A meter that reads correctly in daylight can underexpose badly once the indicated shutter time stretches into seconds. Meter a moonlit landscape at, say, EV -3 and the cell may hand you 30 seconds; expose for exactly that and the negative comes back thin, because at low light levels the film has stopped responding in proportion to exposure. This is reciprocity failure, and the gap between the indicated time and the time the film actually needs grows the longer the shutter stays open. Understanding the effect, and the data manufacturers publish for it, is what separates a usable night or pinhole negative from a wasted one.

The Schwarzschild law and its exponent

The Bunsen-Roscoe reciprocity law states that photochemical effect is the product of intensity and time, so halving the light and doubling the time should yield the same density. The law holds across the normal range of shutter speeds and breaks at both extremes. W. de W. Abney reported deviations as early as 1893, and in 1899 Karl Schwarzschild, working with silver bromide gelatine plates, quantified the long-exposure end: density follows I × t^p = constant, the Schwarzschild law, where the exponent p is less than one. Schwarzschild measured p = 0.86 for his plates; for photographic emulsions it generally falls between 0.7 and 0.9.

That exponent of less than one is the whole story. If p were exactly 1 the reciprocity law would hold and no correction would be needed. Because p < 1, a film at low intensity accumulates density more slowly than the metered time predicts, and the shortfall compounds as the time grows. The per-film correction exponent Ilford publishes, written P and always greater than one, is simply the inverse manoeuvre: it is the power you raise the metered time to in order to undo the p < 1 deficit. The “doubling is not enough” rule of thumb and the formula are the same idea seen from two ends.

Why sensitivity falls off

The mechanism is photochemical, and it is specifically a problem of the long, dim exposure — low-intensity reciprocity failure. A silver halide grain only becomes developable once a cluster of reduced silver atoms, commonly reckoned at three to four atoms, has formed at a sensitivity speck. Building that cluster takes several photon hits within the lifetime of the intermediate sub-latent-image specks. In a bright exposure the photons arrive fast enough that the cluster reaches its stable threshold before anything decays. At a trickle of photons the specks regress between hits, decaying back before the cluster stabilises, so a grain that should have been exposed simply is not. Ilford’s technical information attributes the loss to this “reduced efficiency in forming stable development centres with lower levels of light”, and it is why effective film speed falls, and falls faster, the longer the exposure runs.

Reading a stock’s reciprocity data

Manufacturers express the correction in two formats, and the difference reflects how each chose to model the curve. Kodak publishes a discrete lookup table. Its datasheet F-4016 for T-MAX 100 lists no adjustment for indicated times from 1/1000 to 1/10 second, then plus one-third stop at 1 second, plus one-half stop at a metered 10 seconds (an adjusted time of 15 seconds), and a full stop at 100 seconds (an adjusted 200 seconds). Note the short end: the same table also calls for plus one-third stop at 1/10000 second. That is high-intensity reciprocity failure, the other broken extreme of the Schwarzschild curve, where photons arrive too fast for the grain to use efficiently — relevant to electronic flash, less so to landscape work, but Kodak documents it.

Ilford instead fits a single power-law exponent per emulsion and gives you the formula Tc = Tm^P, where Tm is the metered time in seconds, Tc the corrected time, and P the per-film factor. From its Technical Information sheet Film Reciprocity Failure Compensation (HARMAN technology, Dec 2023): P = 1.31 for HP5 Plus and XP2, 1.26 for FP4 Plus, Delta 100 and Kentmere 100, 1.41 for Delta 400, 1.33 for Pan F Plus and Delta 3200, 1.43 for SFX. A higher exponent means a steeper penalty at long times. That same document records a change of method: Ilford’s older Fact Sheets used a single graph built on one factor for every film, until they measured a speed-reduction factor per emulsion and switched to publishing the individual exponents. The figures cited here are the post-revision numbers, and they can change between document revisions.

One difference matters in practice. Ilford states that exposures of one second or shorter need no compensation. Kodak does not: its T-MAX 100 table already asks for plus one-third stop at 1 second, with no compensation only out to 1/10 second. The two makers do not agree on where the threshold sits, so read the sheet for the film in your camera rather than carrying one rule across brands.

How far the spread runs between films

Film choice changes the magnitude of the problem more than any technique can. From one 30-second meter reading, three stocks diverge sharply. On HP5 Plus, Tc = 30^1.31 ≈ 85 seconds; a metered minute, 60^1.31, becomes about 210 seconds, roughly three and a half minutes; a metered 5 seconds, 5^1.31, is only about 8 seconds. On FP4 Plus or Delta 100, with P = 1.26, the same 30 seconds needs about 73 seconds. Kodak’s T-MAX 100 has improved reciprocity by design and needs little correction and no special processing at normal exposures.

At the immune end sits Fujifilm Neopan 100 Acros, built on the firm’s Super Fine-Sigma grain technology and sold for astronomical and night work: its datasheet asks for no compensation at all below 120 seconds, and only plus one-half stop from 120 up to 1000 seconds. At the punishing end sit traditional cubic-grain emulsions. Fomapan 100 Classic’s datasheet lengthens a metered 10 seconds eightfold, to 80 seconds, and a metered 100 seconds sixteenfold, to 1600 seconds — more than 26 minutes against the same scene where Acros wants barely a correction. For long-exposure work the film is the first decision, not the last.

Contrast, metering and the safety margin

Two secondary effects accompany the correction. Contrast tends to rise. Shadows sit deeper in the reciprocity region than highlights, so they suffer more failure and the negative’s tonal range expands; Ilford notes that “pulling the development may be required” when the range of light levels in the scene is wide. A 10 to 20 per cent cut in development time is a sensible starting point to calibrate from, not a fixed figure. At very low light the meter itself loses accuracy, so manufacturers concede that extreme exposures may need trial and error. Bracketing by a stop is prudent insurance. The published figures are a reliable starting point, not a guarantee of a perfect negative.