text: The Beer–Lambert law can be applied to the analysis of a mixture by spectrophotometry, without the need for extensive pre-processing of the sample. An example is the determination of bilirubin in blood plasma samples. The spectrum of pure bilirubin is known, so the molar attenuation coefficient  is known. Measurements of decadic attenuation coefficient  are made at one wavelength  that is nearly unique for bilirubin and at a second wavelength in order to correct for possible interferences. The amount concentration  is then given by
  For a more complicated example, consider a mixture in solution containing two species at amount concentrations  and . The decadic attenuation coefficient at any wavelength  is, given by
  Therefore, measurements at two wavelengths yields two equations in two unknowns and will suffice to determine the amount concentrations  and  as long as the molar attenuation coefficients of the two components,  and  are known at both wavelengths. This two system equation can be solved using Cramer's rule. In practice it is better to use linear least squares to determine the two amount concentrations from measurements made at more than two wavelengths. Mixtures containing more than two components can be analyzed in the same way, using a minimum of  wavelengths for a mixture containing  components.
  The law is used widely in infra-red spectroscopy and near-infrared spectroscopy for analysis of polymer degradation and oxidation (also in biological tissue) as well as to measure the concentration of various compounds in different food samples. The carbonyl group attenuation at about 6 micrometres can be detected quite easily, and degree of oxidation of the polymer calculated.