In photography and holography, reciprocity refers to the inverse relationship between the intensity and duration of light that determines exposure of light-sensitive material. Within a normal exposure range for film stock, for example, the reciprocity law states that exposure = intensity × time. Therefore, the same exposure 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 for a photographic emulsion, where the exposure is measured in lux seconds.
In photography, reciprocity refers to the relationship between different choices of aperture and shutter speed that result in identical exposure. Photochemicals exist for which the equation holds true in common cases. Outside of the normal range, the reciprocity law does not describe the actual behavior of light-sensitive material. This is known as reciprocity failure. At very low light levels, for example, the corresponding increase in duration required to produce an exposure can be higher than the formula states. That is, at 1/2 of the light required for a normal exposure, the duration may have to be more than doubled to expose the media.
In most situations there is an inverse linear relationship between aperture and shutter speed, with a wider aperture requiring a faster shutter speed for the same exposure. For example, an exposure value of 10 may be achieved with an aperture of f/2.8 and a shutter speed of 1/125 s. The same exposure can also be achieved by doubling the aperture to f/2 and halving the shutter speed to 1/250 s; or by halving the aperture to f/4.0 and doubling the shutter speed to 1/60 s.
However, during very long exposures, film responds much more slowly than usual due to the fact that light is in fact composed of quanta known as photons, and film in turn is composed of discrete grains. The light sensitive grains within the film, crystals of a silver halide, must be hit by a certain number of photons within a certain timeframe in order for the light-driven reaction to occur and the latent image to form. In particular, if the surface of the silver halide crystal or film grain has approximately four or more ionised silver atoms, corresponding to an absorption of four or more photons, it is rendered developable.
This breakdown in the linear relationship between aperture and shutter speed is known as reciprocity failure. Each different film "emulsion" has a different response to long exposure. Some films are very susceptible to reciprocity failure, and others much less so. Some films that are very light sensitive at normal illumination levels and normal exposure times lose much of their their sensitivity at long exposure times, becoming effectively a "slow" film for long exposure. Conversely some films that are "slow" under normal exposure duration retain their light sensitivity better at long exposures. Compared at very long exposure times, Kodak's T-Max 100 speed film is faster than Tri-X 400 speed. Most film manufacturers publish data on the necessary reciprocity corrections.
For example, for a given film, if a light meter indicates a required EV of 5 and the photographer sets the aperture to f/11, then ordinarily a 4 second exposure would be required; a reciprocity correction factor of 1.5 would mean that the actual exposure would need to be extended to 6 seconds. Reciprocity failure generally occurs at exposures of longer than 1 second and below 1ms for film, and above 30s for paper.
Reciprocity effects can also occur within the tonal range of a photographic scene when at the limit of exposure, resulting in burnt highlights while losing detail in the shadows. The composition of the film stock used, and in particular the relative amounts of silver bromide, silver chloride and silver iodide, can adjust this tonal response for the desired effect.
The linear relationship of exposure also breaks down at extremely high levels of illumination, but this is generally of more concern to physicists than photographers, as such short (<1 ms) exposures are only required for such subjects as exploding atomic bombs and particle physics, or when taking high-speed motion pictures with short duration shutters (1/10,000 or shorter).
Reciprocity failure can also be seen when using a technique to achieve a smaller aperture by firing a flash multiple times within the same exposure to achieve greater depth of field. In a completely dark room with even the indicator lights on a camera taped over, the shutter can be left open on its Bulb setting and the flash fired repeatedly.
Since each f-stop difference allows either twice as much or half as much light, doubling the number of times the flash is fired gives twice as much light or a one f-stop difference.
So if a single flash gives an exposure value of f4, firing it twice would give twice as much light for an aperture of f5.6, firing it 4 times would give f8, 8 times would give f11...
This multiple flash technique encounters reciprocity failure after achieving an increase of about 3 f-stops or 8 firings of the flash unit.
Reciprocity Failure is a huge concern in the field of film based astrophotography. Deep-sky such as galaxies and nebula are often so faint that they are not even visible to the unaided eye. To make matters worse, many object's spectra do not line up with the most sensitive areas of film. Now add in the fact that many of these targets are small and require long focal lengths, which can push the focal ratio far above f/5. Combined, this makes these targets extremely difficult to capture with film, and exposures from 30 minutes to well over an hour are typical. As a typical example, capturing an image of the Andromeda Galaxy at f/4 will take about 30 minutes to get a decent image. To get the same density at f/8 would require an exposure of at least 120 minutes! When you are trying to track an object (remember, the Earth is moving all during the exposure) every minute is difficult - so reciprocity failure is one of the biggest motivations for astronomers to switch to digital imaging.
A similar problem exists in holography. The total energy required when exposing holographic film using a continuous wave laser (i.e. for several seconds) is significantly less than the total energy required when exposing holographic film using a pulsed laser (i.e. around 20–40 nanoseconds) due to a reciprocity failure. It can also be caused by very long or very short exposures with a continuous wave laser. To try to offset the reduced brightness of the film due to reciprocity failure, a method called latensification can be used. This is usually done directly after the holographic exposure and using an incoherent light source (such as a 25-40W light bulb). Exposing the holographic film to the light for a few seconds can increase the brightness of the hologram by an order of magnitude.