TRUE ABSORPTION SPECTRUM 711 



pigments in the cell. Plotted on a semilogarithmic scale (log log [Tq/T] as 

 function of X), the curves with and without scattering would run parallel. 

 If this were the case, the ratios in table 22.VII derived from the transmission 

 curves, log (To/T), would be unaffected by scattering. Closer examination 

 shows why scattering can produce a distortion of the absorption curves 

 in the sense observed. This can be shown with the help of the simple 

 example discussed on page 673 — that of repeated reflections in a plane- 

 parallel absorption cell. The equation usually applied for the calculation 

 of the absorption coefficient, a, is: 



(22.11) a = (1/d) log i^To/T) 



where d is the depth of the absorption cell, and T and Tq the fluxes trans- 

 mitted through the solution and the pure solvent, respectively. This 

 equation was sho\^Ti on page 674 to be a first approximation, neglecting the 

 difference in the reflectances of the two cells. As mentioned on page 674, 

 correct expressions for T and To can be obtained by summation of infinite 

 series. This summation leads to the following relationship : 



(22.12) T = To 10-"^ ( i - ,rio-.«. ) 

 and thus to : 



„ = l[,o.^'-,o.(L^i;i5;=^)] 



Since the term in parentheses is > 1, equation (22.13) shows that the value 

 of a, calculated in the usual way from (22.11), is too large and that the rela- 

 tive error increases with decreasing absorption. With r = 0.1 and To/T = 

 1.01, i. e., an absorption of only 1%, the error in a is 2%. Such an error 

 can be neglected in most absorption measurements. What matters to us, 

 however, is the fact that the percentage error depends on the value of a 

 and therefore changes with wave length. In other words, it causes a distor- 

 tion of the transmission curve. 



The character of this distortion — increase of apparent a values for all 

 wave lengths, but particularly for those in which the true absorption coef- 

 ficient is small — remains the same in scattering media, where the effect 

 becomes much stronger than in plane-parallel cells filled with transparent 

 materials. 



The loss of selectivity by scattering can be even more pronounced in 

 absorption spectra, log (//*S), than in transmission spectra, log (To/T). 

 Radiations that would be only weakly absorbed by straight passage through 

 a leaf (e. g., green or extreme red light) become more strongly absorbed 



