The Effect of Absorption on the Characteristic Curve of Thick Emulsions

A general theorem is presented which makes it possible to express the probability of a certain fraction of grains of an emulsion of finite thickness d becoming developable as a result of an exposure E, provided that the emulsion absorbs light exponentially according to beer's law, and provided also that a power series expression is available for the probability of a single grain becoming developable as a result of the same exposure The theorem allows testing of the relation between exposure and developability of grains without the necessity of grain counts on single grain layer emulsions. It is applied to the specific case of the Poisson distribution of exposure to obtain a power series representation for the Poisson distribution to exposure in thick emulsions. The consequences of this formula are to be worked out in a future paper. The usefulness of the theorem is not restricted to the absorption of light quanta only, for it applies to any particles whatsoever which are absorbed according to Beer's law in a medium where photochemical or nuclear reactions are produced by the bombarding radiation