Beer–Lambert law

The Beer-Lambert law is commonly applied to chemical analysis measurements to determine the concentration of chemical species that absorb light. It is often referred to as Beer's law. In physics, the Bouguer–Lambert law is an empirical law which relates the extinction or attenuation of light to the properties of the material through which the light is travelling. It had its first use in astronomical extinction. The fundamental law of extinction (the process is linear in the intensity of radiation and amount of radiatively active matter, provided that the physical state is held constant) is sometimes called the Beer-Bouguer-Lambert law or the Bouguer-Beer-Lambert law or merely the extinction law. The extinction law is also used in understanding attenuation in physical optics, for photons, neutrons, or rarefied gases. In mathematical physics, this law arises as a solution of the BGK equation. Bouguer-Lambert law: This law is based on observations made by Pierre Bouguer before 1729. It is often attributed to Johann Heinrich Lambert, who cited Bouguer's Essai d'optique sur la gradation de la lumière (Claude Jombert, Paris, 1729) – and even quoted from it – in his Photometria in 1760. Lambert expressed the law, which states that the loss of light intensity when it propagates in a medium is directly proportional to intensity and path length, in the mathematical form used today. Lambert began by assuming that the intensity I of light traveling into an absorbing body would be given by the differential equation: which is compatible with Bouguer's observations. The constant of proportionality μ was often termed the "optical density" of the body. Integrating to find the intensity at a distance d into the body, one obtains: For a homogeneous medium, this reduces to: from which follows the exponential attenuation law: Beer's law: Much later, in 1852, the German scientist August Beer studied another attenuation relation.