagnetic coupling. Chemical interactions in contrast change the polarizability and thus absorption.