Beer’s law – why integrated absorbance depends linearly on concentration

Based on derivations from dispersion theory and, recently, from simple electromagnetic theory, it was shown lately that the assumption of strict linear dependence of absorbance on concentration, employed by Beer’s law, is only approximately correct. In this contribution we demonstrate, that while Beer’s law may not be valid for a single spectral point, it is nevertheless preserved for the integrated absorbance. This is a consequence from certain so-called sum rules which have been derived in the middle of the last century from the Kramers-Kronig relations. One of these sum rules is implicitly valid for absorbance and links it to a second one for the dielectric function. Based on this linkage we prove that for the integrated absorbance Beer’s law stays valid and show this based on an example.