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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. History 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: − d I = μ I d x , {\displaystyle -\mathrm {d} I=\mu I\mathrm {d} x,} 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: ln ⁡ ( I 0 / I ) = ∫ 0 d μ d x . {\textstyle \ln(I_{0}/I)=\int _{0}^{d}\mu \mathrm {d} x.} For a homogeneous medium, this reduces to: ln ⁡ ( I 0 / I ) = μ d , {\displaystyle \ln(I_{0}/I)=\mu d,} from which follows the exponential attenuation law: I = I 0 e − μ d . {\displaystyle I=I_{0}e^{-\mu d}.} Beer's law: Much later, in 1852, the German scientist August Beer studied another attenuation relation. In the introduction to his classic paper, he wrote: "The absorption of light during the irradiation of a colored substance has often been the object of experiment; but attention has always been directed to the relative diminution of the various colors or, in the case of crystalline bodies, the relation between the absorption and the direction of polarization. Concerning the absolute magnitude of the absorption that a particular ray of light suffers during its propagation through an absorbing medium, there is no information available." By studying absorption of red light in colored aqueous solutions of various salts, he concluded that "the transmittance of a concentrated solution can be derived from a measurement of the transmittance of a dilute solution". It is clear that he understood the exponential relationship, as he wrote: "If λ {\displaystyle {\lambda }} is the coefficient (fraction) of diminution, then this coefficient (fraction) will have the value λ 2 {\displaystyle \lambda ^{2}} for double this thickness." Furthermore Beer stated: "We shall take the absorption coefficient to be the coefficient giving the diminution in amplitude suffered by a light ray as it passes through a unit length of an absorbing material. We then have, according to theory, and as I have found verified by experiment, λ = μ D {\displaystyle \lambda =\mu ^{D}} where μ {\displaystyle \mu } is the absorption coefficient and D {\displaystyle D} the length of the absorbing material traversed in the experiment." This is the relationship that might properly be called Beer's law. There is no evidence that Beer saw concentration and path length as symmetrical variables in an equation in the manner of the Beer-Lambert law. Beer–Lambert law: The modern formulation of the Beer–Lambert law combines the observations of Bouguer and Beer into the mathematical form of Lambert. It correlates the absorbance, most often expressed as the negative decadic logarithm of the transmittance, to both the concentrations of the attenuating species and the thickness of the material sample. An early, possibly the first, modern formulation was given by Robert Luther and Andreas Nikolopulos in 1913. Differences between Bouguer and Beer in application areas While the observations of Bouguer and Beer have a similar form in the Beer–Lambert law, their areas of observation were very different. For both experimenters, the incident beam was well collimated, with a light sensor which preferentially detected directly transmitted light. Beer specifically looked at solutions. Solutions are homogeneous and do not scatter light (Ultraviolet, visible, Infrared) of wavelengths commonly used in analytical spectroscopy (except upon entry and exit). The attenuation of a beam of light within a solution is assumed to be only due to absorption. In order to approximate the conditions required for the Beer Lambert law to hold, often the intensity of transmitted light through a reference sample ( I R ) {\displaystyle (I_{R})} consisting of pure solvent is measured, and compared to the intensity of light transmitted through a sample ( I S ) {\displaystyle (I_{S})} , with the absorbance of the sample taken as: log .... Discover the D Lambert popular books. Find the top 100 most popular D Lambert books.