Newton's rings

Lifted from the contact printing frame and its light source, whose T2 is the acceptance test named throughout and which owns the anti-Newton trade; from enlarger optics and design, which owns the choice between a glass and a glassless carrier; and from commissioning the enlarger, whose certificate carries the row that records which carrier is fitted and whether its glass is anti-Newton. Part XVII owns the popping negative that makes the pattern move during an exposure, and the exposure record that makes any interim correction repeatable.

What you see

Closed, irregular grey loops on the print, nested one inside another like the contour lines of a hill, that are not on the negative. They are not perfect circles and they are not evenly spaced: the spacing tightens where the loops crowd together and opens out where they do not, and one sheet can carry two or three separate nests with clear film between them.

Count them. There will usually be a handful — five or ten — not dozens, and the outermost is the faintest. That number is a signature rather than an accident, and the reason for it is in the physics below: Newton himself, quoted by Rayleigh, recorded that with the naked eye he “could not discern above eight or nine of those rings”.

Two scales, depending on where the sandwich is:

• On a contact print the loops are the size they are in the frame — a few millimetres to a few tens of millimetres across — and their edges are as crisp as anything else on the sheet.
• On an enlargement made with a glass carrier they are magnified with everything else, so a 5 mm nest at the negative becomes a 30 mm one at 6×: large, soft-edged, and very easily read as a stain, as uneven development, or as a fault in the paper.

Then look at the negative. On a light box, under a loupe, there is nothing there. A ring you can find on the film is not this entry.

Then look at the closed sandwich itself, under a bright oblique light, before you expose anything. The fringes are directly visible, and by reflected light they are coloured — a soap-bubble sequence of blues, greens and straw-yellows — while on the print they are grey. That difference is not a puzzle: the paper records the light that came through, which is the complement of the light that came back, integrated over everything the emulsion can see.

What the dry print shows	What it is	Where it goes
Closed irregular loops, absent from the negative, in a different place after the sandwich is reopened and re-closed	Newton’s rings — this entry	T2
A fine, even, grain-like texture laid over the whole image with no loop structure	Anti-Newton glass, its texture printing	uneven contact print
Loops or arcs in exactly the same place on every print	Something physically there — a drying mark, a fingerprint, a film of grease on the glass	black spots
Iridescent blue or greenish surface markings, on the print or plate itself, usually nearer the margins	Silver sulphide, which Wall’s dictionary lists as Iridescent Surface-marking	silver mirroring
A ring-shaped brown or yellow mark that is on the dry negative under a loupe	A chemical stain	oxidation stain
A broad soft patch with no fringe structure, in a different place on each print	The negative not flat, or popping in the beam	buckled-sheet softness
Smooth darkening towards the corners, no loops	The light, not the sandwich	uneven contact print

On an alternative-process sheet the same nests appear in the image colour of the process — pale loops through a cyanotype’s blue — because the mechanism is in the light path and does not care what the sensitiser is.

Likely causes

Every one of them is a statement about the gap between two smooth surfaces, and none of them is chemistry.

1. A glass negative carrier with plain glass in it. The commonest cause in an enlarger, and it arrives the day the reader fits a glass carrier to cure a different fault — a negative that would not lie flat.
2. A contact frame closed hard, or backed softly. Ware specifies a baseboard covered with a felt blanket or porous plastic to take up surface unevenness, which is exactly right and is also what makes rings likelier: a compliant backing lets the film settle into optical contact over a wide area instead of touching at a few high points.
3. Anti-Newton glass fitted the wrong way round. The textured face must go against the film. Turned over, it presents its polished face to the base — so the fringes form as if the glass were plain — while its texture is still in the light path and still prints. The worst of both.
4. A near-collimated head. A condenser head will show a pattern that a diffusion head averages into invisibility in the same carrier, for the reason given under the retardation equation below.
5. A glass plate negative in a printing frame, which puts two polished glass surfaces face to face. This is the configuration in which the effect was first described, and it is the worst case the course teaches.
6. A negative warming in the beam. Heat changes the shape of the film, so the gap changes and the pattern moves part way through the exposure. Part XVII’s break/fix page owns the popping negative; the same movement smears fringes rather than displacing an image.

Not this entry at all: anything you can find on the negative, and anything that repeats in the same place print after print. Both are excluded in one sheet by the test below.

What is happening: the chemistry and physics

Nothing chemical happens at all. This is the entry the glossary warns about: a ring on a print looks like a stain, stains have chemical causes, and a reader can lose an evening reformulating a developer that was never involved.

Two reflections and a wedge of air

Where the film base lies almost against the glass there is a very thin layer of air between them. Light arriving at the sandwich is reflected twice — once at the base-to-air surface and once at the air-to-glass surface — and the two reflections travel different distances before they recombine. Rayleigh gives that difference, for a plate of index μ and thickness t, as

δ = 2 μ t cos a′

Retardation of the second reflection (Rayleigh, § 8)

where a′ is the angle of refraction inside the plate. Here the plate is the air, so μ = 1 and δ = 2t cos a′; at near-perpendicular incidence that is simply twice the gap.

The half-wave loss, and why perfect contact prints nothing

One more term has to be added, and it is the whole reason the pattern reads the way it does. A reflection off a medium of higher refractive index turns the wave through half a cycle; a reflection off a medium of lower index does not. OpenStax states the rule directly: a 180° phase change on reflection at an interface beyond which is a medium of higher index, and no phase change from a medium of lower index. It does not matter which way round the sandwich is stacked. Whichever of the two solids the light meets first, it leaves a denser medium for a thinner one at the near surface of the gap — no shift — and meets a denser medium again at the far surface — half a cycle. There is exactly one such shift, always, so the two reflections start out half a cycle apart before the gap has contributed anything at all.

2 t = n λ

Dark in reflection, bright in transmission

So the reflected light cancels wherever twice the gap is a whole number of wavelengths, including n = 0. Rayleigh puts it in one sentence: when the first and third media are the same, the central spot in the system of Newton’s rings is black even though the original light contain a mixture of all wave-lengths. OpenStax says the same thing about a wedge of air between two microscope slides — a dark band forms where the slides touch — and about a film much thinner than a wavelength, where the two rays are exactly out of phase and destructive interference occurs at every wavelength at once.

Rayleigh states the black centre for the case where the outer media are the same. What his result actually needs is that both of them be denser than the film between, which the base and the glass both are, so the rule carries over to the darkroom sandwich as it does to his two lenses.

The practical consequence is the one that surprises people. True optical contact produces no pattern: it is uniformly clear in transmission, everywhere. The rings appear in the zone where contact is almost perfect, and they are, as the contact frame’s T2 says, a sign of a good frame rather than a bad one. You cannot get rid of them by pressing harder in the hope of squeezing the gap out, because the gap is already less than a micrometre and the place you are trying to reach — zero — is not somewhere pressure reliably gets you.

Why closed loops, and how to read the gap off them

A gap that varies smoothly across a surface has closed level curves, in the same way that a hillside does, and each fringe is one such curve. Rayleigh writes the condition for the nth dark ring where the upper surface is curved:

½ n λ = a + b x²

The nth dark fringe over a curved surface (Rayleigh, § 8)

with a the least distance between the surfaces at the point of closest approach and b the curvature. Two things fall out of it. The centre of each nest is the point of nearest contact, and the value of a there decides whether that centre is light or dark. And the spacing is set by the curvature, so a slow, shallow wedge gives few, widely spaced loops while a sharply curved one crowds them together — which is why the pattern is a map and not a decoration. OpenStax puts the same relation the way an optician uses it: each successive ring of a given colour marks an increase of only half a wavelength in the separation.

🧮Reading the gap off the ring count

Each ring outward is one further half-wavelength of gap. For light across the 380 to 780 nm span over which this course’s own emitter datasheets plot visible output, half a wavelength is 0.19 to 0.39 µm.

A nest of six rings therefore maps a wedge that climbs roughly 1.1 to 2.3 µm from its centre to its outer ring. Set that against the film it forms on: ILFORD publish FP4 Plus roll film as 0.110 mm of acetate, which is 110 µm. The entire fault lives inside a gap about one fiftieth the thickness of the base it forms against — far too small to see, to feel through a closed frame, or to shim.

This is arithmetic on two published figures, not a measurement. It is offered so that the reader can convert a ring count into a distance and stop thinking of the fault as a stain.

Why there are only ever a few rings

White light is a mixture, and each wavelength satisfies 2t = nλ at a different gap. Near the centre the orders of every colour nearly coincide, so the fringes are strong. Further out they slide apart, overlap, and blend back into white. That is why Newton could count eight or nine and no more, and it is the reason the pattern is localised: beyond about a micrometre of separation the sandwich looks perfectly clear, whatever it is doing at the scale of a wavelength.

Why the print sees a shallower version than your eye does

Rayleigh gives the reflected and the transmitted intensities as two expressions whose sum is unity. For weak reflections — and a glass surface in air is a weak reflector — the reflected intensity swings between zero and about four times the reflectance of one surface. Your eye, looking at the sandwich, is looking at that whole swing, from nothing to everything, so the fringes are vivid. The paper is looking at its complement: a shallow dip in a bright field.

Two honest limits on that. Rayleigh’s expressions assume the outer media are identical, and here they are film base on one side and glass on the other, so the dark fringes do not go quite to zero. And this course has no sourced refractive index for the film bases it uses, so no figure is given for the depth of the dip. The shape of the result is what matters: shallow, and not therefore invisible. ILFORD’s own safelight sheet takes about 0.04 in density as a change that means conditions are inadequate — borrowed here, as elsewhere in the course, as the only published statement it has of what is detectable on paper — and a shallow modulation clears that bar easily enough to spoil a print.

Why a diffuse head hides what a condenser head shows

The retardation is 2t cos a′, so it depends on the angle at which the light crosses the gap. A collimated beam crosses it at one angle and every ray agrees on the phase; a diffuse beam crosses it at many, and the higher orders, where a small change in a′ moves the fringe by a whole order, average away. The low orders near the centre survive, because there the retardation is small and so is its variation with angle.

Rayleigh reaches the same place from the other end, in a note of 1900: as one goes to high interference “it becomes necessary to pay great attention to the perpendicularity of the incidence”. This application to enlarger heads is the course’s own reasoning from his relation, not a published photographic result, and it predicts something a reader can check on one sheet — the same negative in the same carrier will show more rings under a condenser head than under a diffuser.

The variable-contrast twist

Variable-contrast paper adds a consequence that graded paper does not have. ILFORD publish what MULTIGRADE is: three blue-sensitive emulsions carrying different amounts of green sensitising dye, of the same inherent contrast and the same blue speed but very different green speeds, so that blue exposure gives high contrast and green exposure gives low. The fringe condition is wavelength-dependent by construction — blue and green have their maxima at different gaps — so a ring pattern does not merely modulate the amount of light reaching the paper. It modulates the blue-to-green ratio across the sheet.

The course’s own inference, stated as one under Rule 7 and not tested here: on variable-contrast paper the rings should print as a variation in local contrast as well as in density, which would explain why they are so often reported as uneven development rather than as fringes. On a graded paper the same sandwich should give density variation alone. A reader who prints the same ringed negative on both has an experiment, and the course would be glad of the result.

Diagnostic questions

• Is it on the negative? Light box, loupe, both sides. If the pattern is on the film, this page has nothing for you; go to the stain and drying-mark entries.
• Do the loops close, and is their spacing uneven? Closed, nested, irregularly spaced loops are a contour map of a gap. Regular concentric circles of even spacing are more likely to be a lens artefact or something turned on a lathe.
• How many rings, and does the outermost fade? A handful that fade outward is the white-light signature. Dozens of hard-edged rings are something else.
• Does the closed sandwich show coloured fringes under a bright oblique light? This is the fastest confirmation there is, and it costs no paper.
• Did it start when you fitted a glass carrier, changed the frame’s backing, or began closing the frame harder? A fault with a date has a very short list of causes.
• Condenser head or diffuser head? If a diffuser head shows them, the gap region is large or the contact is very nearly perfect.
• Glass plate negative? Two polished surfaces are the worst case, and the reader should expect the fault rather than be surprised by it.

!The confirming test: reopen the sandwich and close it again

Change exactly one thing — the seating of the sandwich — and print the same negative again. Same exposure, same paper, same developer, same everything else. Open the carrier or the frame, lift the negative clear, put it back, and close it.

• The nest appears in a different place, or with a different number of rings, or splits into two. It is interference: the pattern is a map of a gap, and you have just redrawn the gap. This is the diagnosis.
• The pattern is identical and in the identical place. It is not interference. Something is physically present — on the glass, on the base, or in the emulsion — and it does not move because it is attached to a surface.
• Nothing appears at all this time. That is consistent with the diagnosis rather than against it, because you may simply have made contact worse. Run it twice more before concluding anything; a fault that comes and goes with reseating is this one.

Then run the frame’s T2 properly, as an acceptance test rather than a post-mortem: a strip of clear developed film base in the frame, closed, under a bright oblique light. Rings in a few small regions are normal and usually invisible at contact scale. Rings over large areas of every negative will print.

No published account of the reopening test was found in this course’s corpus; it is offered as reasoning from the mechanism, being the only variable that changes the gap without changing anything in the light path.

Corrective action

Do not take it to a bath. Nothing in the developer, the fixer or a reducer touches a fault that lives in the air between two surfaces, and Wall’s dictionary is a caution rather than a guide here: his Iridescent Surface-marking is a real defect with a real remedy — silver sulphide, rubbed off with spirit or swabbed with a reducer — and it is the defect Newton’s rings get mistaken for. Rubbing a print because the marks looked iridescent is how a diagnosis error becomes a damaged print.

Reseat and reprint first. It is free, it is the confirming test, and often enough the second seating moves the nest into a part of the frame where it does not matter, or removes it. Where a print must go out tonight, this is the whole repair.

Then change the surface, not the force. This is the decision the page exists to make clear, and the reason pressure is the wrong control is that the two faults sit at opposite ends of the same variable:

• Press harder and the gap goes towards zero, where the rings live.
• Let the gap open and the rings vanish — and the print goes soft, because Ware’s penumbra relation, blur = gap × aspect value, turns a gap into blur under any source of appreciable angular size, with 0.3 mm of blur taken as the onset of a fuzzy image.

There is no pressure that gives neither, so the fix has to be the surface:

1. A glassless carrier, where the format allows it. The optics page owns the trade in full — a glassless carrier adds no surfaces, cannot make rings and cannot trap dust, and it does not guarantee flatness, which is a problem that grows with format.
2. Anti-Newton glass, textured face against the film. The texture holds the surfaces apart by more than a wavelength, so the fringes cannot form. Its cost is that the texture is now in the light path and prints as a fine grain-like structure over the whole image, worst at contact scale. Fit it because T2 showed rings actually printing, not as a default. The course could not source a manufacturer’s or conservator’s account of how anti-Newton glass is made or of what its texture costs in resolution, and that gap is recorded on the contact frame page rather than filled in here.
3. Mark the textured face the day the glass arrives, with a spot of paint on the edge, and check it after every clean. A sheet fitted the wrong way round gives the fringes and the texture together.
4. A diffuse head instead of a condenser, where the enlarger allows a choice. It suppresses the higher orders for the reason given above, and it changes contrast rendering and dust rendering at the same time, so it is a design decision rather than a repair.
5. On a printing frame, look at the backing. Ware’s felt blanket or porous plastic is there to take up surface unevenness and it should stay, but it is also what allows contact to become good enough for fringes. If the rings are severe and the negatives are flat sheets, a firmer backing trades a little contact for fewer rings — and T1 and T3 then have to be re-run, because pressure is what those tests measure.
6. Let the negative settle before final focus where the head warms it, so that the gap that exists at the start of the exposure is the gap that exists at the end.

What you cannot do is burn or dodge them away. Burning changes density over an area; the rings are a modulation already recorded in the exposure, and adding exposure to a ringed region gives a darker ringed region. If a print with a known ring pattern leaves the darkroom, write it on the back with the carrier and the glass, using the exposure record convention, so that the next print of that negative starts from information rather than from memory.

Prevention

Decide the carrier at commissioning, and record it. The enlarger certificate already carries the row — glass or glassless, anti-Newton or not — and an enlarger whose configuration is written down is one whose faults can be attributed a year later. The same applies to the frame: which glass, which backing, and the date they were fitted.

Run T2 as an acceptance test. A strip of clear film base, a closed frame or carrier, a bright oblique light, before there is a print to lose. It takes a minute and it is the difference between knowing your sandwich makes rings and discovering it on a sheet of fibre paper.

Look at the sandwich under the enlarger before you expose, every time, with the lamp on and the lens open. The fringes are visible by reflection at the negative stage, and they are the only fault on this list that announces itself before the exposure rather than after the print has dried.

Expect them where two polished surfaces meet, and stop treating them as a surprise. A glass plate negative in a printing frame, or a glossy-based film in a glass carrier, is the configuration in which this effect was first described. It has been understood since the seventeenth century and quantified since the nineteenth; what it needs from a darkroom is not a remedy but a decision about what goes against the film.

And keep the two faults paired in your mind. Rings mean contact is nearly perfect; a soft, smeared print means it is not. They are the two ends of one variable, they cannot both be cured by the same adjustment, and a printer who knows that will change the glass instead of the springs.