| # Absorption spectrometry: using measurements at different light frequencies Matrices > Matrix products > Example Return to the absorption spectrometry setup described here. The Beer-Lambert law postulates that the logarithm of the ratio of the light intensities is a linear function of the concentrations of each gas in the mix. The log-ratio of intensities is thus of the form for some vector , where is the vector of concentrations, and the vector contains the coefficients of absorption of each gas. This vector is actually also a function of the frequency of the light we illuminate the container with. Now consider a container having a mixture of ‘‘pure’’ gases in it. Denote by the vector of concentrations of the gases in the mixture. We illuminate the container at different frequencies . For each experiment, we record the corresponding log-ratio , , of the intensities. If the Beer-Lambert law is to be believed, then we must have for some vectors , which contain the coefficients of absorption of the gases at light frequency . More compactly: where Thus, is the coefficient of absorption of the -th gas at frequency . Since 's correspond to ‘‘pure’’ gases, they can be measured in the laboratory. We can then use the above model to infer the concentration of the gases in a mixture, given some observed light intensity log-ratio. See also: Absorption spectrometry: the Beer-Lambert law.