Beer–Lambert law
/ BEER-LAM-bert /
Imagine looking down into a swimming pool. Tinted water looks deeper-coloured the further down you peer, and a glass of strong squash looks darker than a watery one. Two simple intuitions hide here: the more absorbing stuff the light passes through, and the more crowded with absorbers each centimetre is, the more light gets swallowed. The Beer–Lambert law turns those intuitions into a clean rule for how much light a solution lets through.
The law states that absorbance — a measure of how much light a sample blocks — is directly proportional to two things: the concentration of the absorbing substance and the path length the light travels through the sample. The proportionality factor, called the molar absorptivity, is a constant for a given substance at a given wavelength and captures how strongly that substance grabs that colour of light. Double the concentration or double the path, and the absorbance doubles.
This straight-line relationship is what makes UV–visible spectroscopy a workhorse for measuring concentrations: read the absorbance, divide out the known path and absorptivity, and you have the amount present. The honest caveat is that the law holds only when solutions are dilute and well-behaved; at high concentrations the absorbers start to interfere with one another, and the neat proportionality bends away from a straight line.
A lab measures a blue copper sulfate solution in a 1 cm cuvette and finds an absorbance of 0.40. Diluting it to half the strength gives an absorbance of 0.20 — exactly halved, just as the law predicts. By comparing against solutions of known concentration, the chemist can read an unknown sample's concentration straight off a calibration line.
Absorbance climbs in step with concentration and path length.
The law works with absorbance, not transmittance: absorbance is proportional to concentration, whereas the fraction of light transmitted falls off exponentially. Plotting transmittance against concentration gives a curve, not a straight line, which is a frequent source of confusion.