Reciprocity (photography)

In photography reciprocity is the inverse relationship between the intensity and duration of light that determines the reaction of light-sensitive material. Within a normal exposure range for film stock, for example, the reciprocity law states that the film response will be determined by the total exposure, defined as intensity × time. Therefore, the same response (for example, the optical density of the developed film) can result from reducing duration and increasing light intensity, and vice versa.

The reciprocal relationship is assumed in most sensitometry, for example when measuring a Hurter and Driffield curve (optical density versus logarithm of total exposure) for a photographic emulsion. Total exposure of the film or sensor, the product of focal-plane illuminance times exposure time, is measured in lux seconds.

The idea of reciprocity, once known as Bunsen–Roscoe reciprocity, originated from the work of Robert Bunsen and Henry Roscoe in 1862.

Deviations from the reciprocity law were reported by Captain William de Wiveleslie Abney in 1893, and extensively studied by Karl Schwarzschild in 1899. Schwarzschild's model was found wanting by Abney and by Englisch, and better models have been proposed in subsequent decades of the early twentieth century. In 1913, Kron formulated an equation to describe the effect in terms of curves of constant density, which J. Halm adopted and modified, leading to the "Kron–Halm catenary equation" or "Kron–Halm–Webb formula" to describe departures from reciprocity.

In photography, reciprocity refers to the relationship whereby the total light energy – proportional to the total exposure, the product of the light intensity and exposure time, controlled by aperture and shutter speed, respectively – determines the effect of the light on the film. That is, an increase of brightness by a certain factor is exactly compensated by a decrease of exposure time by the same factor, and vice versa. In other words, there is under normal circumstances a reciprocal proportion between aperture area and shutter speed for a given photographic result, with a wider aperture requiring a faster shutter speed for the same effect. For example, an EV of 10 may be achieved with an aperture (f-number) of f/2.8 and a shutter speed of 1/125 s. The same exposure is achieved by doubling the aperture area to f/2 and halving the exposure time to 1/250 s, or by halving the aperture area to f/4 and doubling the exposure time to 1/60 s; in each case the response of the film is expected to be the same.

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