On the light fading of a reflecting dye layer

摘要

A theory is presented of the light-fading kinetics of a layer consisting of an initially uniform molecular dispersion of dye in a transparent binder in optical contact with an ideally reflecting substrate, it being assumed that the product of fading is also transparent. The method is based on that used for a transmitting system and involves the mathematical formulation of the problem in terms of the variations with depth in the layer and time of exposure of the light fluxes in and out of the layer and the dye concentration. It is shown that the general solution to the partial differential equation for dye concentration for the reflecting system is the same as that for the transmission case but, whereas an exact analytical solution is available for the latter case, the particular solution obtaining in the former case involves the numerical solution of an auxiliary equation. It is also shown that the initial curvatures of plots of reflection density versus time of exposure, which for some materials have been experimentally observed to vary from positive to negative with increasing initial density, can be explained in terms of practical densitometry.