Exposure, Density and the Logarithm

Two quantities have to be measured before anything else in sensitometry can be said: how much light went in, and how dark the film came out. Neither is difficult. What makes them usable together is a piece of arithmetic you already have — the base-ten logarithm — applied to light instead of to hydrogen ions.

By the end of this page you should be able to take a lamp, a timer and a step wedge, and write down the exposure every step of that wedge delivered; take a negative and a light meter, and write down a density; and read the axes of a manufacturer’s published curve without guessing what the numbers mean.

Exposure is a product, not a setting

In ordinary speech “exposure” means a shutter setting, or a frame of film, or the act of taking a picture. In sensitometry it is none of those. Exposure, written H, is illuminance multiplied by time.

H = E × t

Photographic exposure

E is the illuminance falling on the emulsion — how brightly lit the film’s surface is — measured in lux. t is the time that illuminance lasts, in seconds. Their product H is therefore in lux-seconds, and that is the unit along the bottom of every characteristic curve in this course. The photographic convention is fixed by ISO 6, cited here by number and nowhere quoted; Kodak’s sensitometry workbook states the same relation as Exposure = Illuminance × Time and works its examples in millilux and millilux-seconds, a thousandth of a lux, because camera-film exposures in lux alone are inconveniently small numbers.

Kodak’s own worked example is a good one to copy. An illuminance meter reads 75 millilux at the film plane and the shutter is open for one fifteenth of a second. Then H = 75 ÷ 15 = 5 millilux-seconds. Nothing more to it than that.

What a lux actually is, since the unit does some quiet work here. It is one lumen per square metre: luminous flux arriving per unit area, weighted by the sensitivity of the human eye across the spectrum. Two things follow. First, lux is a photometric unit, not a radiometric one — it counts light the way an eye counts it, not the way a photon detector does, so a source rich in blue and poor in green delivers more photographic effect per lux to a blue-sensitive emulsion than the number suggests. That is exactly why the standards specify an illuminant as well as a quantity, a point the speed lesson returns to. Second, it is per square metre, so it does not depend on how big the illuminated patch is; a lux meter held at the baseboard reads the same whether the enlarger is projecting a 35 mm frame or a whole sheet, provided the light falling on the cell is the same.

The reason the product is what matters — rather than the brightness or the duration separately — is the reciprocity law: half the light for twice the time is assumed to produce the same result. That assumption is what allows a single number on the horizontal axis to stand for an unlimited number of different lamp-and-timer combinations. It is also only approximately true, and it fails at both extremes. Part IV owns the mechanism and Part VI owns the correction; this page simply notes which assumption it is standing on.

!Illuminance is at the film, not at the subject

A light meter pointed at a scene measures the luminance of the subject. The illuminance at the film plane is a different quantity, smaller by everything the lens and the aperture do to the light. When this part talks about exposure it means the illuminance on the emulsion, which is why sensitometry is done with a contact-printed step wedge under a known lamp rather than with a camera: it removes the lens from the measurement entirely.

The logarithm, extended rather than re-taught

Part III taught the base-ten logarithm once, for pH, and said explicitly that Part XIII would build on it rather than repeat it. So, in one sentence: the base-ten logarithm of a number is the power of ten that makes it, log 1000 = 3 and log 0.001 = −3, and going back the other way is the antilog, 10 raised to that power.

What pH did not need, and sensitometry does, is the behaviour of logarithms under multiplication.

log (a × b) = log a + log b, and log (a ÷ b) = log a − log b

The rule that does all the work

Read that as: multiplying quantities means adding their logarithms. Every convenience in the rest of this part is a consequence. Exposure is a product, E × t, so on a log axis it is a sum: doubling the time moves you a fixed distance to the right no matter what the illuminance was. Density is a logarithm of a ratio, so stacking two filters adds their densities. And a factor of two — one stop — is always the same distance, because log 2 = 0.301, whatever it is a factor of two of.

0.30 is the number to memorise. One stop, one step, one doubling: 0.30 in log exposure. Three of those is 0.90, close enough to 1.0 that a factor of ten and three stops are nearly the same move, which is why log scales and stop scales get confused. They are not the same: eight is not ten. Ten stops is 3.01 in log H; ten times the light is 1.00.

Photographers count in factors of two, so their natural base is 2 and their natural unit is the stop. Sensitometry counts in factors of ten, because that is what makes density and exposure share one scale. Converting is a single multiplication:

Δ log H = 0.301 × (number of stops) and stops = Δ log H ÷ 0.301

Stops to log exposure and back

If you want the stop count directly from a ratio rather than from a log difference, the base-two logarithm does it, and it is one division away from the base-ten one you already have:

log₂ x = log₁₀ x ÷ log₁₀ 2 = log₁₀ x ÷ 0.301

Base two from base ten

So a subject spanning 128 to 1 is log 128 = 2.107 in log terms and 2.107 ÷ 0.301 = 7.0 stops. There is no separate arithmetic to learn; there is one logarithm and a conversion factor.

The antilog is the return trip, and you will need it more often than you expect, because a speed number is an antilog and a transmittance is an antilog. It is the 10^x key on any calculator: if log H = −2.10 then H = 10^(−2.10) = 0.0079 lux-seconds. A useful sanity check while you are learning is that the whole-number part of a logarithm tells you the decimal place and the fractional part tells you the digits: 10^2.30 = 200 and 10^(−0.70) = 0.20 share the same fractional part, 0.30, and therefore the same leading digit 2.

Kodak’s workbook, incidentally, prefers step to stop for a factor of two in exposure, reserving “stop” for a change made at the lens aperture. The distinction is worth knowing when you read older literature; this course uses “stop” for the factor of two and says so here once.

Why both axes are logarithms

There are two good reasons and one that gets over-claimed.

Compaction. A subject on a bright day spans a luminance range of thousands to one, and a step wedge spans a thousand to one in transmission. An arithmetic axis from 1 to 1000 wastes nine tenths of its length on the top decade and crushes everything interesting into the last millimetre. A logarithmic axis from 0 to 3 gives each decade the same space. Kodak’s workbook makes exactly this argument and no other structural one.

How large a range is that in practice? The workbook’s own latitude example takes a scene whose brightest important object is 60 times brighter than its darkest, which is log 60 = 1.8 in log exposure, and sets it against a film curve covering 3.0. Two numbers, one subtraction, and you know there is 1.2 in log H of room to place the scene — four stops, split between the under- and overexposure ends. That calculation is the whole of exposure latitude, and it is only that easy because both quantities are logarithms. This course does not quote a figure for a “typical” scene range, because it has not verified one against a survey it can cite; 60 to 1 is Kodak’s worked example, not a measured average, and it is used here as an example and nothing more.

Additivity. This is the reason that actually changes what you can do. Because densities add, a ladder of equal density steps is a ladder of equal exposure intervals, and you can compute the exposure at every step of a wedge by subtraction instead of by dividing repeatedly. That property is what makes a step wedge an instrument rather than a set of grey patches.

And the one to be careful with. It is often said, and Kodak’s workbook says it in scare quotes, that the eye works “logarithmically” — that 0, 1 and 2 density units look like equal steps of brightness where 0.1, 0.2 and 0.3 in transmittance would not. Stated as an approximation over a limited range that is a reasonable working claim, and it does describe why a print’s tonal scale looks even. Stated as a law of vision it is more than the evidence in this course’s corpus supports, and nothing on these pages depends on it. The axes are logarithmic because of compaction and additivity, which are arithmetic facts; the eye is a bonus, not a premise.

Transmittance, opacity, density

Three names for one measurement, which is why the definitions get muddled.

Transmittance, T, is the fraction of the light that gets through: shine 100 lux at a negative, measure 25 lux on the far side, and T = 0.25. It runs from 1 (nothing stopped) down towards 0.

Opacity, O, is its reciprocal, 1/T, so the same negative has an opacity of 4. Opacity answers “how many times more light must I put in to get one unit out?” — which is the question a printer is actually asking.

Density, D, is the base-ten logarithm of the opacity.

D = log₁₀ O = log₁₀ (1 / T) = −log₁₀ T

Density

Worked at the values worth knowing by heart:

Transmittance T	Light passed	Opacity O = 1/T	Density D = log₁₀ O
1.0	all of it	1	0.00
0.5	half	2	0.30
0.25	a quarter	4	0.60
0.1	a tenth	10	1.00
0.01	a hundredth	100	2.00
0.001	a thousandth	1000	3.00

Two things fall out of that table. A density of 0.30 is one stop, exactly as a log exposure interval of 0.30 is one stop — the two axes are in the same currency, which is why a sensitometric plot is drawn with 0.30 of density occupying the same distance on the paper as 0.30 of log exposure. Kodak’s workbook gives that as a construction rule, and it is not cosmetic: the contrast-index construction on the third lesson of this part measures a distance along a sloping line and is simply wrong if the scales differ.

And the range of a real negative is smaller than beginners expect. Base-plus-fog sits near 0.10 to 0.20; a well-exposed pictorial negative’s highlights rarely pass 1.4 or so. The whole picture lives in about 1.2 density units — a factor of sixteen in transmitted light.

✕Density is not contrast

This course keeps the two words apart everywhere, and this is the page that earns the distinction. Density is how dark one point is: a single number, a property of one patch. Contrast is how much darker one point is than its neighbour for a given difference in the light that reached them: a rate, the slope of the curve, a property of a pair of points. A negative can be dense and flat, or thin and contrasty, and the two faults have different causes — density answers mostly to exposure, contrast mostly to development. Saying “that negative is too dense” when you mean “too contrasty” sends you to the wrong control, and it is the single most common way an otherwise careful darkroom worker chases the wrong variable for a month.

Transmittance against density

• T = 10 to the power minus D

Show the numbers behind this plot

Transmittance falls from 1.0 at zero density along a decaying curve: 0.50 at density 0.30, 0.32 at 0.50, 0.10 at 1.00, 0.010 at 2.00 and 0.001 at 3.00. The fall is steepest at the left, so the first stop of density costs half the light and the last stop of density between 2.7 and 3.0 costs only about a thousandth of it. Equal steps of density are equal ratios of transmittance, never equal amounts.

Series	Density D	Transmittance T (fraction of light passed)
T = 10 to the power minus D	0.00	1.00
T = 10 to the power minus D	0.10	0.79
T = 10 to the power minus D	0.20	0.63
T = 10 to the power minus D	0.30	0.50
T = 10 to the power minus D	0.40	0.40
T = 10 to the power minus D	0.50	0.32
T = 10 to the power minus D	0.60	0.25
T = 10 to the power minus D	0.80	0.16
T = 10 to the power minus D	1.00	0.10
T = 10 to the power minus D	1.20	0.06
T = 10 to the power minus D	1.40	0.04
T = 10 to the power minus D	1.60	0.03
T = 10 to the power minus D	1.80	0.02
T = 10 to the power minus D	2.00	0.01
T = 10 to the power minus D	2.40	0.00
T = 10 to the power minus D	3.00	0.00

This is the definition plotted, not a measurement of any material: it is why densities are quoted rather than transmittances, since equal density steps are equal photographic steps all the way down. 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.

Densities add, and that is what a step wedge is

Put two filters in the beam. The first passes a fraction T₁ of the light, the second passes T₂ of what reaches it, so the pair passes T₁ × T₂. Take logarithms and the multiplication becomes addition:

D(total) = D₁ + D₂

Additivity of density

A step wedge is that property manufactured. A Stouffer T2115 carries 21 patches whose densities rise in nominal increments of 0.15 from about 0.05 to 3.05 — a total range of 3.00, which is a thousand to one in transmission, in 21 equal ratios. Each 0.15 step is half a stop. Contact-print it onto film under a uniform lamp and each patch delivers a known exposure, computed by subtraction rather than measured:

log H(step) = log H(source) − D(step)

Exposure behind one step of a wedge

That single subtraction is the reason sensitometry can be done at home at all. You need to know the exposure at one place — under the clear edge of the wedge — and the wedge itself supplies every other value on the axis.

It also explains a piece of vocabulary you will meet in Part XIV. A wedge exposed all at once under one lamp is an intensity-scale exposure: every patch is exposed for the same length of time and differs only in how much light arrived. The alternative is a time-scale exposure, where one uniform patch of film is given a series of different durations, as in a printing test strip. The two are equivalent only where the reciprocity law holds, and where it does not they give measurably different curves — which is why a sensitometer is built around a wedge rather than a shutter, and why the lab in this part exposes for a few seconds rather than a few minutes.

!Nominal is not calibrated

Part IX established this and this part inherits it without softening it. Stouffer’s 0.15 increment is the nominal figure for the uncalibrated parts. Only the CC parts are supplied with the density of each step measured, and Stouffer states that those are calibrated against a NIST standard reference material. Every log H value you compute from an uncalibrated wedge carries the wedge’s unquantified step error into your exposure axis, which is one of the reasons a home curve gives good relative numbers and poor absolute ones.

Where each number on the exposure axis comes from

1. 1Lamp and timer — measured once, as illuminance times time; here log H 3.35 in millilux-seconds
2. 2Step wedge, 21 patches — nominal 0.15 apart, 0.05 to 3.05
3. 3Film, emulsion up, in contact — each patch receives log H of the source minus that patch density

Subtraction, not division: the whole horizontal axis of a characteristic curve is built from one measured exposure and a ladder of densities.

What density is physically

Density is an optical measurement, but it is measuring something material, and the chain from one to the other is worth having straight.

Developed silver stops light in two ways: it absorbs it, and it scatters it. Absorption is the electrons in a metal particle taking energy out of the wave. Scattering is the same particle sending light off in some other direction, still in the world but no longer travelling towards your detector, which is lost light as far as the reading is concerned. That distinction looks like hair-splitting and is not: absorbed light is gone whatever instrument you use, while scattered light can be recovered by an instrument that collects widely enough — and that is the whole of the geometry problem two paragraphs below.

Hurter and Driffield set the whole thing out in 1890 in terms that are still recognisable — they used T for transparency and O for opacity, noted that T × O = 1, and defined density as the number of absorbing particles per unit area multiplied by an absorption coefficient. Two differences from modern practice are instructive.

They worked in natural logarithms. Their relation was D = log_e O, not log₁₀ O. The modern base-ten convention makes a density of 1.0 mean exactly a tenth, which is far more useful, but it means an H and D density figure read from an 1890 paper is 2.303 times the modern one for the same negative. If you ever compare their numbers with a datasheet, that factor is why they look wrong.

They asserted that density is directly proportional to the silver per unit area and used it that way. For their materials and their purposes it served. The modern statement adds a term:

D = P × m, where m is silver mass per unit area and P is covering power

Density and silver

Covering power is the density obtained per unit mass of silver per unit area, and it is not a constant. Part IV derived it in the Nutting form and showed it goes as one over the particle size: the same mass of silver divided into smaller particles gives more density, which is why a filamentary developed grain is so efficient and why a solvent developer, which grows more compact particles, returns slightly less density for the same silver. So density is a measure of silver and of how that silver is laid down, and the course keeps density and silver mass as separate ideas for exactly that reason.

There is a third thing the number depends on, and it is not a property of the negative at all: the geometry of the measurement. Because a silver image scatters, the density you read depends on how much of the scattered light your instrument collects. Diffuse density collects it from all directions; specular or projection density collects only what carried straight on, and reads higher. ISO 5-2 — cited here by number and nowhere quoted — separates the two and specifies a geometry for each, which is why Kodak prints “Densitometry: diffuse visual” beside its published curves rather than leaving it to be assumed. The practical consequence is the Callier effect, and it is the reason one negative prints harder under a condenser enlarger than under a diffuser.

Stops, EV and log H

Three scales, one quantity, and a conversion you will do constantly.

Change	In stops or EV	In log H	As a factor
One third of a stop	1/3	0.10	1.26
Half a stop	1/2	0.15	1.41
One stop	1	0.30	2
Two stops	2	0.60	4
Three and a third stops	3 1/3	1.00	10
Ten stops	10	3.01	1024

Exposure value, EV, is a scale in which one unit is one stop, so an EV difference converts to log H by the same 0.30. That matters when a spot meter is used as an interim densitometer, and it matters when a subject’s luminance range is measured: a scene reading EV 8 in the shadows and EV 15 in the highlights spans 7 stops, which is 7 × 0.30 = 2.1 in log luminance. Hold that number; the third lesson multiplies it by a slope to predict what the negative will do.

Be careful with EV in one respect. A difference in EV is unambiguous — it is a number of stops. An absolute EV number is tied to a metering convention and to a film speed setting, so two meters can report different absolute values for the same wall while agreeing perfectly about the seven stops between wall and window. Sensitometry only ever needs the difference, which is one less thing to calibrate.

Going the other way, density to per cent transmission, is the antilog:

T = 10^(−D), and per cent transmission = 100 × 10^(−D)

Density to transmittance

Density	Per cent transmission	Read as
0.10	79 %	base-plus-fog on a clean film
0.30	50 %	one stop
0.45	35 %	a thin shadow
0.75	18 %	a mid-tone on many negatives
1.20	6.3 %	a well-placed highlight
2.00	1.0 %	approaching blocked
3.05	0.089 %	the last step of a 21-step wedge

Running that table backwards is the skill that matters at the bench. A patch that visibly passes about a fifth of the light has a density near 0.7; a patch you can just see a bright lamp through has a density somewhere above 2. Neither is a measurement, but both are enough to tell you whether your exposure series has landed in the right part of the wedge before you commit a whole roll to it.

Reading a manufacturer’s axes

Published curves use three different horizontal scales and rarely explain which.

Absolute log H in lux-seconds. Kodak prints its Tri-X and T-Max characteristic curves this way, with the axis running from about −4.0 up to 1.0, because a camera film needs only small fractions of a lux-second. Negative numbers on the axis are normal and mean nothing sinister: log H = −2.0 is 0.01 lux-seconds.

Millilux-seconds. Kodak’s teaching workbook uses these instead, which shifts every number up by exactly 3.00 and makes the axis positive. A speed point at log H −2.10 in lux-seconds is the same point as log H 0.90 in millilux-seconds. When you compare a worked example from the workbook with a curve from a datasheet, check the unit before you conclude anything.

Relative log exposure. ILFORD’s contrast-control literature plots its paper curves this way, with no absolute scale at all. That is entirely legitimate — the shape and the horizontal separation of the curves is the whole message — but it means no speed can be read from such a plot, only a comparison.

Alongside the axis, a serious published curve states what was done: Kodak’s carry the developer, the temperature, the agitation, the four development times and the densitometry condition, all on the plot. A curve without those is not a measurement, it is a picture of one.

Do the maths

🧮The exposure behind every step of a wedge

You are setting up the step-wedge lab later in this part. The enlarger is raised, the lens stopped down, and a lux meter on the baseboard reads 8.0 lux with no wedge in the beam. You expose for 4.0 seconds.

1. Exposure at the clear edge. H = E × t = 8.0 × 4.0 = 32 lux-seconds. Its logarithm is log 32 = 1.51.

2. Exposure behind step 1 (nominal density 0.05): log H = 1.51 − 0.05 = 1.46, which is 10^1.46 = 28.8 lux-seconds.

3. Exposure behind step 11 (nominal density 1.55): log H = 1.51 − 1.55 = −0.04, or 0.91 lux-seconds. The axis has crossed zero; nothing has gone wrong.

4. Exposure behind step 21 (nominal density 3.05): log H = 1.51 − 3.05 = −1.54, or 0.029 lux-seconds.

5. What the series covers. From step 1 to step 21 is 3.00 in log H, which is 3.00 ÷ 0.301 = ten stops. That is more than any pictorial film uses, which is the point: a single strip brackets the whole response from below the toe to above the shoulder.

6. A check worth making. If the film is nominally ISO 100 and you want its speed point somewhere in the middle of the wedge rather than off the end, you need the clear-edge exposure to be roughly 1.5 to 2.0 log units above the speed-point exposure. Section 4 of the speed lesson tells you what that exposure is; if the arithmetic says your lamp is too bright, stop the lens down another two stops rather than shortening the time below a second, where reciprocity failure would start to bend the axis you are trying to calibrate.

Recap

• Exposure H is illuminance times time, in lux-seconds. The product is what the emulsion responds to, and treating it as a single number assumes the reciprocity law, which is an approximation.
• Density is the base-ten logarithm of the reciprocal of transmittance. D 0.30 passes half the light, D 1.00 a tenth, D 3.00 a thousandth.
• Logarithms turn multiplication into addition, which is why densities add, why a step wedge is a ladder of equal exposure intervals, and why one stop is 0.30 wherever it appears.
• Both axes are drawn to the same scale, 0.30 of density occupying the same distance as 0.30 of log exposure, because the constructions in the next two lessons measure distances along a slope.
• Density measures silver and how the silver is divided, through covering power, and what the instrument reads also depends on its geometry.
• Check the unit on any published curve: lux-seconds, millilux-seconds and relative log exposure are all in use, and they differ by 3.00, by an arbitrary offset, or by everything.

Check your understanding

Question 1. A negative area transmits 4.0 per cent of the light falling on it. What is its density, and how many stops darker is it than an area of density 0.40?

• Density 0.04; about 1 stop darker
• Density 1.40; about 3 1/3 stops darker
• Density 25; about 8 stops darker
• Density 1.40; about 4 2/3 stops darker

Show the answer and why

Answer: Density 1.40; about 3 1/3 stops darker

T = 0.040, so O = 1/0.040 = 25 and D = log 25 = 1.398, call it 1.40. The difference from 0.40 is 1.00 in density, and one stop is 0.301, so 1.00 ÷ 0.301 = 3.32 stops. Notice which of the wrong answers are tempting: 0.04 is the transmittance written as a decimal rather than its logarithm, and 25 is the opacity, which is the number before you take the logarithm. Opacity, transmittance and density are three ways of saying the same thing, and mixing them up is the commonest arithmetic error on this page.

Question 2. You contact-print a 21-step wedge onto film with a lamp and timer that deliver 60 lux-seconds at the clear edge. What log exposure does the step of nominal density 2.30 deliver, and how much is that in lux-seconds?

• log H = 4.08, or about 12 000 lux-seconds
• log H = 1.78, or about 60 lux-seconds
• log H = −0.52, or about 0.30 lux-seconds
• log H = 2.30, or about 200 lux-seconds

Show the answer and why

Answer: log H = −0.52, or about 0.30 lux-seconds

log 60 = 1.78 at the clear edge. The wedge subtracts its density: 1.78 − 2.30 = −0.52. The antilog is 10 raised to −0.52 = 0.30 lux-seconds, which is the same as 60 ÷ 10 raised to 2.30 = 60 ÷ 200. Both routes must agree, and checking them against each other is the quickest way to catch a sign error. The first wrong answer adds the density instead of subtracting it, which would describe a wedge that amplified light.

Question 3. Why does a sensitometric plot insist that 0.30 of density occupy the same distance on the paper as 0.30 of log exposure?

• Because it makes the curve look more symmetrical
• Because the contrast measures are slopes and constructions measured along the line, so a distorted aspect ratio changes the number you read off
• Because density and log exposure have the same units
• Because the standard requires all graphs to be square

Show the answer and why

Answer: Because the contrast measures are slopes and constructions measured along the line, so a distorted aspect ratio changes the number you read off

A slope of density over log exposure is dimensionless, and a gradient of 1.0 is a line at 45 degrees only when the two scales match. That is cosmetic for gamma, which is a ratio of two differences you could compute from a table. It stops being cosmetic for contrast index, whose construction places marks at 0.2 and 2.2 units measured along a sloping straightedge: stretch one axis relative to the other and the straightedge lands somewhere else, and the number changes. Kodak gives the equal-scale rule as a construction instruction for exactly this reason.

Question 4. A spot meter reads the darkest important shadow of a scene at EV 7 and the brightest important highlight at EV 14. What is the subject log-luminance range?

• 7.0
• 2.1
• 0.30
• 21

Show the answer and why

Answer: 2.1

One EV is one stop is a factor of two is 0.301 in log terms. Seven of them is 7 × 0.301 = 2.11, so the subject spans 2.1 in log luminance, or about 128 to 1. This is the number that gets multiplied by the slope of the film curve to predict the negative density range, and it is the reason a photographer with a spot meter is already doing sensitometry without a densitometer: the meter measures the input axis directly, in the same currency the curve is plotted in.

Question 5. Two negatives are read on the same densitometer and both give 1.20. One was developed in a solvent developer that grows compact grains, the other in a non-solvent developer that leaves filamentary ones. What can you say about the silver?

• They contain the same mass of silver per unit area, because density measures silver
• The solvent-developed negative almost certainly holds more silver per unit area, because compact particles have lower covering power
• The filamentary negative holds more silver, because filaments are larger
• Nothing at all, because density and silver are unrelated

Show the answer and why

Answer: The solvent-developed negative almost certainly holds more silver per unit area, because compact particles have lower covering power

Density is covering power times silver mass per unit area, and covering power goes roughly as one over the particle size, so dividing the same mass more finely raises the density. Compact grains have lower covering power, so reaching the same density takes more silver. Hurter and Driffield treated density as directly proportional to silver and were not far wrong for their materials, but the modern statement needs the covering-power term, which Part IV derives in the Nutting form. This is also part of why a fine-grain developer appears to cost speed: some of the apparent loss is optical rather than photographic.

Question 6. A published curve is labelled "relative log exposure" with no units. Which of these can you legitimately read from it?

• The film speed, by finding the speed point and taking its antilog
• The contrast, and the horizontal separation between curves, but not the speed
• Nothing, because a relative axis carries no information
• The speed, provided you assume the axis starts at zero lux-seconds

Show the answer and why

Answer: The contrast, and the horizontal separation between curves, but not the speed

Slopes and horizontal separations survive an arbitrary shift of the axis, because a shift adds the same constant to every value and differences are unaffected. Speed does not survive it, because speed is the absolute exposure at a criterion point and the axis has thrown that away. ILFORD plots its variable-contrast paper curves on a relative axis precisely because the message there is the change in exposure range between filtrations, not any absolute sensitivity. Assuming a zero, as the last option suggests, is inventing the very number the plot declined to publish.

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