INTRODUCTION AND METHODS 



only 25 per cent at Ag, then doubling the concentration can make 

 little difference to the light absorbed at Aj, while there is plenty of 

 scope left at Ag for further absorption. As the concentration in- 

 creases, the absorption spectra approach the theoretical limit for 

 infinite concentration which is, of course, 100 per cent absorption of 

 all wavelengths. With decreasing concentration, the absorption 

 spectra (when expressed as percentages of their respective maxima) 

 approach a limiting curve shown by the dotted Hne in Fig. 1.6 (B). 



Absorption spectra thus have the disadvantage that their shape 

 depends on the concentration of the solution. This makes it difficult 

 to compare results from solutions of different strengths. 



However, there is another way of expressing results which is free 

 from this objection. Consider the visual pigment solution of depth / 

 (Fig. 1.5) to be made up of an infinite number of thin plates dl. 

 Then, if the intensity of light incident on one of these plates is /, a 

 portion, dl^ of the light will be absorbed. If the solution is homo- 

 geneous the fraction, dljl, of light absorbed will be the same for 

 each plate and will depend on the thickness, dl, the concentration c, 

 and a coefficient a^, peculiar to the absorption characteristics of the 

 pigment and the wavelength, A, of the light. Thus, 



dljI =oiA.c.dl 

 Integrating this between the hmits / = Zinc and / = /trans, we have, 



loge hnclhians = Of-x . C . I 



The quantity loge /inc//trans is the optical density. In most work 

 common, not natural, logarithms are used. In these units the optical 

 density is given by, 



Dx = logio /lnc//trans = (X-X . C . //2-303 

 In Fig. 1.7 (A) are shown the density spectra (i.e. the variation of 

 Dx with A) for the same pure visual purple solutions as were illus- 

 trated in Fig. 1.6(A). Density spectra have the advantage over 

 absorption spectra that, when expressed as percentages of their 

 respective maxima (Fig. 1.7 (B)), they become identical, irrespective 

 of the concentration. This readily follows from the definition of 

 optical density, for, if the density Dx at the wavelength A is expressed 

 in terms of the density Z>max at the maximum, we have, 

 Dx _ ccxc . I _ ccx 

 DmsiX otmax C . / OCmax 



the concentration and optical-path terms canceUing out, 



15 



