606 VI. CAROTENOIDS AND RELATED COMPOUNDS 



designated as E (1%, 1 cm.). It can be determined for each carotenoid for 

 each specific wave length by calculation from the following general formula: 



E (1%, 1 cm.) = {1/cd) log (l/D 



where c = concentration of substance in grams per 100 milliters, d = 

 length of light path through solution in centimeters, and log (l/T) = optical 

 density. l/T is the reciprocal of the fraction of "incident" light which is 

 transmitted through the solution. It is frequently replaced by the expres- 

 sion, log (lo/Ix), where h is the incident light and Ix is the transmitted 

 light. If 90% of the incident light is absorbed in the solution, 10% is 

 transmitted, and the value for log (l/T) becomes 1.00. Thus log 100% 

 (incident light) - log 10% (transmitted light) = 2 - 1 = 1.00. When 

 the instrument is set at 100% transmittance for the pure solvent, the 

 expression log (l/T) is the optical (or photometric) density. This figure is 

 read directly from the dial setting on such instruments as the Beckman 

 spectrophotometer. In most cases, one attempts to have solutions of such 

 concentration that the optical densities recorded will be between 0.3 and 

 0.8. However, in many cases there is still a direct correspondence with 

 Beer's law when solutions of such concentration as to give an optical density 

 over 1.0 are employed. The maximum optical density possible when 100% 

 absorption occurs is 2.0. 



Because of the small concentrations of carotenoids usually employed, it 

 has been the custom to express the extinction values in this case as molec- 

 ular extinction values (£'moi. or e). These may be calculated by the modi- 

 fied formulas given below: 



6 = (l/cd) log (l/T) 



where c = concentration in gram molecules per liter (moles), d = length of 

 light path through the solution in centimeters, log (l/T) = optical density, 

 and: 



€ = (1/cd) In (l/T) 



The In e formula is used in place of the log e when it is desirable to compress 

 data in comparing substances having a widely different value for e on the 

 same graph. 



The absorption spectrum of carotene and of xanthophyll is readily 

 demonstrated from the spectrogram given in Plate 1. Thus, one sees that 

 both carotene and xanthophyll, in alcoholic solution, exhibit three absorp- 

 tion bands of different widths, which also vary in position depending upon 

 the particular carotenoid employed. When carbon disulfide is employed 

 as the solvent, only two bands are visible, and these are placed at a some- 

 what higher wave length. 



