674 LIGHT ABSORPTION BY PIGMENTS IN VIVO CHAP. 22 



of the weakening that hght suffers in passing through the absorbing me- 

 dium). A second approximation, which can be substituted for (22.2b), is: 



(22.5) A = To - T + I{1 - r)[r(l - lO-^^-^j] 



where a is the absorption coefficient of the soUition and d the thickness 

 of the cell. In this equation, consideration has been given to one reflection 

 from the front wall (factor 1 — r) and one reflection from the back wall 

 (factor in brackets) . However, these reflections are only the beginning of 

 an infinite series (as with two mirrors on opposite walls) . The exact equa- 

 tion for A in terms of the properties of the blank cell is : 



(22.6) A = {To - T) + {Ro - R) 



where Ro and R are the total light fluxes reflected by the blank cell and the 

 solution cell, respectively. 



If a and r are known, exact values of To, T, Ro and R can be obtained 

 by the summation of infinite power series. 



If the light "trapped" between the walls leaves the cell after an odd number of pas- 

 sages, it is added to the transmitted ilux; if it escapes after an even number of passages, 

 it is added to the reflected flux. Consequently, the series for T contains only even 

 powers of r and odd powers of 10""'^, and the series for R only odd powers of r and even 

 powers of lO""''. (The ratio of the sums for T and To is given in equation 22.12.) 



If a and r are unknown, R (and Ro) must be determined experimentally. 



Since repeated reflection lengthens the average path of the light in the 

 absorption cell, it increases absorption. In the case of homogeneous solu- 

 tions in plane-parallel glass cells, this increase represents only a minor cor- 

 rection (to be estimated on page 711); we mention it merely to illustrate 

 the complications in the measurement of light absorption that arise from 

 the presence of phase boundaries. In nonhomogeneous systems, the com- 

 plications are similar in principle, but much more important quantita- 

 tively. Reflections are not only more numerous, but also stronger (because 

 of the varying angles with which the light strikes the interfaces) ; and they 

 are supplemented by refractions and total inner reflections, which all af- 

 fect the length of the path of the light beam and the direction in which it 

 leaves the medium. 



Leaves and thalli are heterogeneous systems, with numerous phase 

 boundaries between ah- channels, cell w'alls, cytoplasm, vacuoles, plastids 

 and starch grains ; and the passage of light through plants or plant organs 

 is, therefore, a very complicated phenomenon. It has been repeatedly dis- 

 cussed—by Willstatter and Stoll (1918), Briggs (1929), Mestre (1935), 

 Seybold and co-workers (19321-2, 1933'-'-, 1934, 1943), Schanderl and 

 Kaempfert (1933), Meyer (1939) and Loomis (1941, 1949), among others— 

 but these discussions have not gone far beyond the qualitative stage. 



