When the arithmetic breaks
Film exposure rests on a simple rule: double the light, halve the time. This reciprocity — the even trade between intensity and duration — holds across a comfortable middle range. Extend the exposure beyond a few seconds, however, and the rule quietly stops working.
The film grows less sensitive the longer it is asked to wait, so the calculated time is no longer the correct time. This is reciprocity failure, and every photographer who has shot by twilight or under a full moon has encountered it, whether they knew the name or not.
The mechanism sits inside the emulsion itself. Silver halide grains capture photons and form what is called a latent image — a cluster of metallic silver atoms too small to see, which developer will later amplify into a visible deposit. At normal exposures the clusters build steadily. At very long exposures, photons arrive so slowly that some partially-formed clusters become unstable and fall apart before the next photon arrives. The latent image regresses. The film records less than the incident light suggests it should, and the resulting negative is thinner than expected.
The fix is additional exposure — but the correction is not linear. A calculated exposure of ten seconds may need fifteen or twenty; a calculated sixty seconds may need two minutes or more. Each film has its own curve, and the manufacturers who still publish data sheets — Kodak, Ilford, Fuji — give reciprocity correction tables for their stocks. These figures are worth consulting rather than guessing: a two-stop underestimate on a moonlit landscape means a second trip to the same hillside.
Colour film adds a further complication. The three dye-forming layers — sensitive to blue, green and red respectively — each fail at a slightly different rate, so long exposures on three-layer film introduce colour casts that no single filtration correction can fully flatten. Tungsten-balanced stock mitigates the problem for artificial-light work; for natural long exposures the cast is often simply accepted as part of the result.
The severity of the effect varies from one emulsion to another, whatever the format; orthochromatic emulsions behave differently from panchromatic ones. The effect is also temperature-sensitive, which is one reason night workers shooting in cold air sometimes find empirical corrections from summer fieldwork do not quite transfer. The effect was characterised mathematically by Karl Schwarzschild in 1900 — the same Schwarzschild who later gave his name to black holes — making it one of the few corners of astrophysics that still reaches into the darkroom.