Pinhole Exposure and Reciprocity Correction

Your camera works at f/200 to f/300. Your meter stops at f/32 and probably at f/22. Your paper is seven stops slower than the film the meter’s scale was designed around, and the exposures it needs are long enough that the material stops obeying the law the meter assumes. There are four separate gaps there, each with its own arithmetic, and this page closes them one at a time and then shows the four applied together to real scenes.

Nothing here re-derives reciprocity failure. Part IV owns the mechanism, Schwarzschild’s exponent and the reason the correction exists at all; go back to reciprocity and the life of the latent image if the why is unclear. This page is the how, in the field, with a stopwatch.

What a meter actually reports

Two instruments, two different questions.

A reflected-light meter — the one in a camera, in a phone app, and in the “reflected” mode of a hand meter — measures the light coming back from whatever it is pointed at, and reports the exposure that would place that reading in the middle of the tonal scale. It does not know whether it is looking at a white wall or a black cat, so it renders both as mid-grey and it is wrong by the same amount in opposite directions.

An incident-light meter — a hand meter with a white dome over its cell, held at the subject and pointed back at the camera — measures the light falling on the subject and reports the exposure that will render the subject’s own tones correctly, whatever they are. For pinhole work in daylight the incident reading is usually the better one, because the scenes are wide, contain sky, and defeat a reflected meter’s averaging.

Both convert a light measurement into an exposure through a calibration constant, and the two relations have the same shape:

N² / t = L S / K

Reflected-light exposure relation

N² / t = E S / C

Incident-light exposure relation

N is the f-number, t the time in seconds, S the arithmetic ISO speed, L the scene luminance in candelas per square metre, E the illuminance in lux, and K and C are calibration constants fixed by the meter’s design. This course has not been able to read ISO 2720, the standard that specifies general-purpose exposure meters, because it is not published free of charge, and it therefore quotes no value for K or C from it. A value for C is derived from cited data later on this page; K is left as a symbol, because everything the reflected route needs on this page can be done in stops relative to a reading, which needs no constant at all.

Exposure value is the same information in one number: EV is the base-two logarithm of N²/t, so f/16 at 1/500 s is EV = log₂(256 × 500) = 17. One EV is one stop.

The sunny-16 rule, and a manufacturer’s version of it

The sunny-16 rule — in bright sun, f/16 at one over the ISO speed — is the zero point every photographer carries in their head. It is worth having a published table behind it rather than folklore, and Kodak print one. The daylight exposure table in the TRI-X data sheet covers “average front-lit subjects from 2 hours after sunrise to 2 hours before sunset”, and for TRI-X 400, which is ISO 400, it reads:

Lighting condition, as Kodak name it	TRI-X 400	Stops below bright sun	Illuminance implied by the constant derived below
Bright or hazy sun on light sand or snow	1/500 at f/22	−0.9 (brighter)	~190,000 lux
Bright or hazy sun, distinct shadows	1/500 at f/16	0	100,000 lux
Weak, hazy sun (soft shadows)	1/500 at f/11	1.1	~47,000 lux
Cloudy bright (no shadows)	1/500 at f/8	2.0	~25,000 lux
Heavy overcast, open shade	1/500 at f/5.6	3.0	~12,000 lux

The second row is sunny-16: 1/500 s for an ISO 400 film is a third of a stop from 1/400, which is inside anybody’s shutter tolerance. What the rest of the table gives you, and the mnemonic does not, is a ladder in stops from a source you can cite: open shade is three stops below bright sun, cloudy bright is two, weak sun is one. Those three numbers do most of the work in the field.

Note the limits Kodak state and do not hide. The table is for front-lit subjects, and there is a footnote for backlit close-ups. It is for the middle of the day, not the first or last two hours. It says nothing about latitude, altitude or season, and a January noon in Britain is not a July noon: the sun is lower, the path through the atmosphere longer, and the table optimistic. Treat it as a starting point that a bracket will correct, which is exactly how it is used below.

Stops, and getting from f/16 to f/250

A stop is a factor of two in exposure. The f-number scale advances in steps of √2 — 2.8, 4, 5.6, 8, 11, 16, 22 — because it is the area of the aperture that matters and the area goes as the square of the diameter. So converting between two f-numbers is a square law, and converting the same thing into stops is a doubled logarithm:

factor = (N₂ / N₁)² and stops = 2 log₂(N₂ / N₁)

Exposure factor between two f-numbers

Everything on this page hangs off that one relation, so it is worth a table you can read off in the field. All of it is relative to a meter reading taken at f/16.

Pinhole f-number	Stops beyond f/16	Multiply the f/16 time by	A 1/125 s reading becomes	A 1/500 s reading becomes
f/100	5.3	39	0.31 s	0.078 s
f/128	6.0	64	0.51 s	0.13 s
f/150	6.5	88	0.70 s	0.18 s
f/180	7.0	127	1.0 s	0.25 s
f/200	7.3	156	1.25 s	0.31 s
f/250	7.9	244	2.0 s	0.49 s
f/267	8.1	278	2.2 s	0.56 s
f/300	8.5	352	2.8 s	0.70 s
f/400	9.3	625	5.0 s	1.25 s
f/512	10.0	1024	8.2 s	2.0 s

The three rows in bold are the reference camera’s settings from the design lesson. Notice that the whole useful range spans about five stops, which is why the geometry lesson’s √f argument matters: tripling the focal distance costs you only about one and a half stops, not nine.

The exposure scaling chart: one reading, four conversions, one time

1. 1Metered time and f-number — a meter reading, a lux reading, or a published daylight table
2. 2× (metered ISO / effective ISO) — paper at ISO 3–6, sheet film at box speed, home-coated unknown until tested
3. 3× (N_pinhole / N_metered)² — the square law; f/16 to f/250 is a factor of 244
4. 4× (f_actual / f_assumed)² — the pinhole’s form of the bellows factor; skip it if the stack has not changed
5. 5Reciprocity correction, last — from the sheet for the material in the camera, applied to the total time from steps 1–4

Order matters. The reciprocity correction is a function of the whole metered time, so everything else is done first.

From a lux reading straight to a time

If you own a lux meter, or are prepared to treat a phone app as one, the incident relation gives the exposure in a single step and skips the f-number conversion entirely. Rearranged for time:

t = N² C / (E S)

Time from illuminance

That needs C, which the course cannot quote. It can, however, derive one from two figures it has already cited, which is a better lesson anyway.

🧮DO THE MATHS: pinning the incident constant from two published numbers

Take Kodak’s daylight row for bright sun with distinct shadows: 1/500 s at f/16 for ISO 400. Take Mike Ware’s figure that the summer sun at midday in English latitudes, striking a surface at normal incidence, illuminates it with about 100,000 lux. Assume the two describe the same light — which is the assumption being tested — and solve the incident relation for C:

C = t E S / N² = (1/500) × 100,000 × 400 / 16² = 80,000 / 256 = 312.5

Round it to C ≈ 310. Now check it against the rest of Kodak’s table by running it backwards to get the illuminance each row implies: f/11 gives 47,000 lux, f/8 gives 25,000 lux, f/5.6 gives 12,000 lux. Those are sensible daylight values, falling by the factor of two the stop ladder demands, and the whole table is internally consistent with a single constant. That consistency is the evidence that the derivation is sound; the exact value is not.

What this is and is not. It is a constant derived here from two cited sources, and it agrees with one to the precision of the other. It is not a quotation from ISO 2720, which this course has not read, and it is not a claim about the constant your meter uses — meters differ, and a meter with a flat receptor and one with a dome do not measure the same quantity. If you own a meter, prefer its reading. If you do not, use 310 and calibrate it once against a bracket, which is a thing you will be doing anyway.

Worked immediately: bright sun, 100,000 lux, ILFORD MULTIGRADE RC paper taken at ISO 3, the wide camera with the 0.20 mm plate at f/250.

t = 250² × 310 / (100,000 × 3) = 62,500 × 310 / 300,000 = 64.6 seconds

The stops route in the previous section, from the same Kodak row through the same speed conversion, gave 65.1 seconds. Two independent paths to the same number is the check worth doing the first time and never again.

✕What a phone lux app is actually measuring

A phone’s ambient-light sensor exists to dim the screen, and it was engineered for that. Four things follow, none of them fatal and all of them worth knowing.

Its spectral response is a filtered silicon photodiode approximating the human photopic curve, and the approximation is the manufacturer’s, not a standard’s. Its angular response is supposed to be a cosine — a true incident meter’s dome does this properly — but it sits flush behind a cover glass in a recess, so it under-reads light arriving from the side. Its absolute calibration is a factory constant, and the app applies a further conversion of its own that you cannot inspect. And it is partly occluded by whatever case you have on the phone.

This course has found no published comparison of phone lux apps against calibrated meters and so gives no accuracy figure. The practical rule follows from the failure modes rather than from a number: a phone app is much better at ratios than at absolutes. Point it at two scenes and the difference between the readings is worth having; take one reading and call it 43,000 lux and you are claiming a traceability that is not there. Calibrate it once, in bright sun, against the Kodak row above — if it reads 100,000 lux there, use it as it stands; if it reads 60,000, keep the factor of 1.7 in your log and apply it.

Effective speed: what the material actually is

Effective speed is the ISO number you have to feed the arithmetic to get a correct exposure with your material, in your processing, in this light. It is not always the number on the box, and for two of the three materials in this part it is not on any box at all.

Photographic paper as a negative. ILFORD state it directly and with a warning attached: “ISO Paper speeds are not the same as Film ISO speeds, MULTIGRADE RC papers have approximately an equivalent Film ISO of 3-6.” That is a range, and a factor of two — one stop — and taking 3 rather than 6 doubles every exposure on this page. Take ISO 3 as the pessimistic starting point, expect the bracket in the commissioning experiment to move it, and write down what you settle on.

HARMAN’s direct positive paper is the other published data point, and unusually it is published for this exact use: the sheet describes it as having a “Slow ISO speed (between ISO 1 - 3)” and gives guide times for pinhole cameras — 1 to 2 minutes in bright summer sunshine, 2 to 3 minutes in bright but indirect sun, 4 to 5 minutes in overcast, 6 to 10 minutes dull or cloudy, and about an hour for a lit interior. Those times are for “a pinhole camera with an aperture made from a pin”, so the f-number is unstated and the numbers cannot be transferred to your camera arithmetically. What they can do is bracket the answer: the 65 seconds computed above, for a slightly faster paper at f/250, lands inside HARMAN’s 1-to-2-minute band for a slower paper at an unknown f-number. If your own calculation had produced 6 seconds or 40 minutes, you would know to look for the mistake.

Sheet film at box speed. FOMAPAN 100 Classic is rated by FOMA at “ISO 100/21°”; ILFORD rate FP4 PLUS at ISO 125/22° and HP5 PLUS at ISO 400/27°. Use those figures as they stand for a first film. A personal exposure index that differs from the box speed is a real and useful thing, but it is established by measurement against a developed curve, and that is Part XIII’s work.

Home-coated plates and papers from Part V have no speed at all until you measure one. The method appropriate at this stage is a comparison bracket: put a known material and the unknown one in the camera one after the other, expose the known one correctly, then expose the unknown one over a range of five sheets at one-stop intervals centred on the same time, and read off which matched. That gives an effective speed to within about a stop, which is enough to work with. It is not a speed point, it carries no development specification, and it is not comparable with anybody else’s number. Part XIII does that properly with a densitometer and a step wedge.

📷Why paper's speed depends on the colour of the light

Part IV’s spectral sensitivity lesson establishes that an undyed silver halide emulsion — which is what ordinary enlarging paper is — responds in the blue and the ultraviolet and stops around 500 nm. An ISO speed, by contrast, is determined under a standard daylight illuminant. Put a blue-only material under a light that is not daylight and its effective speed moves, in the direction the light moves.

Two consequences you will meet in this part. Open shade is bluer than sunlight, because it is lit by sky rather than by the sun, so paper is faster in shade than the stop ladder alone predicts — which partly offsets the reciprocity penalty that the longer exposure brings, and pulls in the opposite direction. Tungsten light is much redder, containing very little of what the paper can use, so paper is far slower indoors than an ISO 3 rating suggests. HARMAN’s hour for a lit interior is that effect made visible.

This course has no number for either shift, because neither manufacturer publishes an effective speed against illuminant for paper used as a camera negative. What it has is the direction of each effect and the instruction to bracket widely indoors, and to log the light’s description alongside the time so that a season of exposures eventually supplies the number.

The extension penalty: a pinhole’s version of the bellows factor

A lens photographer working close has to add exposure, and the reason is a definition. The f-number of a lens is computed from its focal length, but the light actually travels the image distance, which is longer whenever the subject is close. Correcting for that gives the familiar bellows factor:

N_eff = N (1 + m), so the exposure factor is (1 + m)²

Bellows factor for a lens

with m the magnification, image size over subject size.

A pinhole has no focal length to be caught out by. The distance in N = f/d is already the image distance, because there is nowhere else to measure it from, so as long as f is the true pinhole-to-emulsion distance the correction is already inside the number. The geometry lesson proves the same thing from the other end, by showing that the illuminance at the film goes as (d/f)² with the subject distance cancelling out.

What replaces it is a question about your own bookkeeping: does the f you used to compute the f-number match the f the camera is actually in?

exposure factor = (f_actual / f_assumed)²

The pinhole extension factor

Situation	f assumed	f actual	Factor	Stops
Film holder puts the emulsion 3 mm deeper than the flat back	50 mm	53 mm	1.12	0.17
The same, at the long setting	120 mm	123 mm	1.05	0.07
One frame added after metering	50 mm	80 mm	2.56	1.36
Both frames added after metering	50 mm	120 mm	5.76	2.53
Frame seated on its spigot, 8 mm short	80 mm	72 mm	0.81	−0.30

When does it matter? Set the threshold where you set every other one — a third of a stop, which is the finest exposure difference most people can hold. A third of a stop is a factor of 2^(1/3) = 1.26, so the extension ratio has to reach √1.26 = 1.12: a 12 per cent change in the focal distance. For a lens that is m = 0.12, about a tenth life size, which is where the familiar rule of thumb about one-tenth magnification comes from; the arithmetic is given here rather than the rule, because the arithmetic transfers to a camera with no focal length in it.

So: the film-holder rows above can be ignored, and the frame rows cannot. Stacking a frame to make a still life bigger costs a stop and a third, and it costs it because N changed — the bellows factor arriving through the front door.

Reciprocity correction in practice

Part IV establishes what reciprocity failure is: below some illuminance the material needs more total exposure than E = I × t predicts, because sparse photoelectrons fail to build stable development centres before the earlier ones decay. It also establishes ILFORD’s exponent form and derives the relation between their P and Schwarzschild’s p. None of that is repeated here. What is repeated is the instruction that follows from it: use the sheet for the material in the camera, and no other.

Manufacturers publish the same physics in three different formats.

Publisher and material	Form	What it says, quoted	P implied
ILFORD, eleven films (Dec 2023 sheet)	exponent	Tc = TmP, with P = 1.26 for FP4+, 1.31 for HP5+, 1.33 for Pan F+, 1.43 for SFX, 1.25 for Ortho+; “exposure times of one second or less will not require any compensation”	as printed
Kodak, T-MAX 100	table	+⅓ stop at 1 s; +½ stop, or 15 s, at 10 s; +1 stop, or 200 s, at 100 s	1.15–1.18
Kodak, T-MAX 400	table	nothing to 1 s; +⅓ stop at 10 s; +1½ stops, or 300 s, at 100 s	1.24
Kodak, TRI-X 320/400	table with development	+1 stop at 1 s and 10 % less development; +2 stops, or 50 s, at 10 s and 20 % less; +3 stops, or 1200 s, at 100 s and 30 % less	1.54–1.70
FOMA, FOMAPAN 100 Classic	multiplier table	×1 from 1/1000 to ½ s; ×2 at 1 s; ×8 at 10 s; ×16 at 100 s, with aperture corrections of 0, −1, −3 and −4 stops	1.60–1.90

The P column is the course’s own back-calculation, done so that five sheets in three formats can be compared on one scale: for a table entry, P = log(T_c) / log(T_m). It is not printed on any of the sheets, and where a sheet gives two points that imply two different exponents — FOMA’s do, 1.90 at ten seconds and 1.60 at a hundred — that is the sheet telling you the exponent is not really constant, which Part IV explains.

Read that table for its spread and not its numbers. At a metered hundred seconds, T-MAX 100 wants 200 seconds, T-MAX 400 wants 300, FOMAPAN 100 wants 1600, and TRI-X wants 1200. Same nominal exposure, same scene, and a factor of eight between the shortest and the longest correction. This is the single biggest reason a pinhole photographer must know what is in the camera.

Corrected exposure against metered exposure, from four makers' own figures

• no correction (the law the meter assumes)
• Kodak T-MAX 100 — published table
• ILFORD FP4 PLUS — published exponent P = 1.26
• ILFORD HP5 PLUS — published exponent P = 1.31
• FOMAPAN 100 Classic — published multipliers

Show the numbers behind this plot

Five rising lines of corrected exposure against metered exposure, over a metered range of one to thirty seconds. The lowest is the reference line where no correction is applied at all, which is what the meter assumes: one second stays one second, three stays three, ten stays ten and thirty stays thirty. Kodak T-MAX 100, from its own published table, is the mildest real material: a metered second needs 1.26 seconds, a third of a stop, and a metered ten seconds needs fifteen. ILFORD FP4 PLUS, computed from the published exponent of 1.26, needs 1 second at 1, 4.0 at 3, 18.2 at 10 and 72.6 at 30. ILFORD HP5 PLUS, from the published exponent of 1.31, sits a little above it at 1, 4.2, 20.4 and 86.1 for the same four metered times. FOMAPAN 100 Classic is far the most severe, and its published multipliers put it above everything else from the start: a metered second needs two seconds and a metered ten seconds needs eighty, which is already above the HP5 line at thirty. The vertical spread at a metered ten seconds runs from fifteen seconds to eighty, a factor of more than five on the same nominal exposure of the same scene; extended to a metered hundred seconds, which is beyond the right edge of this plot, the makers' published figures run from two hundred seconds for T-MAX 100 to sixteen hundred for FOMAPAN 100, a factor of eight.

Series	Metered (indicated) time, seconds	Corrected time, seconds
no correction (the law the meter assumes)	1.00	1.00
no correction (the law the meter assumes)	3.00	3.00
no correction (the law the meter assumes)	10.00	10.00
no correction (the law the meter assumes)	30.00	30.00
Kodak T-MAX 100 — published table	1.00	1.26
Kodak T-MAX 100 — published table	10.00	15.00
ILFORD FP4 PLUS — published exponent P = 1.26	1.00	1.00
ILFORD FP4 PLUS — published exponent P = 1.26	3.00	4.00
ILFORD FP4 PLUS — published exponent P = 1.26	10.00	18.20
ILFORD FP4 PLUS — published exponent P = 1.26	30.00	72.60
ILFORD HP5 PLUS — published exponent P = 1.31	1.00	1.00
ILFORD HP5 PLUS — published exponent P = 1.31	3.00	4.20
ILFORD HP5 PLUS — published exponent P = 1.31	10.00	20.40
ILFORD HP5 PLUS — published exponent P = 1.31	30.00	86.10
FOMAPAN 100 Classic — published multipliers	1.00	2.00
FOMAPAN 100 Classic — published multipliers	10.00	80.00

The ILFORD curves are computed from the exponents ILFORD publish; the Kodak and FOMA lines join only the points those makers actually print, and both makers publish a further point at a metered 100 seconds that is off the top of this plot — 200 s for T-MAX 100 and 1600 s for FOMAPAN 100. Nothing here was measured by this course, and none of it transfers to a material other than the one named. The curve is drawn to show the shape, not measured from a real material. Your own materials will differ, and measuring them is what the sensitometry part of the course is for.

Applying it takes one line and a caution. Do the speed, aperture and extension arithmetic first, which gives the metered time T_m. Then look up or compute T_c for the material in the camera. Never do it the other way round: the correction is a function of the whole metered time, so correcting a partial figure corrects the wrong number.

The caution is ILFORD’s own, and it should be read as the honest limit of an extrapolation: “For very long exposures at very low light levels then some other variables come in to play such as the accuracy of the light measurement. This means that some trial and error may be required.” A metered time of a hundred seconds is inside the range these sheets illustrate. A metered time of a thousand is not.

What the correction does to contrast

The correction is not only a matter of total exposure. ILFORD state that “you may also find that the contrast is increased with long exposures”, and give the reason: the shadows are at a lower illuminance than the highlights, so the shadows suffer the failure more, and the tonal scale stretches at the bottom. Their remedy is “pulling the development… reducing development time”. Kodak put numbers on the same instruction in the TRI-X table — 10 per cent less development at one metered second, 20 per cent at ten, 30 per cent at a hundred — which is the most explicit published guidance of the five sheets here and worth using as the model for any film whose maker gives none.

Part IV owns the mechanism; the field consequence is simply that a long exposure and a normal development time are two decisions, not one, and the log should record both.

Severe failure, mild failure, and the special case of paper

The spread in the table above sorts the materials into two camps and one anomaly.

Mild. The Kodak T-MAX films are the mildest here: T-MAX 400 needs nothing at all until ten metered seconds and only a stop and a half at a hundred. For pinhole work, where a great many exposures land between one second and a minute, a mild film removes most of the correction from the problem.

Severe. FOMAPAN 100 and TRI-X are the severe ones, wanting three stops or more where a T-MAX film wants one. Neither is a worse film; the failure is a property of the emulsion, as Part IV explains, and the same crystal chemistry that gives a film its other characteristics gives it this. But choosing FOMAPAN for a night exposure and then working from a half-remembered correction will lose the negative.

Paper is the anomaly, and the honest statement is that the data does not exist. ILFORD’s reciprocity sheet is titled for films and lists eleven of them; no paper appears on it. The MULTIGRADE RC technical sheet gives ISO range, ISO speed and safelight recommendations and publishes no reciprocity correction. HARMAN’s direct positive sheet gives whole-exposure guide times for pinhole cameras — which have whatever failure the paper has already baked into them — rather than a correction to apply. This course has found no manufacturer publishing a reciprocity correction for photographic paper used as a camera negative, and it will not invent one.

Three things follow, and all three are workable.

1. Bracket wider on paper than on film, because you are carrying an unquantified correction. Two stops either side rather than one, on the first outing.
2. HARMAN’s guide times are the only published anchor. They apply to their paper in an unspecified camera, so they cannot be transferred; but a computed answer far outside their bands is a signal to recheck the arithmetic.
3. Build the curve yourself. Every logged exposure is one point: metered time computed, actual time given, result judged. After a season of them, plot actual against metered on log-log paper, fit a straight line, and its slope is your paper’s P. That is a real measurement of a real quantity that nobody has published, made with a camera you built, and it is one of the more satisfying things this course asks for.

Filters, previewed

A filter factor is the number you multiply the exposure by to compensate for what a filter removes. Kodak print them for each film, and the reason they print them per film rather than per filter is the whole lesson:

KODAK WRATTEN filter	Factor on T-MAX 100, daylight	Factor on T-MAX 100, tungsten
No. 8 (yellow)	1.5	1.2
No. 15 (deep yellow)	2	1.5
No. 25 (red)	8	4
No. 47 (blue)	8	25
No. 58 (green)	6	6
Polarising	2.5	2.5

Kodak add the warning in their own words: “Filter factors for other Kodak black-and-white films are different.”

A filter factor is a property of three things at once — what the filter passes, what the light source contains, and where the material is sensitive. Read the blue row: 8× in daylight and 25× in tungsten, for the same filter, because tungsten light has less blue in it to pass. Read the red row the other way: 8× in daylight and 4× in tungsten, because tungsten has more red.

Now apply that to paper. Paper is blue-sensitive and stops around 500 nm. A red filter passes almost nothing paper can record, so the “factor 8” from a panchromatic film’s sheet is meaningless there — the true factor is enormous and effectively unusable. A blue filter, by contrast, costs a blue-sensitive material very little, because it passes exactly what the material was going to use. Part VII gives the numbers for the filters this course actually uses; the rule to carry until then is that a filter factor belongs to a material-and-illuminant pair, never to a filter.

Four worked examples

Every one of these is done in the same order — speed, aperture, extension, reciprocity — and every intermediate number is shown so it can be checked.

🧮Example 1 — a sunlit wall, on paper, at f/250

The camera. Wide setting, f = 50 mm, with the 0.20 mm plate rather than the 0.25 mm one the design lesson chose for that setting: N = 50/0.20 = f/250. At 50 mm the optimum band runs from 0.211 to 0.285 mm, so 0.20 is a whisker below it — the picture will be very slightly diffraction-limited rather than geometry-limited, which changes the sharpness a little and the exposure arithmetic not at all. Substituting the plate that is already in the camera is what a real session does; the point is that you know what you substituted.

The material. ILFORD MULTIGRADE RC, taken at the pessimistic end of the maker’s range: ISO 3.

The light. Bright sun, distinct shadows. Kodak’s daylight row for ISO 400 gives 1/500 s at f/16.

Speed. From ISO 400 to ISO 3 is a factor of 400/3 = 133.3. t = (1/500) × 133.3 = 0.267 s at f/16.

Aperture. From f/16 to f/250 is (250/16)² = 244.1, which is 2 log₂(250/16) = 7.9 stops. t = 0.267 × 244.1 = 65 s.

Extension. None: the f-number was computed for the configuration the camera is in. Factor 1.

Reciprocity. No published correction exists for this paper. The computed 65 s sits inside HARMAN’s published 1-to-2-minute band for a slower paper in bright sun, which suggests the uncorrected figure is not badly wrong, but it is not evidence about ILFORD’s paper.

The exposure given: 60 seconds, bracketed at 30 and 120. Log all three, and log which one you would print.

🧮Example 2 — the same wall in open shade

Everything is identical except the light. Kodak’s “Heavy overcast, open shade” row is 1/500 at f/5.6, which is 2 log₂(16/5.6) = 3.03 stops below the bright-sun row: a factor of 8.16.

t = 65 × 8.16 = 531 s, about 9 minutes.

Now the two unquantified effects, pulling in opposite directions. Reciprocity makes it longer. Nine minutes is deep into failure for any material, and if the paper behaved like FP4 PLUS — which is an assumption, not a fact — the exponent 1.26 would take 531 s to 531^1.26 = about 2,700 s, three quarters of an hour. Spectral response makes it shorter. Open shade is lit by blue sky, and the paper is blue-sensitive, so its effective speed rises; the course has no number for how much.

Which wins? Almost certainly reciprocity, because an exponent of 1.26 is a factor of five here and no plausible spectral shift is. But “almost certainly” is not a number, and this is exactly the case the bracket exists for. Expose at 9, 18 and 36 minutes, and record all three against the same subject so the comparison is real. This one experiment, repeated a few times, is where your paper’s P comes from.

🧮Example 3 — a tungsten-lit still life, close

The camera. Long setting, f = 120 mm, the 0.40 mm plate: N = f/300. Subject 400 mm from the hole, so m = f/u = 120/400 = 0.30.

The reading. An incident meter at the subject, pointed back at the camera, reads 1/4 s at f/4 for ISO 100.

Speed. ISO 100 to ISO 3 is a factor of 33.3: t = 0.25 × 33.3 = 8.3 s at f/4.

Aperture. f/4 to f/300 is (300/4)² = 5625: t = 8.3 × 5625 = 46,700 s, which is thirteen hours. Something is wrong, and it is not the arithmetic.

What is wrong is the material. Tungsten light is red, paper is blue-sensitive, and the ISO 3 figure was determined under daylight. HARMAN’s own sheet says an hour for a lit interior on a paper of ISO 1 to 3 — so their measured penalty for interior light is already inside that hour, and thirteen computed hours means the daylight speed cannot be carried indoors. Change the material: put a sheet of FP4 PLUS in a film holder at ISO 125 and repeat. Speed factor 100/125 = 0.8, so t = 0.25 × 0.8 = 0.2 s at f/4, and × 5625 = 1,125 s, nineteen minutes metered. Then ILFORD’s exponent for FP4 PLUS: log 1125 = 3.051, × 1.26 = 3.844, so T_c = 10³·⁸⁴⁴ ≈ 7,000 s, about two hours — an extrapolation far beyond anything their sheet demonstrates, so bracket it hard.

Extension. Here is the trap the still life sets. m = 0.30 would cost a lens (1.30)² = 1.7, or 0.75 stop. It costs the pinhole nothing, because N = 120/0.40 was computed from the real pinhole-to-emulsion distance and there is no focal length hiding inside it. But if you had metered for the 50 mm body and then stacked both frames to get this framing, you would owe (120/50)² = 5.76, 2.5 stops — the same correction, arriving by a different door.

🧮Example 4 — a lit street at night, where the correction is the exposure

The camera. Long setting, N = f/300. The material. ILFORD HP5 PLUS sheet film at its box speed of ISO 400, P = 1.31.

The reading. A reflected reading off a lit shopfront, ISO 400: 1/15 s at f/2.8.

Aperture. f/2.8 to f/300 is (300/2.8)² = 11,480, which is 13.5 stops. T_m = (1/15) × 11,480 = 765 s, about 12¾ minutes.

Reciprocity. T_c = 765^1.31. Take logs: log 765 = 2.884, × 1.31 = 3.778, so T_c = 10^3.778 = 6,000 s, one hour and forty minutes.

Look at what just happened. The correction multiplied the exposure by 7.8, which is nearly three stops — larger than any other single factor in the calculation except the aperture conversion itself. At the wide setting it would be worse still, because the metered time would be shorter but the exponent would still be applied. At night, on a severe film, the reciprocity correction is not a refinement of the exposure; it is most of the exposure.

Three cautions to log with it. ILFORD’s sheet illustrates the relation at ten seconds, not at 765, so this is an extrapolation and they say as much. The contrast will rise, so plan on 10 to 20 per cent less development on Kodak’s model. And an hour and forty minutes of a street is a picture of the average of that street over an hour and forty minutes, which is a different photograph from the one you metered.

🕰Wall's rule of thumb, and whether it survives the arithmetic

Wall’s 1912 Dictionary of Photography tells the pinhole photographer that “a prolonged exposure is required, about twenty or thirty times the ordinary one for any given subject”, and prints Alfred Watkins’ table of needle sizes against plate distances, whose ratios run from about f/39 to f/60.

Check it. A period lens at f/11 against a pinhole at f/56 is (56/11)² = 25.9 times, which is inside “twenty or thirty” and 4.7 stops. So the rule is not folklore: it is the square law, worked once by somebody and then remembered. It also shows how much the range has moved. Watkins’ pinholes were four to six times faster than the ones in this part, because his plates were slower and his cameras longer, and the factor of 156 at f/200 that this page opens with would have been useless to him.

The exposure log

Every number on this page is a prediction, and a prediction that is not written down before the fact is not a prediction. The exposure log is the instrument that turns a season of exposures into a measurement, and it is the reason the last section can promise you a personal reciprocity curve.

The exposure log, one row per sheet, with a worked entry

1. 1Before the shutter opens — date and time; camera and configuration; plate id; measured f; effective aperture; subject; material and effective ISO; metered light; computed exposure; reciprocity correction and its source
2. 2After processing — filter and factor; what moved; processing (developer, dilution, temperature, time, agitation); result against a grey scale; what to change
3. 3The worked row — one sheet, all fields, so that a stranger could repeat it

Units are fixed so a season of rows can be plotted: millimetres for f, seconds for time, EV or lux for light, degrees Celsius for temperature. Every field either was measured or names where the number came from.

Three arguments for the discipline, in increasing order of how much you will care.

It makes an exposure repeatable. The immediate payoff: a good sheet you cannot repeat is luck, and luck does not accumulate.

It makes the failures diagnosable. When the break/fix page at the end of this part asks you why a negative is soft or thin, the answer is nearly always in a field you either recorded or did not. A thin negative with a logged plate letter and a logged focal distance is a two-minute diagnosis; the same negative with neither is a guess.

It is the only route to numbers nobody has published. Two of them are named on this page: the effective speed of your paper in your processing, and the reciprocity exponent of a material for which no manufacturer publishes one. Both come out of a scatter of logged rows — computed time on one axis, actual time that worked on the other — and neither can be got any other way. That is why the log is described in this course as a scientific instrument rather than a diary: it is the only instrument in the part that measures something new.

The order of operations, to run before every exposure

1. 1Measure the lightA meter reading, an illuminance in lux, or a named row in a published daylight table — and record which of the three it was.
2. 2Multiply for speedMetered ISO divided by effective ISO. Paper 3 to 6; sheet film at box speed; a home-coated material has no speed until you bracket it.
3. 3Multiply for apertureThe square of the ratio of the pinhole f-number to the metered one. From f/16 to f/250 that is 244.
4. 4Multiply for extensionThe square of the ratio of the actual pinhole-to-emulsion distance to the one the f-number assumed. It passes a third of a stop at 12 per cent.
5. 5Apply reciprocity, lastThe maker's own sheet for the material actually in the camera. Name the sheet and its edition in the log.
6. 6Log the prediction, then exposeThe computed time and its bracket are written before the shutter opens, or they are not a prediction.

The order is not arbitrary: every published reciprocity correction is indexed on the total metered time, so it can only be applied once the other three multiplications are done.

Recap

• A reflected meter reports what would put its subject in mid-scale; an incident meter reports what the light on the subject demands. For wide daylight scenes with sky in them, prefer incident.
• The exposure relations N²/t = LS/K and N²/t = ES/C need constants this course could not read from ISO 2720. Working in stops relative to a reading needs no constant, and a value of C ≈ 310 is derived here from Kodak’s daylight table and a cited figure of 100,000 lux for midday summer sun.
• Stops are factors of two and f-numbers are a square law: factor = (N₂/N₁)². From a meter’s f/16 to f/250 is 7.9 stops, a factor of 244.
• Effective speed is not always box speed. ILFORD publish ISO 3–6 for MULTIGRADE RC as a negative material; HARMAN publish ISO 1–3 and pinhole guide times for their direct positive paper; sheet film goes at box speed; a home-coated material has no speed until you bracket it against a known one.
• A pinhole has no separate bellows factor, because N = f/d already uses the image distance. What it has is an extension factor (f_actual/f_assumed)², which passes a third of a stop at a 12 per cent change and reaches 2.5 stops when both frames go on.
• Reciprocity is applied last, from the sheet for the material in the camera, and the spread between materials at a metered hundred seconds is a factor of eight. Long exposures also raise contrast; Kodak’s TRI-X table is the most explicit published guidance on pulling development for it.
• Nobody publishes a reciprocity correction for paper used as a camera negative. Bracket wider, use HARMAN’s guide times as a sanity band, and build your own curve out of the log.
• A filter factor belongs to a material-and-illuminant pair, never to the filter. Kodak’s blue filter is 8× in daylight and 25× in tungsten on the same film.
• The log is the instrument. Ten fields before the shutter opens, five after, and the two numbers nobody has published fall out of a season of rows.

Check your understanding

Question 1. Your meter reads 1/250 s at f/11 for ISO 100. You are shooting MULTIGRADE RC paper taken at ISO 4, in the camera at the normal setting: 80 mm with the 0.30 mm plate. What is the computed exposure before any reciprocity correction?

• About 15 seconds
• About 59 seconds
• About 236 seconds
• About 4 seconds

Show the answer and why

Answer: About 59 seconds

Speed first, then aperture. The f-number is N = 80/0.30 = 267. Speed: from ISO 100 to ISO 4 is a factor of 25, so the time at f/11 becomes (1/250) × 25 = 0.10 s. Aperture: from f/11 to f/267 is (267/11)² = 589, so t = 0.10 × 589 = 58.9 s, about a minute. In stops that is 2 log₂(267/11) = 9.2 stops of aperture on top of 4.6 stops of speed, which is 13.8 stops in total — a factor of about 14,700 between what the meter said and what you give, and a good illustration of why the arithmetic has to be written down rather than estimated. Option 1 uses the metered ISO by mistake for the aperture step; option 3 doubles the speed factor; option 4 forgets the speed conversion entirely.

Question 2. The same scene, the same camera, but now a sheet of ILFORD HP5 PLUS at ISO 400 in a film holder. The computed metered time comes out at 15 seconds. What exposure do you actually give, and why?

• 15 seconds; reciprocity failure does not apply below a minute
• About 34 seconds, from ILFORD’s exponent Tc = Tm^1.31
• About 30 seconds, because you always double a long exposure
• About 120 seconds, because HP5 PLUS is a severe film

Show the answer and why

Answer: About 34 seconds, from ILFORD’s exponent Tc = Tm^1.31

ILFORD publish the exponent P = 1.31 for HP5 PLUS, and Tc = Tm^P: 15^1.31 = 10^(1.31 × log 15) = 10^(1.31 × 1.176) = 10^1.541 = 34.8 s, so about 34 seconds. Their sheet also states that exposures of one second or less need no compensation, which is why option 1 has the threshold in the wrong place — the correction starts at one second, not one minute. Option 3 is folklore with no material attached to it, and it happens to be nearly right here and would be badly wrong at 100 seconds, where the same exponent asks for 410 s and not 200. Option 4 confuses HP5 PLUS with the genuinely severe materials: on the same 15-second metered time FOMAPAN 100 would want well over two minutes, and TRI-X somewhere between. The correction belongs to the emulsion, and the only defensible source for it is the sheet for the film in the holder.

Question 3. You meter and compute an exposure for the camera at the wide setting, 50 mm, then decide the subject is too small and stack both extension frames to reach 120 mm before opening the shutter. If you keep the pinhole plate the same and use the exposure you computed, what happens?

• Nothing: a pinhole has no bellows factor
• The negative is underexposed by about 2.5 stops, because the true f-number went up with the focal distance
• The negative is overexposed by about 2.5 stops
• The negative is underexposed by about 1.2 stops, from the square-root law

Show the answer and why

Answer: The negative is underexposed by about 2.5 stops, because the true f-number went up with the focal distance

A pinhole has no separate bellows factor, which is what makes option 1 tempting, but that statement means something precise: the correction is already inside N = f/d, provided f is the distance the camera is actually in. Change f and you change N. With the same plate, going from 50 mm to 120 mm takes N from f/200 to f/480, and the exposure factor is (120/50)² = 5.76, which is 2.53 stops. Give the 50 mm exposure and the sheet is two and a half stops short. The lesson generalises: the pinhole extension factor is (f_actual / f_assumed)², it passes a third of a stop at a 12 per cent change in f, and it is the reason every configuration gets its own row in the register. Option 4 quotes the √f law, which describes how the f-number changes when the hole is also re-optimised for the new focal distance — not this case, where the plate stayed put.

Question 4. Why does this page insist that the reciprocity correction is applied last, after the speed, aperture and extension conversions?

• Because the manufacturers list it last on their data sheets
• Because the correction is a function of the total metered time, so applying it to a partial figure corrects a number that was never going to be the exposure
• Because it is the least important of the four
• Because the correction is additive in stops and the others are multiplicative

Show the answer and why

Answer: Because the correction is a function of the total metered time, so applying it to a partial figure corrects a number that was never going to be the exposure

Every reciprocity form on this page — ILFORD’s exponent, Kodak’s tables, FOMA’s multipliers — is indexed on the indicated or metered time: the time that would have been correct if the material obeyed the reciprocity law. That number only exists once the speed, aperture and extension conversions are done. Correct at ten seconds and then multiply by an aperture factor of 244 and you have applied a ten-second correction to a two-hour exposure. The error is not small: with ILFORD’s exponent, correcting 10 s and then scaling gives 20.4 × 244 = 4,978 s, while correcting last gives (10 × 244)^1.31 = 2,440^1.31 ≈ 27,000 s, five and a half times larger. Option 4 has it backwards — the correction is a power law, not an additive one, which is exactly why the order cannot be swapped.

Question 5. A student reads Kodak’s filter table, sees that a No. 25 red filter has a factor of 8 in daylight, and fits one over the pinhole to darken the sky on a paper negative, adding three stops. What actually happens?

• The sky darkens as intended and the exposure is correct
• The picture is drastically underexposed, because the paper is blue-sensitive and a red filter removes almost everything it can record; the factor of 8 belongs to a panchromatic film, not to this material
• The picture is overexposed by three stops
• Nothing changes, because filters have no effect on a lensless camera

Show the answer and why

Answer: The picture is drastically underexposed, because the paper is blue-sensitive and a red filter removes almost everything it can record; the factor of 8 belongs to a panchromatic film, not to this material

A filter factor is not a property of the filter. It is the product of what the filter passes, what the light source contains, and where the material is sensitive — which is why Kodak print a different table for every film and add the warning that "filter factors for other Kodak black-and-white films are different". Their No. 25 factor of 8 was determined on a panchromatic film that responds across the visible spectrum and therefore still receives plenty of red. An undyed silver halide paper responds in the blue and ultraviolet and stops near 500 nm, so a deep red filter removes very nearly all of the exposure and the true factor is enormous. Kodak’s own table shows the mechanism in the other direction: the blue No. 47 costs 8× in daylight but 25× in tungsten, because tungsten light has less blue to pass. The general rule to carry into Part VII is that a filter factor belongs to a material-and-illuminant pair.

Question 6. Why does the exposure log require the computed time and the reciprocity source to be written down before the shutter opens, rather than reconstructed afterwards?

• It is a formality that makes the notebook look complete
• Because the fields written before the exposure are a prediction, and the difference between prediction and result is the only measurement that yields your paper’s effective speed and its unpublished reciprocity exponent
• Because manufacturers require it for warranty purposes
• Because the developer time depends on it

Show the answer and why

Answer: Because the fields written before the exposure are a prediction, and the difference between prediction and result is the only measurement that yields your paper’s effective speed and its unpublished reciprocity exponent

A number written after you have seen the negative is contaminated by the negative. Written first, the computed time is a falsifiable claim; written afterwards it is a rationalisation, and a page of rationalisations cannot be plotted. Both of the quantities this part promises you come out of that difference. Plot the actual time that worked against the computed metered time on log-log axes over a season of exposures, and the slope of the line is the reciprocity exponent for a material no manufacturer publishes one for; the intercept, compared with the ISO you assumed, is your paper’s real effective speed in your processing. That is why this course calls the log an instrument. It also has a mundane virtue: the break/fix page at the end of this part diagnoses a soft or thin negative from the logged plate letter and focal distance in two minutes, and cannot diagnose it at all without them.

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