Last updated: 2026-06-16

Understanding the Beer-Lambert law

The Beer-Lambert law links how much light a solution absorbs to how much absorbing material it contains:

Absorbance is defined from the light that enters and leaves the sample: $A = \log_{10}(I_0 / I)$. An absorbance of 1 means the sample transmits one tenth of the light; an absorbance of 2 means one hundredth.

Worked example

A coloured complex has a molar absorptivity of ε = 5,000 L·mol⁻¹·cm⁻¹ at its absorption maximum. In a standard 1 cm cuvette it reads an absorbance of 0.75. What is its concentration?

Going the other way, a 2 × 10⁻⁴ mol/L solution of the same complex in the same cuvette would absorb:

Why the law is linear

Each thin layer of solution removes a fixed fraction of the light passing through it. Working in logarithms turns that repeated multiplication into a simple sum, which is why absorbance — not transmittance — is the quantity that grows in direct proportion to concentration and path length. Double the concentration and you double the absorbance; double the cuvette length and you double it again.

Reading concentration from absorbance

Quantitative spectrophotometry runs the law backwards. Rather than trusting a single textbook ε, an analyst usually prepares several standards of known concentration, measures each one, and plots absorbance against concentration. The slope of that calibration line equals ε × l, and an unknown sample's concentration is read off the line from its absorbance.

When the law fails

Beer-Lambert behaviour is reliable only while the solution is dilute, usually below an absorbance of about 1. At higher concentrations the absorbing molecules begin to interact and the local refractive index shifts, so the calibration curve bends away from a straight line. Instrument effects — stray light, a beam that is not perfectly monochromatic — and chemical changes such as dissociation or fluorescence add further deviations. The practical fix is to dilute the sample until its absorbance lands in the instrument's linear window of roughly 0.1 to 1.0.