Abstract

In a previous paper, the author analyzed the low intensity reciprocity-failure curve by means of probability formulas applied to the exposure conditions required to establish the stable sub-latent-image speck. Experiments have shown that low intensity reciprocity failure results from instability of the latent image in its initial stages of formation due to thermal motion. The theory given is based on the postulate that a stable subspeck can be formed in a grain only when that grain receives a multiplet hit of size 2, 3, or, in general, s quanta within a small critical time period τ. By application of the probability theory, it is possible to calculate what fraction of grains will acquire a stable subspeck when a large number of identical grains are subjected to an exposure of total duration, t, in which the average number of effective quanta per grain in the whole exposure is y. By varying the time and intensity factors of exposure reciprocally, the reciprocity failure can be calculated and compared with experiment. If it is assumed that the critical τ-period is a constant invariable quantity for all grains, it can be shown that the reciprocity-failure curve has a slope at low intensities that is characteristic of the number of quanta required to establish the stable subspeck, the slope being zero for one quantum,−1 for two quanta,−2 for three quanta, etc. In the present paper, the theory is extended to the case of variable τ-period among the grains, and it is found that the same simple conclusions as to slope of the reciprocity-failure curve hold in this case as were found in the constant τ-period case.

© 1950 Optical Society of America

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