Bouguer-Lambert-Beer Absorption Law

Leif Gerward

Department of Physics, Technical University of Denmark, DK-2800 Lyngby/Denmark.

Introduction

It is well known that the intensity [math]I[/math] of light (or other electromagnetic radiation) should decrease exponentially with the distance d that it enters an absorbing medium, i.e.

[math]I=I_{0}exp(-\mu d)\tag {1} where \ltmath\gtI_{0}[/math] is the intensity of the incident radiation, and μ is the linear absorption (or attenuation) coefficient. Equation (1) is usually known as Lambert’s law of absorption (e.g. Ballentyne and Lovett, 1970). However, there is some confusion about the origin of that law, since other names are Lambert–Beer’s law and Bouguer’s law. Therefore, it should be interesting to know a little more about the scientists associated with the Absorption Law, and about their contributions to the subject.

As it turns out, the story has already been told. Fred Perrin (1948) has published a note with the somewhat provocative title “Whose Absorption Law?” Perrin’s paper, however, appeared almost sixty years ago, and few may be aware of it today. Thus, for the benefit of the reader of the Bulletin, it should be worthwhile once again to discuss the origin of the Absorption Law. I have also extended the scope of the present paper by including biographical sketches of Bouguer, Lambert and Beer.