What is the Beer–Lambert law?

Under specified conditions, the Beer–Lambert law expresses absorbance as A=εcl, where ε is the molar absorption coefficient of the absorbing species at a particular wavelength and in a particular medium, c is concentration, and l is absorption path length. It describes proportionality between absorbance, concentration and path length when other conditions remain constant, not a universal conversion that automatically applies to every sample.

Every quantity in the equation carries experimental conditions. ε changes with wavelength, species form and surrounding medium. Effective path length must be known and stable during measurement, and the sample should be sufficiently homogeneous with appreciable scattering and chemical reactions avoided where possible. If spectral bandwidth spans a rapidly changing absorption region, the averaged recorded signal may also depart from ideal monochromatic conditions.

In practical quantification, linearity is generally assessed with a standard curve or dilution series rather than assumed from a single reading. If halving the concentration still produces a substantial change after correcting for dilution, or residuals show a systematic trend, sample, reference, path-length or instrument conditions may be outside the method's applicable range.

Common causes of failure include molecular interactions at high concentration, changes in acid–base or binding equilibria, particle scattering, stray light, finite bandwidth and photometric nonlinearity. Restored linearity after dilution can help locate the issue, but the species state must also be checked for dilution-induced changes. The Beer–Lambert law describes a relationship under controlled conditions; it does not replace verification of sample composition and method validity.