I = I010−ε[J]l
The quantity ε is called the molar absorption coefficient (formerly, and still widely,the ‘extinction coefficient’). The molar absorption coefficient depends on the frequencyof the incident radiation and is greatest where the absorption is most intense. Itsdimensions are 1/(concentration × length), and it is normally convenient to express itin cubic decimetres per mole per centimetre (dm3 mol−1 cm−1). Alternative units aresquare centimetres per mole (cm2 mol−1). This change of units demonstrates thatε may be regarded as a molar cross-section for absorption and, the greater the crosssectionalarea of the molecule for absorption, the greater its ability to block the passageof the incident radiation.
The Beer–Lambert law is an empirical result. However, it is simple to account for its
form. The reduction in intensity, dI, that occurs when light passes through a layer of
thickness dl containing an absorbing species J at a molar concentration [J] is proportional
to the thickness of the layer, the concentration of J, and the intensity, I,
incident on the layer (because the rate of absorption is proportional to the intensity).