Beer–Lambert law

Under applicable conditions, absorbance is proportional to the concentration of the absorbing substance and the path length.

Converting an absorbance reading to concentration may look like simply substituting values into a formula. What determines its reliability is whether the sample, path length and instrument conditions remain within the valid range of the linear relationship.

The physical relationship behind the equation

IUPAC describes the Beer–Lambert law for collimated monochromatic radiation in a homogeneous, isotropic medium: absorbance A is proportional to absorbing-species concentration c and absorption path length l. The proportionality constant ε is the molar absorption coefficient at the specified wavelength and state of the substance.

Thus, while ε remains constant, doubling concentration or path length doubles the ideal absorbance. A short path length can bring the absorbance of a concentrated sample back into a measurable range. Normalizing a short-path result to another path length requires a verified actual path length.

Linear ranges in practice

Nucleic acid or protein quantification commonly uses absorbance at a specified UV wavelength together with an established conversion factor or absorption coefficient. Standard-curve methods likewise depend on an acceptable functional relationship between response and concentration over a defined range.

Linearity requires a Blank compatible with the sample matrix, a homogeneous sample and a stable chemical form. Changes in pH, association or dissociation, reaction equilibria and the solvent environment can change ε. The original conversion may then cease to apply even if the instrument is functioning normally.

Deviations are not always caused by excessive concentration

Finite spectral bandwidth combines different absorption at neighboring wavelengths; scattering particles attenuate transmitted light; stray light adds signal in highly absorbing regions; and detector or electronic nonlinearity changes the response. Each can make the absorbance–concentration relationship depart from an ideal straight line.

A good linear fit alone therefore does not prove method accuracy: systematic bias over a short interval can also look linear. Reliable assessment also considers residuals, reference materials, path length, repeatability and the method's specified range. The Beer–Lambert law provides a basis for quantification, not an unconditional guarantee for every sample and reading.

When results no longer follow the dilution ratio, check sample chemistry, scattering, Blank, path length, bandwidth and stray light in turn, rather than simply changing the concentration conversion factor.