Bellows factor omitted

Lifted from Break/Fix — unexpectedly soft images and wrong reciprocity corrections, case 7, error 3, with the mechanism from pinhole exposure and reciprocity correction.

What you see

A thin negative with a normal rebate, from a session in which the camera was reconfigured. The symptom is indistinguishable from a missed reciprocity correction on the negative alone.

The tell is in the log rather than in the picture — a computed time from one configuration and a configuration line that changed after it.

Likely causes

1. A frame stacked or removed to reframe a subject, changing the focal distance, and the time not recomputed.
2. A time computed at the bench for one configuration and given in the field in another.
3. A log whose configuration was written after the exposure rather than before it, so that the change was never a decision.

!The course's own wording, because the name of this row is misleading

The register calls this row “bellows factor omitted”, and the course’s exposure lesson establishes that a pinhole has no bellows factor in the sense a lens has one. The f-number of a lens is computed from its focal length while the light travels the image distance, which is what a bellows factor corrects for. In a pinhole, N = f/d already uses the image distance, because there is nowhere else to measure it from, so the correction is inside the number already.

What replaces it is a bookkeeping question — does the f you used to compute the f-number match the f the camera is actually in? The lesson’s own summary is that stacking a frame to make a still life bigger costs a stop and a third, and that it costs it because N changed, “the bellows factor arriving through the front door”. The entry keeps the register’s name and states the mechanism the course actually established.

What is happening: the chemistry and physics

Illuminance at the film goes as the square of the aperture ratio, so changing the focal distance changes the exposure by

exposure factor = (f_actual / f_assumed)²

Extension penalty for a pinhole

Metered and computed for the body alone at f = 50 mm, then both frames stacked to f = 120 mm to reframe, and the time not recomputed — (120/50)² = 5.76, which is 2.53 stops underexposed.

The subject distance does not enter it. The geometry lesson shows the illuminance going as (d/f)² with the subject distance cancelling out, which is why the pinhole’s version of this correction is about the camera and not about how close the subject is.

Diagnostic questions

• What is (f_actual / f_assumed)²? Compute it from the log’s own two numbers. If it accounts for the density, the diagnosis is made.
• Did the configuration change between the computation and the exposure? That is the question the log answers and the negative cannot.
• Is the rebate normal? It must be, or the fault is not exposure.
• Is the discrepancy a clean ratio of two squares? 5.76, 2.25, 1.44 and the like are the signatures of a changed focal distance; a reciprocity error rarely lands on one.
• Rule out the reciprocity errors by recomputing the whole chain in order — speed, aperture, extension, reciprocity.

Corrective action

Nothing on the negative. Re-shoot with the exposure recomputed for the configuration the camera is actually in.

Recompute N whenever the stack changes, before the sheet goes in.

Prevention

Write the configuration in the log before the frames go on. A configuration recorded afterwards is a memory; recorded before, it is a decision, and a decision can be checked against a computation.

Compute the exposure in the order the lesson gives — metered reading, speed, aperture, extension, then reciprocity last, because the reciprocity correction is a function of the whole time up to that point.

Mark each frame with the focal distance it adds, so that a stack can be read at a glance in poor light.