PRESENTATION OF DATA 145 



Beer's Law of Absorption 



The absorption law is used in various forms. Beer (1852) used it 

 for solutions to describe the absorption of monochromatic light in 

 which the solvent contributed nothing to the absorption. If we con- 

 sider the absorbing layers as having molecular structure, and if we can 

 say that each molecule absorbs an equal fraction of the energy which 

 passes over it, then Beer's law expresses the absorptions in terms of 

 concentrations of the absorbing layers. 



Let c be the concentration of a solution; then, if 7 is the entering 

 intensity and Id the reduced intensity upon leaving an absorbing layer 

 of thickness d, Beer's law states that 



Id = he~ acd 



where a is called the absorption coefficient. Beer's law holds only when 

 the absorbing property of a molecule is not influenced by the proximity 

 of its neighbors, which condition is not always true. 



It must be emphasized that the laws of absorption apply only to 

 monochromatic radiation and cannot be rigorously applied to the 

 absorption of narrow bands of spectral wavelengths or to the absorption 

 of extended spectral regions. 



Extinction Coefficient 



A common practice (after Bunsen and Roscoe) is to express the 

 absorption as the reciprocal of the thickness which is necessary to 

 weaken the light to one tenth of its incident value. This definition 



gives 



I d = I Q lQT kd and I d = I l(T tCd 



or 



logio — = kd and logi — = eCd 

 Id id 



where k is called the extinction coefficient, and e is the molecular extinction 

 coefficient. The extinction coefficient (k) is used when the molecular 

 weight of the absorbing material is not known, The concentration C is 

 expressed in moles per liter. 



Presentation of Data 



Figure IV-8 illustrates the use of transmissivity (Id/Io) in presenting 

 data. Graph 1 in this figure shows how the transparency of an 0.08-mm 

 thickness of human epidermis varies with the incident energy at the 

 wavelengths designated (Lucas [1931]). Superimposed is graph 2, 



