Reciprocity Failure applies to analog, silver-halide-based films, resulting in non-linear behavior between exposure time and exposure result.

The problem with silver halide film is that most emulsions require the absorption of several photons to activate the halide into a stable higher-energy state. If an insufficient number of photons is received, the halide will transition to a higher energy state that isn't stable and then after some (very) short period of time, decay back down to the unexposed, minimal-energy state.

If the rate of photon arrival is high, a halide molecule absorbing only a single photon is likely to absorb another photon before it decays again, so the rate of arrival doesn't really matter and the film exhibits reciprocity.

If the rate of photon arrival is low, there is a finite probability that a partially energized halide will decay before absorbing the next photon. As the illumination decreases (and therefore the photon arrival rate slows), the probability of decay increases accordingly and the effective sensitivity of the film is reduced because more of the incoming photons are effectively lost to the decay process.

Ref.: Analogue Photography and Film FAQ: Reciprocity Failure

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