Low Intensity Reciprocity-Law Failure in Photographic Exposure: Energy Depth of Electron Traps in Latent-Image Formation; Number of Quanta Required to Form the Stable Sublatent Image*†

Abstract

A method is outlined whereby the energy depth, ∊, of the traps for the initially trapped electrons in latent-image formation can be determined from measurements of reciprocity-law failure at two different temperatures, T1 and T2. The analysis leads to the equation for determining ∊, logt2t1=0.434∊k(1T1-1T2),where t1 and t2 are the exposure times of two low intensity exposures of equal density and equal efficiency made at the two temperatures, and k is the Boltzmann constant.Experimental reciprocity-law failure curves for different temperatures are given for a series of emulsions, including results obtained with surface, internal, and total development. The average value of ∊ found from several commercial emulsions using total development is 0.77 ev, and for one experimental emulsion using internal development, 0.65 ev.A theoretical study of low intensity reciprocity-law failure is carried out by probability equations derived by L. Silberstein. These equations are used to calculate the fractions of grains that acquire a just-stable sublatent-image speck under the conditions that its establishment requires the absorption of 1, 2, or 3 quanta within a critical time, τ. It is found from this analysis that the reciprocity-failure curves approach the limiting slopes of 0, 1, or 2 at low intensities for the respective cases of singlet, doublet, or triplet hits in time, τ. This gives a sharp criterion for distinguishing between these cases, and comparison of experimental and theoretical curves indicates that the absorption of 2 effective quanta within a time, τ, is required to form the stable subimage speck.Experimental reciprocity-failure curves at different temperatures indicate that the curves at different temperatures have the same shape but are shifted in the direction of lower intensity with lowered temperature. An explanation of this phenomenon is obtained from the theoretical treatment of the reciprocity-failure curves in terms of the critical time, τ.Finally, the reciprocity-failure characteristic of the developable latent-image is derived from the curve for the stable subimage by assuming that the subimage is formed by 2 quanta within a time, τ, and then brought to developable size by the addition of 6 more quanta. This procedure yields a reciprocity curve that is in good agreement with experimental measurements carried out here and that is also of the generally correct shape to represent the reciprocity-failure characteristic at low intensities.