Beer-Lambert Law, more commonly known as Beer’s Law, states that the optical absorbance of a chromophore in a transparent solvent varies linearly with both the sample cell pathlength and the chromophore concentration. Beer’s Law is the simple solution to the more general description of Maxwell’s far-field equations describing the interaction of light with matter. In practice, Beer’s Law is accurate enough for a range of chromophores, solvents and concentrations, and is a widely used relationship in quantitative spectroscopy.
Absorbance is measured in a spectrophotometer by passing a collimated beam of light at wavelength λ through a plane parallel slab of material that is normal to the beam. For liquids, the sample is held in an optically flat, transparent container called a cuvette. Absorbance (Aλ) is calculated from the ratio of light energy passing through the sample (I0) to the energy that is incident on the sample (I):
Aλ = -log (I/I0)
Beer’s Law follows:
Aλ = ελbc
ελ = molar absorptivity or extinction coefficient of the chromophore at wavelength λ (the optical density of a 1-cm thick sample of a 1 M solution). ελ is a property of the material and the solvent.
b = sample pathlength in centimeters
c = concentration of the compound in the sample, in molarity (mol L-1)
In an absorbance experiment, light is attenuated not only by the chromophore, but also by reflections from the interface between air and the sample, the sample and the cuvette, and absorbance by the solvent. These factors can be quantified separately, but are often removed by defining I0 as the light passing through a sample “blank” or “baseline” or reference sample (for example, a cuvette filled with solvent but zero concentration of the chromophore is used as the blank).
Many factors can affect the validity of Beer’s Law. It is usual to check for the linearity of Beer’s Law for a chromophore by measuring the absorbance of a series of standards. This “calibration” can also remove errors in the experiment, the equipment, and the batch of reagents (such as cuvettes of unknown pathlength).