Beers and Lamberts laws

Log (Iq/I) is a dimensionless quantity (strictly speaking, a logarithm of a ratio of light intensities) and is defined as absorbance. Absorbance is the quantity measured and plotted in spectrophotometry. Thus Beer s law states that absorbance is proportional to concentration. 

The second relationship is Lambert s law, (named after the German physicist Johann Heinrich Lambert) which states that the intensity of a beam of parallel, monochromatic light decreases exponentially as the light travels through a thickness of homogeneous medium , expressed mathematically as 

These two fundamental equations are so similar that they can be combined into one relationship, the Beer-Lambert law or equation, which can be expressed as 

Here k is yet another constant, the value of which depends on the units used for the concentration term, c, and on the path length, although this is usually 1 cm. 

If the units of concentration are molarity (i.e. number of moles per litre), then the constant is (the Greek letter epsilon ) and is known as the molar absorptivity, with units of L mol-1 cm-1, although the units are seldom expressed, is equal to the absorbance of a 1 m solution in a cell of path length 1 cm and is usually a large number, approximately 10 000-20 000. In this case the Beer-Lambert equation is written as 

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The Beer law is similar to the Lambert law with the exception that the absorption coefficient is expressed as the product of a unit absorption coefficient and the concentration of particles. In general, this definition is more fundamental and appropriate for application to dispersed media, where the concentration can be directly measured. If there are particles in the medium, depending on their size with respect to the wavelength of the incident radiation, they scatter as well as absorb the incident radiation. With increasing concentration, the multiple scattering effect becomes significant, and the Beer law deviates from the experimental measurements, especially if the size of the particles is comparable to the wavelength of radiation. Under these conditions, the complete radiative transfer equation should be solved. For solid materials, the Beer and Lambert laws are identical. 

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