322 nutting: absorption of light 



PHYSICS. — On the absorption of light in heterogeneous media. 

 P. G. Nutting. Eastman Kodak Company. Rochester, 

 N. Y. 



Photographic density depends upon the size and number of the 

 imbedded silver grains and to a shght extent upon their form 

 and distribution as well. The mathematical problem of relating 

 density to grain is obviously to be treated by probability theory 

 rather than by infinitesimal analysis. The solution here presented 

 will be of interest to students of the theories of radiation and of 

 entropy in discontinuous systems, in that it is a much simpler 

 problem treated by similar probability methods. 



Suppose snowflakes of a given size to be falling with perfect 

 irregularity upon a surface. When a given number per unit area 

 have fallen, what will be the mean relative areas covered and 

 uncovered? In the plate grain problem as in the snowflake prob- 

 lem, the distribution is completely irregular, but in a volume 

 instead of a plane. The grains are contained in a layer of the 

 order of 10 to 20^ thick and are themselves 0.5 to 3m in diameter, 

 irregular in outline and fairly uniform in area in any one plate. 

 The grains are not crystals, but aggregates of finely divided silver 

 resembling platinum black or soot, of very high absorbing and 

 low reflecting power. This reflecting power has not yet been 

 directly determined, but estimates based on scattering make it 

 well under 2 per cent. In the following discussion both reflec- 

 tion and diffusion are neglected, tho both may be readily entered 

 in the equations. 



Consider the absorbing body divided into layers about 1 grain 

 thick, parallel with the surface, so that there will be but a negli- 

 gible amount of overlapping of grains in any one layer. That 

 certain grains lie partly in two successive layers is of no conse- 

 quence, since in the equations they are counted but once in the 

 layer in which their greater bulk lies. In the first layer let there 

 be ni, grains per unit area and let ai be their average projected 

 area. Then the probability of a ray of light being stopped by 

 this layer is the ratio of the covered to the total area, or as ni Oi 

 to 1. Similarly the probability of a ray passing the first layer is 



