According to Lambert, for parallel, monochromatic radiation that passes through an absorber of constant concentration, the radiant intensity decreases logarithmically as the path length, l, increases arithmetically (Lambert’s law). According to Beer, the transmittance of a stable solution is an exponential function of the concentration, c, of the absorbing solute (Beer’s law). When both path length and concentration are variable, the combined Beer–Lambert law is given as follows:

I _t = I _o exp ( - k c l ) or, log _e ( I _o / I _t ) = k c l

where I _o and I _t are the incident and transmitted intensities, respectively and k is a constant but is a function of wavelength.

Although the quantity I/I ₀ (i.e. the transmittance) is measured easily, a graph of transmittance versus concentration will be a logarithmic curve and therefore, it is not the best quantity to deal with. Therefore, the Beer-Lambert Law is considered in the logarithmic form.

Converting to the base 10 logarithm, the equation becomes:

log ( I _o / I _t ) = A = ε c l

where A = absorbance and ε , another constant = absorptivity (formerly called the extinction coefficient ). The absorptivity depends on the wavelength of light as well as on the identity of the absorbing substance and the identity of the solvent. If the concentration is measured in mol.L ⁻¹ , the absorptivity is called the molar absorptivity.

Spectra are plotted either as absorbance, A, or as the transmittance, T, against wavelength, wavenumber or frequency, where T = ( I _t /I _o or sometimes as percentage transmittance = 100 T. The Beer-Lambert law applies equally to infrared absorption spectra. A can have any value from 0 to infinity. T must be between 0 and 1.

One can find from the above mathematical form of the Beer-Lambert law that it is a straight line equation with zero intercept. That is, a plot of absorbance versus concentration should be a straight line passing through the origin whose slope is (ε.l). If the path length of the sample is 1 unit (say, 1 cm), the slope equals the numerical value of ε. Therefore, in order to verify the validity of Beer-Lambert Law, a number of absorbance–concentration data points should be obtained for a sample that are measured in a given sample holder of unit path length. Calibration graphs of A against c may be plotted to verify that the linearity of Beer-Lambert law. It is worth noting that a certain degree of data scatter usually occurs due to personal errors in measurements. Therefore, it is necessary to obtain a best fit straight line. In addition to these small scatters in data points, sometimes deviations from linearity occur though there are no known exceptions to the Beer-Lambert law. The deviations from linearity may arise from high analyte concentrations, chemical associations, and instrumental origin. Real deviations arise from changes in the refractive index of the analytical system; these changes will be significant only in high-absorbance differential measurements. The Beer–Lambert law is well obeyed by many substances at low to moderate concentrations. Dilute solutions will give better linearity of results. Deviations occur at higher concentrations where absorptivity depends on the concentration. Specific chemical effects such as association of the molecules of the substance affects the analyte species which changes the nature and hence ε of the absorbing species. When the incident radiation is polychromatic (or measured in a part of the spectrum other than at an absorbance maximum), the Beer-Lambert plot shows a negative deviation. There are also other limitations of the beer-Lambert law.