Employing Theories Far beyond Their Limits—The Case of the (Boguer-) Beer–Lambert Law

For spectroscopists, the (Bouguer-)Beer–Lambert law is unquestionably an essential principle, since it is inseparably linked with one of the most important quantities in spectroscopy, the absorbance. In spite of its importance, a quantitative discussion of the legitimacy of relating the transmittance, the quantity that is usually measured, to the absorbance by assuming a logarithmic relation between both quantities cannot be found in literature. In this contribution, we quantitatively discuss, based on examples, the errors that can be introduced by disregarding the exact solution based on Maxwell's equations and show that these errors can easily exceed one order of magnitude. We also re-derive the Beer–Lambert law, thereby providing guidance as how to convert transmittance into absorbance properly.