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XIX. Quantum Theory of Photographic Exposure. 



By L. SlLBERSTEIN, Ph.D.* 



1. rriHE purpose of the present paper is to describe a first 

 JL attempt at a light-quantum theory of photographic 

 exposure, or of the production of the so-called latent image, 

 with the immediate consequences of such a theory and some 

 of its experimental tests. 



The silver-halide grains of an emulsion spread over a plate 

 or a film base may be considered (apart from the smallest 

 grains) as small flat plates, of comparatively small thickness, 

 which in a dry emulsion lie almost parallel to the base. The 

 sizes a (areas) of these plates range from submicroscopic ones 

 up to 18 or 20 square microns. Even the most uniform 

 emulsions obtainable in practice consist of grains of different 

 sizes, the distribution of sizes among the grains being in 

 each case characterized by what is technically called " the 

 frequency curve " of an emulsion. In what follows the 

 number, per unit area of the photographic plate, of grains 

 whose areas range from a to a -{-da will be denoted hyf(a)da 9 

 and a photographic emulsion will be shortly referred to as 

 being of the type /(a). For certain emulsions /(a) is, with 

 good approximation, an exponential, for others a Gaussian 

 error-function of the area a, and so on. 



2. Without, for the present, dwelling any longer upon 

 details of this kind, we may pass at once to our main 

 subject. 



According to Einstein's well-known hypothesis of 1905 

 light does not consist in a continuous distribution of energy, as 

 in the classical theory, but is entirety split up into light quanta 

 or discrete parcels of very concentrated monochromatic light, 

 each parcel containing a quantum of energy, hv = h\/c, 

 in obvious symbols. Somewhat more generally we may 

 assume that only a fraction olE of the total light energy 

 E is thus split into concentrated parcels, the remainder 

 E = (l — ct)E being distributed continuously t> without 

 however prejudicing the possibility of E being zero. 

 Then, if E be the energetic value of a monochromatic 



* Paper read December 28, 1921, at the Toronto meetiug of the 

 American Physical Society in affiliation with Section B of the American 

 Association for the Advancement of Science. Communication No. 139 

 from the Research Laboratory of the Eastman Kodak Company. 



t Somewhat as in E. Marx's theory of " concentration places " or of 

 " light specks'' as suggested by Sir J. J. Thomson. 



Phil Mag. S. 6. Vol. 44. No. 259. July 1922. S 



