Reciprocity Law Failure

(Schwarzschild effect), a phenomenon manifested in the fact that, all other conditions being equal, the same exposure H = Et of a photographic material has a different photographic effect for different ratios of the illumination E of the photosensitive emulsion and the exposure time t. This noninterchangeability of the intensity and duration of the illumination of the photosensitive emulsion, which violates the Bunsen-Roscoe law, was first studied in detail by K. Schwarzschild in 1899–1900. Reciprocity law failure is of great importance for graphic photography and especially for photographic photometry, in which a photosensitive emulsion is used for quantitative measurement of optical radiation.

As a result of reciprocity law failure, the basic functional dependence of the photographic process—the characteristic curve D = f (log H)—proves to be unambiguously defined: its shape, slope, and position with respect to the exposure axis depend on the length of time for which the photographic material is exposed. Reciprocity law failure is shown graphically by reciprocity curves, which represent the dependence on the exposure time or illumination of the exposure HD required to produce a given optical density D:log H_D = f (log t), where E = const., or correspondingly log H_D =∅(log E), where t = const. Here it is assumed that certain conditions of development of the photographic material are maintained.

A typical reciprocity curve (Figure 1) is concave. Its two gently sloping segments approximately satisfy the Bunsen-Roscoe reciprocity law (for exposure times ≤ 10 -⁵ sec and ∽ 10^_1 to 3 × 10^-3 sec). The exposure time t₀ on the second gently sloping segment, which corresponds to the minimum of log H_D, is called the optimum exposure time, since the photosensitivity of the photographic material, S = /H_D, is a maximum for this exposure.

Figure 1. Typical reciprocity curve for a highly sensitive photographic material

The shape of the reciprocity curve depends on the optical density D (the reference density; Figure 2) for which the curve has been constructed, and also on the development time, the type of photographic material and the temperature of the photosensitive emulsion. At the same time, the shape is virtually independent of the wavelength of the incident radiation. Photographic materials exist that have a very low reciprocity law failure for long exposure times; this is especially valuable for astronomical applications of photography. No reciprocity law failure is observed in the photographic action of radiations for which the energy of each individual quantum is high (X rays and gamma radiation).

Figure 2. Family of reciprocity curves of a photographic material; the curves correspond to different reference optical densities for the same development time f_dev. The circles on the curves correspond to optimum exposure times. A rise in the curves signifies a decrease in the photosensitivity of the material. Convergence of the curves signifies an increase in the contrast coefficient 7.

Reciprocity law failure is due mainly to two physical factors: (1) the relative durations of the electron and ionic stages in the formation of the latent photographic image, and (2) the process of thermal diffusion (regression) of the silver centers of the image. At high illuminations and short exposure times, the first factor plays the primary role, whereas at low illuminations and long exposure times the second factor is predominant.