Beer was educated at the technical school and gymnasium of his native town until 1845, when he went to Bonn to study mathematics and the sciences under the mathematician and physicist Julius Plücker, whose assistant he became later.
In 1848 he won the prize for his essay, "De Situ Axium Opticorum in Crystallis Biaxibus," and obtained the degree of Ph.D. Two years later he was appointed lecturer at the University of Bonn.
In 1852, Beer published a paper on the absorption of red light in coloured aqueous solutions of various salts.
Beer continued to publish the results of his scientific labors, writing in 1854 Einleitung in die höhere Optik (Introduction to the Higher Optics).
Beer's law is commonly written in the form A = εcl, where A is the absorbance, c is the concentration in moles per liter, l is the path length in centimeters, and ε is a constant of proportionality known as the molar extinction coefficient.