ABSORBANCE LAW, DERIVATION

When radiation passes through a thin layer of an absorbing medium, (dx), the reduction of intensity, (-di), is proportional to the intensity, (I), the concentration of the absorber, (c), and the transition probability, a, which is also called the absorption coefficient.

-di = a.c.I.dx (1)

For sample thickness, L, and incident radiation intensity, Io, the equation integrates to:

-log I/Io = a.c.L (2)

The product a.c.L is called the absorbance, and the above equation (2) is the absorbance law. I/Io is the transmittance---the property that is normally measured.. People sometimes call equation (2) Beer’s law, or the Lambert-Beer law, or the Beer-Lambert-Bouger law; but as a simple fact of physics, the name absorbance law is more appropriate.

As the frequency varies across a single absorption line, the absorption coefficient, a, varies according to the line shape. This shape changes with total pressure, but when a is integrated over a whole line, the integral is constant, independent of the total pressure