Beer–Lambert Law (A = εbc)

Shine light of one wavelength through a coloured solution and the fraction that survives depends on three things: how strongly the molecule grabs that wavelength (the molar absorptivity ε), how far the beam travels through the liquid (the path length b), and how many absorbers are in the way (the concentration c). Absorbance — the logarithm of the light lost — is simply their product, which is why a spectrophotometer reading converts to concentration with a single division. NADH at 340 nm has ε = 6220 L·mol⁻¹·cm⁻¹, so a 5.00 × 10⁻⁵ M solution in a standard 1.00 cm cuvette reads A = 6220 × 1.00 × 5.00 × 10⁻⁵ = 0.311, and every enzyme-kinetics assay in biochemistry runs on exactly that arithmetic.

The law was assembled by three people across 120 years. Pierre Bouguer noticed in his 1729 Essai d'Optique that equal thicknesses of glass each swallowed the same fraction of light; Johann Heinrich Lambert put it into logarithmic form in Photometria (1760); and August Beer showed in 1852 that concentration behaves exactly like thickness. The common trap is forgetting that ε is quoted per centimetre while concentrations are per litre — mix in a path length in metres and the answer is off by a hundred. The other trap is linearity: above roughly A = 2 almost no light reaches the detector, molecules start interacting, and the straight line bends, which is why analysts dilute a strongly coloured sample rather than trusting an off-scale reading.