Development as Amplification

A developer has to do something that sounds impossible. It must find, in the dark, a cluster of about four silver atoms sitting on the surface of a crystal containing two hundred million silver ions, and then reduce every one of those ions to metal — while leaving the crystal next door, identical in every respect except that it holds no cluster, untouched.

It manages this without any means of detection at all. There is no sensing step. The whole of the selectivity comes from a single property of the chemistry, and this page is about earning that one sentence:

A developer is an electron donor whose potential is sufficient to reduce silver ions at a silver speck, but insufficient to reduce them, in any reasonable time, on a bare crystal.

Every practical fact about development — why exposure becomes density, why contrast grows with time, why an unexposed film eventually fogs, why a solvent developer gives finer grain and slightly less speed — is a consequence of that sentence, and most of them are consequences of the four words in any reasonable time.

All developers are reducing agents; not all reducing agents are developers

The reaction is one you already know from Part III. It is the same half-reaction that stains your fingers black and that made the print-out image in Part I:

Ag⁺ + e⁻ → Ag

The half-reaction development performs, several hundred million times per crystal

In a crystal the silver ion does not arrive from solution; it is already there, and what leaves is the halide:

AgBr + e⁻ → Ag + Br⁻

Chemical development, per formula unit: the silver stays, the bromide goes into the developer

The electrons come from the developing agent, which is oxidised in the process. That is why a used developer is a weaker developer, why sulfite is in the bottle at all, and why the tray goes brown: all subjects that belong to Part VIII, which owns formulation.

Sheppard and Mees put the necessary condition and the insufficient condition side by side in 1907, and the sentence has not needed improving: all developers are, chemically speaking, reducing agents, but the converse does not hold. Plenty of reducing agents with ample potential are useless as developers, because they reduce the unexposed crystals just as readily as the exposed ones and give you a uniformly black sheet.

⚗Why thermodynamics alone cannot pick a developer

It is tempting to imagine choosing a developing agent from a table of standard reduction potentials: find one whose potential sits above the silver couple and below whatever margin you need, and you are done. It does not work, and Sheppard and Mees explain exactly why.

They credit Bredig with pointing out the importance of the reduction potential as a function of a developer, and then add the qualification that matters: there is no strict proportionality between potential and reaction velocity. They offer an analogy that is worth keeping — velocity is like a current, potential like a voltage, and there is a “resistance” in between which is difficult to define and harder to measure.

That is the distinction Part III drew between what a reaction will do and how fast it does it. A potential tells you which way the reaction runs downhill. It tells you nothing about how long it takes to get there, and in development the timing is the entire product. The silver speck does not change the thermodynamics. It changes the rate, and it changes it by an enormous factor, which is why a bare crystal and an exposed crystal can be given the same developer, in the same tray, for the same three minutes, and one of them ends up metallic silver and the other does not.

The cluster as an electrode

The picture that makes the selectivity intelligible is electrochemical. Treat the silver speck as a tiny electrode in contact with both the developer solution and the crystal, and everything falls into place.

Silver metal conducts. The developing agent, arriving at the speck from solution, gives up electrons to it — that is an anodic reaction, and the oxidised developer diffuses away. Those electrons travel through the metal to the silver–halide interface, where they meet silver ions from the lattice and reduce them; that is the cathodic reaction, and the new silver atoms add to the speck. The bromide ion left behind goes into solution, where in a real developer it joins the bromide already present and becomes a restrainer — again, Part VIII’s subject.

The speck therefore grows, and the growing metal is still an electrode. A bigger electrode collects electrons faster, so development accelerates as it proceeds, until the crystal runs out of silver halide to reduce. On a bare crystal there is no electrode: electrons have to be handed directly to a silver ion embedded in an insulating ionic lattice, which is a far slower process. That difference in rate is the whole of development selectivity.

One crystal developing: the speck as an electrode

1. 1The latent-image cluster — about four silver atoms — the only difference between this crystal and the one below
2. 2Developer gives up electrons at the speck — the anodic reaction; oxidised developer diffuses away
3. 3Electrons conduct through the metal — possible only because the speck is a metal, not an ion
4. 4Silver ions reduced at the metal–halide boundary — the cathodic reaction; bromide released to the solution
5. 5The filament grows — threads and branches, not a solid lump
6. 6A crystal with no speck — not immune, only slower — this is where fog comes from

Drawn to teach the sequence, not to scale and not from a micrograph. The crystal of a modern film is about 0.2 micrometres across; the speck at that scale would be smaller than the width of these lines.

The induction period, and why exposure becomes density

Watch a print in the tray and you see the mechanism directly. Nothing happens; nothing happens; and then the image arrives. ILFORD puts numbers on the wait: with Multigrade developer at 1+9 on a correctly exposed resin-coated print, the image will begin to appear after approximately 10 seconds; on fibre-based paper with the same family of developers, after 35 seconds.

That wait is the induction period, and it is the most useful single observation on this page, because it is where the exposure went.

Sheppard and Mees identified what the latent image actually changes, and it is not what most accounts assume. Their microscopy and their kinetics together showed that the developable and undevelopable halide differ in degree rather than absolutely, and that the reactivity conferred by exposure appeared to lie rather in the starting of development by curtailing an induction period than in a change of the rate of reduction.

Read that twice, because it inverts the naive picture. Exposure does not make a crystal reduce faster once it is going. It makes it start sooner. And the size of the cluster sets how much sooner: a crystal with a large cluster presents a large electrode from the first second and begins at once; a crystal with a bare-threshold cluster has to grow its electrode from almost nothing and starts late; a crystal with a sub-threshold cluster, or none at all, starts later still — but it does start, eventually, which is the next section.

Three crystals in the same tray: density against development time

• Heavily exposed crystals
• Lightly exposed crystals
• Unexposed crystals — fog

Show the numbers behind this plot

Three curves of the density a population of crystals contributes, against development time, all in the same developer at the same temperature. The heavily exposed curve starts rising almost immediately, within a few seconds, climbs steeply and levels off at a high plateau by about two minutes: those crystals are exhausted, every silver ion in them reduced, and further time adds nothing. The lightly exposed curve stays flat for about half a minute, then rises more gradually and levels off at a lower plateau, reached later, because fewer crystals in that population carried a developable cluster. The unexposed curve stays flat for far longer, about three minutes, and then begins a slow climb that never levels off within the plotted range: this is fog, and its distinguishing feature is that it has no plateau because it is limited by how long you wait rather than by how much silver is available. Two vertical guides mark the normal development time, where the two exposed curves have separated as far as they will and fog is still negligible, and three times that time, where the exposed curves have gained almost nothing further but fog has risen substantially, so contrast has fallen. A note records that the curve shapes are drawn to teach and were not measured from any material.

Series	Development time (minutes)	Density contributed
Heavily exposed crystals	0.00	0.00
Heavily exposed crystals	0.15	0.05
Heavily exposed crystals	0.40	0.35
Heavily exposed crystals	0.70	0.66
Heavily exposed crystals	1.00	0.82
Heavily exposed crystals	1.50	0.94
Heavily exposed crystals	2.00	0.98
Heavily exposed crystals	3.00	1.00
Heavily exposed crystals	4.00	1.00
Heavily exposed crystals	5.00	1.00
Heavily exposed crystals	6.00	1.00
Lightly exposed crystals	0.00	0.00
Lightly exposed crystals	0.30	0.00
Lightly exposed crystals	0.50	0.03
Lightly exposed crystals	0.80	0.12
Lightly exposed crystals	1.20	0.26
Lightly exposed crystals	1.80	0.38
Lightly exposed crystals	2.50	0.45
Lightly exposed crystals	3.50	0.49
Lightly exposed crystals	4.50	0.50
Lightly exposed crystals	6.00	0.50
Unexposed crystals — fog	0.00	0.00
Unexposed crystals — fog	1.00	0.00
Unexposed crystals — fog	2.00	0.01
Unexposed crystals — fog	3.00	0.02
Unexposed crystals — fog	4.00	0.05
Unexposed crystals — fog	5.00	0.09
Unexposed crystals — fog	6.00	0.14

Drawn to teach the three shapes, not measured. The one feature that carries the argument is that the two exposed curves have plateaux and the fog curve does not: an exposed crystal runs out of silver halide, an unexposed population runs out of nothing but your patience. 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.

Three practical statements follow from that plot, and they are the bridge from this page to the sensitometry of Part XIII.

Exposure becomes density because the number of crystals carrying a developable cluster rises with exposure, and each developed crystal contributes its whole silver content. Hurter and Driffield established the other half of that chain in 1890 — that density is proportional to the mass of silver per unit area — so more crystals developed means proportionally more density.

Contrast grows with development time because the heavily and lightly exposed populations separate. Early on, only the heavily exposed crystals have started, so the difference between them is small in absolute terms; as development continues the heavily exposed population reaches its plateau while the lightly exposed one is still climbing, and the gap widens — then narrows again as the lightly exposed population also plateaus and fog begins to lift the shadows.

There is a limit, and it is fog. ILFORD state that fibre-based prints may be developed to six minutes without any noticeable change in contrast or fog with their paper developers, which puts a useful figure on how much slack a modern material has. Beyond such a limit, more time buys you base density rather than image.

!Developability is a threshold, and the developer sets where it is

One more result from Sheppard and Mees, easy to miss and important enough to state on its own. Working out why the characteristic curve shifts along the log-exposure axis when development is retarded, they concluded that the density obtained does not represent the whole mass of the photo-product, but only that minimum necessary to render the grain developable for a particular development energy.

In other words there is no single, material-wide number of atoms that means “developable”. A vigorous developer will start on clusters that a weak one ignores, and clusters too small for the weak developer will show up when it is replaced by a stronger one. That is why the same film has one speed in one developer and another speed in another; it is why film speed and effective film speed are kept apart by the course’s terminology; and it is the reason the four-atom threshold of the latent image page has to be read as an approximate minimum rather than a switch.

Filamentary silver, and how big the amplification is

If you develop a negative and look at a grain under sufficient magnification, you do not find a neat lump of silver where the crystal used to be. You find a tangle. The Image Permanence Institute describes the developed image of a gelatin dry plate as being formed of ribbon-like (filamentary) silver particles, and notes the consequence: those particles produced great opacity and a neutral-black image colour.

Both halves of that sentence matter, and the second is the one photographers feel. A tangle of thin filaments intercepts far more light per gram than a compact particle of the same mass, because what blocks light is projected area and a filament is nearly all surface. It is also large compared with the wavelength of light in every direction that matters, so it absorbs across the spectrum rather than selectively — hence neutral black, against the reds, purples and browns of the colloidal print-out silver that the silver page explained.

🔬Why filaments? The honest answer

The course can tell you confidently that developed silver is filamentary, from conservation sources that identify photographs by it, and what follows from the shape. It cannot tell you from any source it holds why the growth is filamentary rather than compact, and the sources that would settle it — James’s Theory of the Photographic Process above all — are cited here but have not been read.

What the electrode picture makes plausible, and what is offered as reasoning rather than as evidence: growth happens only where the metal touches the halide and the solution can reach, so it is concentrated at a moving tip rather than spread over the whole speck; a thread that has begun to grow presents a better collector of electrons than a flat face and therefore grows faster still; and the gelatin around the crystal offers no template that would favour a compact shape. That is a hypothesis consistent with the mechanism, not a result, and this course marks the difference.

🧮How big is the amplification? The arithmetic, with every assumption named

No source this course holds states an amplification factor. So here is a calculation from numbers that are sourced, with the assumptions written out so you can attack them.

Step 1 — how much silver is in a fully developed sheet. Ware gives the silver coating weight of modern silver-gelatin enlarging papers as 1 to 1.6 grams per square metre. Take the low end, 1.0 g/m², and the relative atomic mass of silver, 107.9:

n = 1.0 g ÷ 107.9 g/mol = 9.27 × 10⁻³ mol

Moles of silver in one square metre

Multiply by Avogadro’s number, 6.022 × 10²³ per mole: 5.6 × 10²¹ silver atoms per square metre. Every one of them needs one electron from the developer, so a fully blackened square metre costs 9.27 × 10⁻³ moles of electrons — which, if you like your quantities in coulombs, is 894 C, about the charge in a small rechargeable cell.

Step 2 — how many crystals that is. Kodak’s double-jet patent gives an average grain size of about 0.2 micrometres for cubic-regular bromoiodide, and says good results come from grains below 0.5 micrometres. Assume the emulsion is a single close-packed layer of 0.2 µm crystals. Each occupies (0.2 × 10⁻⁶ m)² = 4 × 10⁻¹⁴ m², so a square metre holds

N = 1 m² ÷ 4 × 10⁻¹⁴ m² = 2.5 × 10¹³ crystals

Crystals in a square metre, assuming one close-packed layer

Step 3 — how much silver the latent image is. At about four silver atoms per crystal, the latent image over that whole square metre amounts to 2.5 × 10¹³ × 4 = 1.0 × 10¹⁴ silver atoms.

Step 4 — the ratio.

5.6 × 10²¹ ÷ 1.0 × 10¹⁴ ≈ 6 × 10⁷

Amplification factor

Of the order of ten million to a hundred million. Equivalently, about 2 × 10⁸ silver atoms per crystal, from a cluster of four.

Now the assumptions, because an order of magnitude is only as good as they are. The close-packed monolayer is the weakest: a real emulsion is a few crystals deep with gaps between them, so the true crystal count could be out by a factor of several either way, and the amplification with it. The four-atom threshold carries Ware’s own hedge. Not every crystal develops, and not every developed crystal is reduced completely. And a paper is not a film. What survives all of that is the exponent: the answer is not 10³ and it is not 10¹², and no plausible correction to the assumptions moves it more than a decade. That is what “an order of magnitude” means, and it is worth more than a precise number you cannot source.

Chemical development, physical development, and the middle case

So far the silver has come from the crystal it lands on. That is chemical development, and IPI’s definition is exactly that: the chemical reduction of silver-halide crystals into metallic silver particles called filamentary silver, in which all the image-forming material is present in the binder and no silver is added by the developing solution.

Physical development is the alternative: development with a solution that itself contains silver ions, which plate out onto the latent-image specks and build the image from outside. IPI notes that the resulting particles differ in shape and size from chemically developed ones, and records which processes used it — collodion and paper negatives, including Talbot’s calotype with its silver nitrate and gallic acid. It is also why physically developed plates look different: IPI describes physically developed gelatin glass plates as usually grey or tan rather than neutral black, which is the particle-shape argument again.

Between the two sits the case that matters most in a modern darkroom.

⚗Solution physical development, and the price of fine grain

Put a silver halide solvent in an ordinary developer and both mechanisms run at once. Sulfite is the usual solvent, and it is in most developers anyway as a preservative — the double role that Part VIII (sulfite-and-preservation) is built around. D-76 is the classic example, and this course names it here only as that example; its formula, its variants and its behaviour belong to Part VIII’s formulary entry.

What the solvent does is dissolve a little silver halide from the crystals into the developer, where it is reduced and re-deposited onto specks that are already developing. Sheppard and Mees studied the same effect with thiosulfate and other silver solvents in 1907, and proposed that complex silver ions in the developer were among the actions in play.

Three consequences, and they come as a package.

Finer grain. Silver deposited from solution fills in around the developing filaments rather than extending them, so the developed grain is more compact and the clumps are smaller.

Slightly lower speed. The solvent attacks the crystals indiscriminately, including the outsides of crystals whose latent image is small; some marginal clusters are dissolved away before they can start. You buy grain with shadow detail.

Warmer tone on papers. More compact particles scatter and absorb differently from filaments — the same particle-size argument as print-out silver — so a solvent developer, or a developer used at a strength where physical development contributes, shifts image colour warm.

Kodak’s own D-76 sheet contains the compact statement of the trade in a different variable: dilute it 1+1 and you get greater sharpness with a slight increase in graininess. There is no free move here, and Part VIII exists to teach you which price to pay.

Fog is kinetics, not thermodynamics

Here is the sentence this page has been driving at. An unexposed crystal is not undevelopable. It is slow. Given enough time, enough temperature or enough developer activity, it will develop, and the density it contributes is fog.

Nothing about the thermodynamics forbids it. The developer’s potential is sufficient to reduce silver ions; it is sufficient everywhere in the tray. What the latent-image speck supplies is a route with a much lower barrier — an electrode. The unexposed crystal has to nucleate its own first silver atoms without one, which is slow, but “slow” and “never” are different words, and Part III taught you to keep them apart.

Sheppard and Mees derived a small consequence of that in 1907 which is worth working through, because it catches out anyone who measures fog carelessly. Let a crystal population contain A crystals changed by light and B crystals unchanged, so the total is C = A + B. The fog strip — a piece that received no exposure — has all C crystals available to fog. The exposed area has only B, because the A crystals are developing as image, not as fog. So:

rate of fogging in the fog strip ∝ (A + B); in the exposed area ∝ B

Fog develops in whatever is left

and therefore, in their words, fog increases faster in unexposed film than in the exposed. Subtract the fog strip’s density from an exposed reading and you have over-subtracted. They state the practical standard they worked to as well: for photochemical investigation you want an emulsion that does not give a fog density higher than 0.15 to 0.2 even on infinite development.

Their microscopy adds the observation that makes fog concrete: even when a fog strip looks quite transparent, appreciable numbers of silver particles can be seen in it under the microscope. There is no such thing as zero fog; there is only fog below the threshold at which you notice it.

=What raises fog, and what it looks like when it happens

Three levers, all of them the ordinary levers of reaction rate.

Time. The longest and most obvious. ILFORD’s six-minute figure for fibre prints tells you how much headroom a good modern combination has; go far past the recommended time on any material and the shadows lift before the highlights gain.

Temperature. Every ten degrees roughly multiplies a chemical rate, and fog is a chemical rate. A developer run warm to save time is a developer run closer to its fog.

Activity. A higher pH, a fresher solution or a more energetic agent all raise the rate — of image development, which you want, and of fog, which you do not. The restrainers and organic antifoggants of Part VIII (restrainers-and-antifoggants) exist to suppress the second more than the first, and the bromide released by the image itself does some of that work for free.

What it looks like. Not, usually, an obviously grey sheet. Kodak’s warning about safelights applies to fog from any source: poor conditions produce a loss in photographic quality before actual fogging is visible. You see flat highlights and a print that will not sparkle, and you blame the negative.

Covering power, and why the same silver gives different densities

Density is not proportional to silver alone. It is proportional to silver and to how that silver is divided up, and the quantity that connects them is covering power: the optical density obtained per unit mass of silver per unit area, in square metres per gram.

Ware sets out the relation, which goes back to Nutting. If the image particles are spheres of radius r and density ρ, and κ is the ratio of a particle’s optical cross-section to its geometric area, then

P = 3κ / (4ρr)

Covering power, in the Nutting form

Everything you need is in the r on the bottom. Covering power is inversely proportional to the linear size of the particle. Halve the particle size, at constant total mass, and you double the density. That is the same argument as the amplification arithmetic, seen from the optical end: what blocks light is total projected area, and dividing a fixed mass into smaller pieces increases area.

Ware works the numbers for the colloidal silver of a salted-paper print: taking r = 10 nm, ρ as that of bulk silver, 10.5 g/cm³, and κ as unity, he gets P ≈ 7 m² per gram, which he notes lies in the middle of the range Berry and Skillman measured for silver deposits; an independent route through the molar extinction coefficient of yellow nanoparticle silver hydrosols gives P ≈ 15, near the top of that range.

Two consequences worth carrying away. A filamentary developed grain has enormous covering power for its mass, which is IPI’s “great opacity” restated — and it is why a modern film needs so little silver. And the trade you met two sections ago now has a second face: a solvent developer that makes the particles more compact lowers covering power, so the same exposure and the same silver give slightly less density. Part of what looks like a speed loss in a fine-grain developer is optical rather than photographic.

The full consequences of particle size and shape — for grain, for resolution, for the choice of film — are the subject of the next page.

Infectious development: the extreme case

One last case, because it shows what happens when the feedback in the electrode picture is allowed to run away.

Lithographic materials are made to give an image with no middle tones at all: black or clear, nothing between. They achieve it with a developer containing a single developing agent and very little sulfite, in which development is autocatalytic — the product of development accelerates further development. A crystal that starts to develop promotes development in its neighbours, so a clump of grains goes from nothing to fully developed almost at once, and the characteristic curve becomes nearly vertical. The practice of running such a developer deliberately dilute and exhausted on ordinary paper — lith printing — turns that runaway into a printing technique.

⁇Infectious development: what this course can and cannot say

The behaviour is not in doubt: lith materials do give near-vertical curves, and the effect is called infectious development because development spreads.

The mechanism is usually attributed to a semiquinone intermediate — a partially oxidised hydroquinone that is itself a developing agent, which normally the sulfite would mop up and which in a low-sulfite developer survives to accelerate the reaction. This course has read no Tier-1 source stating that mechanism, and it is set out here as the account the literature gives rather than as a verified result. The name of the intermediate is not something to take on trust from this page.

What can be said on this page’s own terms is that infectious development is the electrode picture with positive feedback: development produces something that makes development faster, so the process runs away, and the material’s contrast is limited only by how fast the runaway propagates. Part VIII owns the oxidation chemistry of developing agents, and the printing parts own the practice.

Recap

• The definition of a developer is a kinetic one: an electron donor with enough potential to reduce silver ions at a silver speck and not enough to reduce them, in reasonable time, on a bare crystal. All developers are reducing agents; the converse does not hold.
• The speck acts as an electrode. Developer gives up electrons to it from the solution, the metal conducts them to the halide interface, silver ions are reduced there and bromide is released. The electrode grows, so development accelerates.
• Exposure curtails an induction period rather than changing the rate of reduction — Sheppard and Mees’s result, and visible in the tray as the ten to thirty-five seconds before an image appears.
• Developability is a threshold set jointly by the cluster and the developer. A more energetic developer finds smaller clusters, which is where the distinction between film speed and effective film speed begins.
• Developed silver is filamentary, which gives it great opacity and a neutral black colour. Why the growth takes that form is not something this course can source.
• The amplification is of order 10⁷ to 10⁸, by the course’s own arithmetic from Ware’s coating weights and Kodak’s grain size, with the assumptions stated.
• Chemical development takes silver from the crystal; physical development takes it from the solution. A solvent developer does both, and buys finer grain with a little speed and a warmer tone.
• Fog is kinetics, not thermodynamics. Unexposed crystals develop given time, temperature or activity, and fog rises faster in an unexposed strip than in an exposed one because there is more left to fog.
• Covering power goes as 1/r. The same mass of silver in smaller particles gives more density, which is why filaments are efficient and why compact, solvent-grown grains are not.

Check your understanding

Question 1. Why can a developer distinguish an exposed crystal from an unexposed one when both contain exactly the same compound?

• Because exposure changes the reduction potential of the silver ions in the crystal
• Because the latent-image speck is a metal, and offers a low-barrier route for electron transfer, so the exposed crystal develops enormously faster rather than being the only one that can develop
• Because the developer molecule binds selectively to exposed crystals
• Because the halide is already partly removed from the exposed crystal

Show the answer and why

Answer: Because the latent-image speck is a metal, and offers a low-barrier route for electron transfer, so the exposed crystal develops enormously faster rather than being the only one that can develop

The distinction is kinetic, not thermodynamic, and this is the single most important idea on the page. The potential of the developer is the same everywhere in the tray, and it is sufficient to reduce silver ions everywhere in the tray. What the speck supplies is an electrode: a piece of metal in contact with both the solution and the crystal, through which electrons can be delivered at a rate a bare ionic lattice cannot match. That is also why the same developer, given three times as long, will develop the unexposed crystals too. Sheppard and Mees made the point in 1907 by noting that there is no strict proportionality between potential and reaction velocity.

Question 2. A film is developed for three times its recommended time in the same developer at the same temperature. What happens to the negative?

• Density and contrast both go on rising in proportion, so the negative simply gets stronger
• Nothing, because the exposed crystals were already fully developed
• The heavily exposed areas gain little further, the fog level rises steadily, and contrast therefore falls while base density rises
• The image is destroyed

Show the answer and why

Answer: The heavily exposed areas gain little further, the fog level rises steadily, and contrast therefore falls while base density rises

Each exposed crystal contains a fixed amount of silver halide, so once it is fully reduced it can contribute nothing more: the heavily exposed population reaches a plateau. Fog has no such plateau, because the number of unexposed crystals available to develop is large and they simply keep starting. So beyond a certain point extra time adds density in the shadows and not in the highlights, which is exactly a loss of contrast. The practical figure is on the ILFORD paper-developer sheet: fibre-based prints may go to six minutes without noticeable change in contrast or fog, which tells you where a good modern material stops being forgiving.

Question 3. A fine-grain solvent developer gives visibly smaller grain and, on test, about a third of a stop less effective speed than the same film in a non-solvent developer. What is the mechanism behind the speed loss?

• The solvent reduces the developer potential
• The solvent dissolves silver halide indiscriminately, including from crystals whose latent image is marginal, so some clusters are lost before they can start development
• The solvent makes the gelatin swell less, so the developer penetrates more slowly
• The solvent bleaches part of the developed image

Show the answer and why

Answer: The solvent dissolves silver halide indiscriminately, including from crystals whose latent image is marginal, so some clusters are lost before they can start development

A silver halide solvent such as sulfite attacks the crystals themselves, and it cannot tell a crystal with a four-atom cluster from one with three. Shadow detail is made of exactly those marginal crystals, so it is the first thing lost, and lost shadow detail is what a speed test measures. Part of the apparent loss is also optical rather than photographic: silver re-deposited from solution builds more compact particles, and covering power goes as one over the particle radius, so more compact silver gives less density for the same mass. The trade is real either way, and it is the reason no one developer is best.

Question 4. Estimate the amplification factor of development, using a paper carrying 1.0 g of silver per square metre, crystals 0.2 micrometres across in a single close-packed layer, and four silver atoms per latent-image cluster.

• About 10³
• About 10⁵
• About 10⁷ to 10⁸
• About 10¹²

Show the answer and why

Answer: About 10⁷ to 10⁸

One gram of silver is 1.0/107.9 = 9.27 millimoles, which is 5.6 × 10²¹ atoms. A square metre of 0.2 micrometre squares holds 1/(4 × 10⁻¹⁴) = 2.5 × 10¹³ crystals, and four atoms each makes 1.0 × 10¹⁴ atoms of latent image. The ratio is about 6 × 10⁷, or roughly 2 × 10⁸ silver atoms grown from a cluster of four in each crystal. The monolayer assumption is the shakiest step and could move the answer by a factor of several, but not by a factor of ten thousand, which is why the useful form of the answer is an exponent rather than a number.

Question 5. Two prints are made from the same negative, one in a developer that works purely chemically and one in a developer with a strong silver halide solvent. The second print looks warmer in tone. Why?

• The solvent leaves a yellow stain in the paper
• The solvent developer deposits silver from solution, giving more compact particles, and particle size and shape decide what wavelengths the image silver absorbs
• The solvent lowers the pH, and warm tones come from low pH
• The solvent removes the optical brightener from the paper base

Show the answer and why

Answer: The solvent developer deposits silver from solution, giving more compact particles, and particle size and shape decide what wavelengths the image silver absorbs

Image colour in a silver photograph is a particle-size effect, the same one that makes print-out silver red or purple while developed silver is black. Filamentary silver, large compared with visible wavelengths and highly divided, absorbs across the whole spectrum and reads as neutral black; more compact particles grown partly from solution absorb selectively and read warm. The Image Permanence Institute records the same thing from the other direction, describing physically developed gelatin plates as grey or tan rather than neutral black. Note that this is an optical explanation, not a chemical one: the silver is the same element either way.

Question 6. You measure the density of an exposed step on a film, and subtract the density of an unexposed fog strip processed alongside it. Sheppard and Mees pointed out a systematic error in that procedure. What is it?

• The fog strip develops less because it has no latent image
• The fog strip has all its crystals available to fog, while the exposed area has only those not already developing as image, so the fog strip over-states the fog present in the image area
• The two pieces are at different temperatures
• Fog is not additive with image density

Show the answer and why

Answer: The fog strip has all its crystals available to fog, while the exposed area has only those not already developing as image, so the fog strip over-states the fog present in the image area

Write the crystal population as A crystals changed by light plus B unchanged. In the fog strip, all A + B are available to fog; in the exposed area, only B are, because the A crystals are already developing as image. Fog therefore accumulates faster in the unexposed strip, and subtracting its density over-corrects. The size of the error grows with exposure, so it distorts the shape of the curve rather than shifting it. The practical answer is not to abandon the fog strip but to know its limits, and to work with a material whose fog stays low: Sheppard and Mees worked to a standard of 0.15 to 0.2 even on infinite development.

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