Beer's Law Derived from Electromagnetic Theory

We present a rigorous derivation of Beer's law from electromagnetic theory which allows to establish the connection of wave optics and Maxwell's equations with quantitative UV/VIS and infrared spectroscopy. As a result of this derivation, the attenuation constant is shown to be a function of the index of refraction. For small concentrations and an index of refraction not very different from unity, however, the empirical law is retrieved. Only for very strong absorptions with attenuation constants beyond 10 l/(mol·cm) and high concentrations, noticeable deviations from the empirical law and its linear concentration dependence are predicted to occur. The derivation is presented in a form, which is not only similar to that leading to the Clausius-Mossotti equation, but also shares the same starting point. Accordingly, it can easily be included in the curricula of physical chemistry.