Absorption of EM radiation by matter - Beers law

When electromagnetic radiation passes through transparent matter, some of it is absorbed. Strong absorption will occur if there is a close match between the frequency of the radiation and the energy of one of the possible electronic or molecular absorption processes characteristic of the medium. A plot of absorbance (A) against wavelength (X) or frequency (v) for a particular material is termed an absorption spectrum. The complexity of the absorption spectrum depends on whether atomic (simple, with a few sharp absorption bands) or molecular (complex, with many broad bands) processes are responsible. 

For monochromatic radiation, the reduction in power as the beam travels through the material is proportional to the number of absorbing particles in the path of the beam, i.e., 

If we invert the logarithmic quotient to remove the negative sign on the right-hand side, and convert for convenience from natural to base ten logarithms, we may reexpress this relationship as follows  

Beer s law (Beer 1852), which, because it builds on earlier observations by Bouguer and Lambert, is also known as the Beer Lambert law. 

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