Assignment: Architecture, Low Viewpoint and the Flat Plane

The intention

Photograph one building twice — once from the ground with the camera levelled and the pinhole shifted, once at a second focal distance — and come back with verticals you can put a rule against.

A building is the subject that makes geometry unavoidable. Every other assignment in this part can be composed by eye and judged by taste. This one has a right answer sitting in it: either the vertical edges of the building are parallel on the negative or they are not, and if they are not, the amount by which they converge is a number you can measure and trace to the angle you tipped the camera. It is also the assignment that puts you on a pavement with a tripod for an hour, which turns out to have its own arithmetic.

Learning objectives

By the end of this session you should be able to:

• State why a pinhole on a flat back renders every straight line in the world as a straight line, from a one-sentence geometric proof rather than from a claim about distortion.
• Predict the convergence of a building’s verticals from the angle the camera is tilted, as a percentage of width across the frame.
• Compute what a given pinhole shift buys at the top of the frame and what it costs at each corner, in stops, and choose a shift from those two numbers.
• Place a camera at ground level and predict the relative image size of foreground and building from m = f/u before exposing.
• Work in a public place without obstructing it, and log the light across a session well enough to explain why the second exposure needed a different time from the first.

Prerequisites

Still Life and Controlled Light for the exposure arithmetic and the three-stop problem, and Seeing Like a Pinhole for framing and the intention field. Part VI’s geometry lesson owns the shift, the cos-fourth law and the tunnel cut-off; nothing here re-derives them.

Safety classification

Level A. No new chemistry at all — the trays are the ones you used for the still life. Everything that is new is about being outdoors, in a public place, with equipment on the ground, for a long time.

• Substances. The same three baths, back indoors, at the same dilutions.
• Energies. The sun, for a session of one to three hours.
• Procedures. A tripod or a ground-level camera in a place other people are using.
• Waste. Used fixer is silver-bearing and is collected.

What is not a hazard here, and why. A pinhole camera on a pavement emits nothing, gets warm at nothing, and contains no moving part that can trap a finger. Long exposures create no hazard of their own; the camera is as inert at forty minutes as at four seconds. The two real risks are entirely ordinary and entirely foreseeable: you are a stationary object in a place designed for people to move through, and you are standing in the sun for longer than you would choose to. Both are managed by where you stand and what you wear, not by anything you put on your hands.

Hazards

Obstruction, and the law about it. In England and Wales, section 137(1) of the Highways Act 1980 provides that a person who “without lawful authority or excuse, in any way wilfully obstructs the free passage along a highway” commits an offence, and a highway includes a pavement. That is not a rule about photography; it is a rule about blocking a footway, and it applies to a tripod exactly as it applies to anything else. The practical control is to leave a clear passing width — a wheelchair, a double buggy and a person with a white cane all need more room than you think — and to stand where you can see people coming rather than behind your camera.

A camera on the ground is a trip hazard, and a low black box on a grey pavement is close to invisible. Put something visible beside it — a bag, a bright jacket — and never walk away from it.

Roads. The Highway Code’s rule 1 is that pavements and footways should be used where provided, and rule 2 that where there is no pavement you keep to the right-hand side so that you can see oncoming traffic. Neither a tripod nor a camera goes on a carriageway, a central reservation or a cycle lane, and no photograph is worth a step backwards into one.

Sun. ICNIRP’s shadow rule is the usable one: when your shadow is shorter than you are, the ultraviolet is at its strongest, which under clear skies in late spring and summer is the four hours around midday. A hat, sleeves and sun cream are the personal protective measures for a session spent standing still in the open, and shade between exposures costs you nothing.

Private land, and permission. A great many places that feel public are not — station forecourts, shopping precincts, university quadrangles, cathedral closes. The course’s rule for this assignment is simple and is not a legal claim: ask first, and accept the answer. A polite question at a desk usually gets a yes, and the yes is worth more than an argument about rights you would rather not have while your shutter is open.

Required PPE

• Sun protection is the PPE for the exposure half of this session: a brimmed hat, covered arms, sun cream, and shade between sheets.
• Something high-visibility near the camera when it is on the ground, so that it is a marked obstacle rather than an unmarked one.
• Back indoors, for the processing half: nitrile gloves, eye protection and one pair of tongs per tray, exactly as for the still life.

Ventilation

Outdoors, ventilation is not among the controls, for the obvious reason. Indoors, an openable window or an extractor in the processing area and not a sealed cupboard, which is ILFORD’s general instruction; extraction is not required because none of the three baths generates a vapour.

Materials

Item	Quantity	Notes
Variable-contrast RC paper	10 sheets	Six for the plan, four spare. Loaded into holders or a changing bag before you leave.
A building	1	Chosen in advance, visited once without the camera.
A printed grey scale on your own paper	1	For reading densities afterwards.
Session log sheet, ruled by time	1	A row every fifteen minutes whether or not you exposed.
Tracing paper or drafting film	1 sheet	For laying over the dry negative to measure verticals.
A long steel rule and a fine pen	—	The measurement of verticals is the assessment.

Chemicals

Chemical	Quantity	Form
Paper developer concentrate	100 mL	Diluted 1+9 to make 1 L; 1 minute at 20 °C for RC paper.
Stop bath concentrate	50 mL	Diluted 1+19 to make 1 L; about 10 seconds. A citric acid stop.
Rapid fixer concentrate	200 mL	Diluted 1+4 to make 1 L; 30 seconds for RC paper. An ammonium thiosulfate fixer.
Water	about 10 L	Dilution and washing.

Equipment

The camera with its flat back, at least two extension frames, the shifted pinhole position and the pinhole register; a tripod with a spirit level, or a small level you can lay on the camera’s top face; a lux meter or a phone app; a timer; a watch; and, back indoors, the trays, graduate, thermometer, tongs and safelight from the still-life session.

The spirit level is not optional on this page. The entire method is “the camera was level”, and an eyeballed level is routinely two or three degrees out, which is a visible convergence.

Estimated cost

Cost band £. Ten sheets of paper and a session’s chemistry. A small spirit level is the one purchase, and it is the cheapest useful thing in this part. Dated prices live in the laboratory planner.

Waste streams

Used fixer is silver-bearing and is collected, with the first change of wash water, into the labelled container Part II established. Used developer and stop carry no silver. Local regulations govern, and they differ between authorities even within the United Kingdom.

Preparation

1. Why the lines stay straight, and why tilting bends them

The proof that a flat-backed pinhole is exactly rectilinear is one sentence, and Part VI gives it: a straight line in the world, together with the pinhole, defines a plane; the image of the line is where that plane cuts the film; and a plane cuts a flat surface in a straight line. No lens can claim zero distortion; a flat-backed pinhole gets it for free.

Straightness is not the same as parallelism, and this is where architectural photographs go wrong. Vertical edges in the world stay vertical in the picture only while the film plane is itself vertical — that is, while the camera is level. Tip the camera up to fit a roofline in and the film plane tips with it, the verticals acquire a vanishing point, and they converge. A pinhole does this exactly as a lens does, for exactly the same reason. There is no pinhole magic here.

The convergence has a number. With the camera tilted up by an angle φ, the vertical vanishing point lies f / tan φ from the centre of the frame, and the apparent width of a vertical-sided building varies in proportion to the distance from that point. Across a 127 mm sheet at f = 50 mm:

Camera tilted up by	Vanishing point, from frame centre	Verticals narrow across the frame by
2°	1,432 mm	8 per cent
5°	572 mm	20 per cent
10°	284 mm	37 per cent
15°	187 mm	51 per cent
20°	137 mm	63 per cent

Two degrees of accidental tilt gives 8 per cent, which you will see and be unable to explain. That is the argument for the spirit level.

2. The shift, what it buys, and what it costs

Tilt against shift: two ways to fit a building in, and only one of them keeps the verticals parallel

1. 1Tilted camera — film plane no longer parallel to the facade; verticals converge to a point f/tan φ from centre
2. 2Levelled camera, shifted hole — film plane parallel to the facade; verticals stay parallel because nothing rotated
3. 3The price of the shift — far corner deeper into the cos⁴ curve, near corner shallower — an asymmetry, not a loss of coverage

Both panels include the same roofline. Only the right-hand one keeps the building's edges parallel, and it pays for it in an uneven sky rather than in a leaning building.

Slide the pinhole up by a distance s, parallel to the film, and the whole image circle slides with it. Nothing rotates, so verticals stay vertical. What changes is which part of the world lands on the sheet: the horizon’s image moves up the film by s, which in the finished picture means the horizon moves down — more building, less pavement — and the top edge of the frame reaches higher.

top of frame = arctan( (h/2 + s) / f ), horizon sits (h/2 + s) / h of the way up the picture

What a shift of s does, on a sheet of height h

For 4 × 5 inch paper standing 127 mm tall on a 50 mm camera:

Shift s	Top of frame, above the axis	Horizon sits	Far corner	Near corner	Asymmetry
0 mm	51.8°	halfway up	−3.73 stops	−3.73 stops	0.00
10 mm	55.8°	58 % up	−4.14	−3.34	0.80 stop
20 mm	59.1°	66 % up	−4.54	−2.96	1.58 stops
30 mm	61.9°	74 % up	−4.93	−2.62	2.31 stops

Corner figures are the cos⁴ law alone, computed from Part VI’s relation, which is a floor: real falloff is worse, because plate thickness adds a tunnel effect on top of it.

🧮DO THE MATHS: what actually limits the shift, and a question with a surprising answer

The received answer is that shift is limited by the image circle running out, as it does behind a lens. For a pinhole that is the wrong limit. A pinhole has no glass with an edge; light gets through it at every angle up to the plate’s own tunnel cut-off, which Part VI gives as arctan(d/t). For a 0.25 mm hole in 0.05 mm shim brass that is 78.7°, and even a 30 mm shift only takes the far corner to 64.8°. Nothing goes dark. Everything just gets dim, unevenly.

So the real limit is the one in the last column of the table: the top of the sky is nearly two and a half stops darker than the bottom of the sky at s = 30 mm, on a material whose whole scale is about three stops. The shift runs out when the sky stops being one tone. In practice, on a 50 mm camera, somewhere around 15 to 20 mm.

Now the surprise. A common exercise asks for the shift needed to include a roofline 15° above the levelled axis. Work it: with no shift at all, the top of a 127 mm sheet at f = 50 mm already reaches 51.8° above the axis. Fifteen degrees is not merely inside the frame, it is a third of the way up it. On a wide pinhole camera you almost never need shift to fit a building in. What you need it for is to stop the composition being half pavement — to put the horizon low without tilting. That is a compositional use, not a geometric necessity, and knowing which of the two you are doing is the point of the calculation.

At the long setting the arithmetic changes character: at f = 120 mm the frame reaches only 27.9°, the corners start just 1.09 stops down, and 20 mm of shift costs an asymmetry of 0.69 stop instead of 1.58. A long pinhole camera is the one that can afford shift, which is exactly the trade a view camera makes.

Petrie, who wanted as little apparatus as possible, reached the same conclusion in 1904: “The sliding and rising front is about the only complication that is useful in serious work; and if a long focus lens is used a large amount of slide can be obtained.”

3. Ground level, and the arithmetic of the low viewpoint

At f = 50 mm on 4 × 5 inch paper the frame takes in 104° across its long side. Put the camera flat on the pavement with the sheet upright and it sees the paving 300 mm in front of it and the top of the building opposite, at the same time.

Subject at	m = f/u	A 1 m thing images
0.3 m (the paving at your feet)	0.167	167 mm — larger than the sheet
0.5 m	0.100	100 mm
3 m (the kerb)	0.0167	17 mm
20 m (the building)	0.0025	2.5 mm

Sixty-seven to one between the paving and the building, for objects of the same real size. That ratio is the assignment’s compositional engine, and it comes from the viewpoint, not from the focal distance: the wide angle is what lets you keep the building in frame while standing that close, and nothing more. Petrie’s 1904 complaint about wide-angle lenses — “for most objects it is very detrimental to have so short a focus, as it distorts and spoils the perspective” — is the same observation from a man who did not want the effect.

Choose your foreground anchor deliberately and measure its distance. A drain cover, a kerbstone, a band of setts, a puddle: something with structure at 0.3 to 1 m that will read at a tenth to a sixth of life size, and which leads the eye toward the building rather than sitting across the picture.

4. Plan the session against the sun

Petrie again, on buildings: “a time-table of the best hours for each part should be drawn up and followed.” That was written when a plate needed a second; it is far more important when your exposure needs two minutes and your session needs two hours.

Solar elevation through the day at 52° N, computed for three dates

• Midsummer (declination +23.4°)
• Equinox (declination 0°)
• Midwinter (declination −23.4°)

Show the numbers behind this plot

Three symmetrical arches of solar elevation against time either side of solar noon, computed for latitude fifty-two degrees north. The midsummer curve is the highest: minus four hours gives thirty-six point six degrees, minus three gives forty-five point five, minus two gives fifty-three point four, minus one gives fifty-nine point two, and solar noon gives sixty-one point five, falling symmetrically afterwards. The equinox curve is much lower and flatter: seventeen point nine degrees at minus four hours, twenty-five point seven at minus three, thirty-two point two at minus two, thirty-six point four at minus one, and thirty-seven point nine at noon. The midwinter curve barely rises at all: minus one point eight degrees at minus four hours, which is below the horizon, four point nine at minus three, ten point one at minus two, thirteen point four at minus one, and fourteen point six at noon. The important feature of all three is the shape rather than the height. Each curve is steepest three to four hours from noon, where midsummer gains eight point nine degrees in an hour, and almost flat within an hour of noon, where midsummer gains only two point two degrees in an hour. So shadows change length fastest at the ends of the day and slowest in the middle, which is the opposite of what most people assume when planning a session.

Series	Hours from solar noon	Solar elevation, degrees above the horizon
Midsummer (declination +23.4°)	-4.00	36.60
Midsummer (declination +23.4°)	-3.00	45.50
Midsummer (declination +23.4°)	-2.00	53.40
Midsummer (declination +23.4°)	-1.00	59.20
Midsummer (declination +23.4°)	0.00	61.50
Midsummer (declination +23.4°)	1.00	59.20
Midsummer (declination +23.4°)	2.00	53.40
Midsummer (declination +23.4°)	3.00	45.50
Midsummer (declination +23.4°)	4.00	36.60
Equinox (declination 0°)	-4.00	17.90
Equinox (declination 0°)	-3.00	25.70
Equinox (declination 0°)	-2.00	32.20
Equinox (declination 0°)	-1.00	36.40
Equinox (declination 0°)	0.00	37.90
Equinox (declination 0°)	1.00	36.40
Equinox (declination 0°)	2.00	32.20
Equinox (declination 0°)	3.00	25.70
Equinox (declination 0°)	4.00	17.90
Midwinter (declination −23.4°)	-4.00	-1.80
Midwinter (declination −23.4°)	-3.00	4.90
Midwinter (declination −23.4°)	-2.00	10.10
Midwinter (declination −23.4°)	-1.00	13.40
Midwinter (declination −23.4°)	0.00	14.60
Midwinter (declination −23.4°)	1.00	13.40
Midwinter (declination −23.4°)	2.00	10.10
Midwinter (declination −23.4°)	3.00	4.90
Midwinter (declination −23.4°)	4.00	-1.80

Computed by this course from the NOAA solar-position equations at latitude 52° N; not measured, and not read from a table. Your own latitude shifts all three curves, and British Summer Time shifts the clock but not the sun. 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.

Two things follow, and the second one is the one people get wrong.

Shadow length changes fastest at the ends of the day. Midsummer at 52° N the elevation climbs 8.9° in the hour between four and three hours before noon, and only 2.2° in the hour before noon. If your picture depends on the length of a shadow across a facade, the middle of the day is the stable place to work and the edges are where it runs away from you.

Shadow direction changes fastest in the middle of the day. The sun’s hour angle advances a flat 15° per hour, but its bearing along the horizon does not: at 52° N in midsummer the azimuth swings 27.6° in the hour around noon, against 17.4° three hours out. So the hours when the light is most stable in length are the hours when it is swinging round fastest in direction.

Hours from solar noon, midsummer at 52° N	Change in elevation	Change in azimuth
−3 to −2	+7.9°	17.4°
−2 to −1	+5.8°	22.6°
−1 to 0	+2.2°	27.6°

Plan accordingly: decide first whether the picture is about a shadow’s length or a shadow’s direction, and put the exposure where the quantity you care about is changing slowly.

5. Compute the exposures, and write the two intentions

Outdoors on ISO 3 paper the arithmetic from the still life gives, using t = N²C/(E S) with C = 310:

Condition	Illuminance	at f/200	at f/300
Bright summer sun, distinct shadows	100,000 lux	41 s	93 s
Hazy sun	50,000 lux	83 s	3.1 min
Bright overcast	20,000 lux	3.4 min	7.8 min
Dull overcast	10,000 lux	6.9 min	15.5 min

None of that carries a reciprocity correction, because nobody publishes one for paper used as a camera negative. Bracket two stops either side on the first sheet of the session, then work from what that sheet tells you.

Write two intentions, one for each view, before leaving the house. Each should name the building, the viewpoint, the focal distance, the shift, where you intend the horizon to sit, and one sentence about what will happen to the people who walk through.

The making

Stage 1 — Arrive, place, level, log (30 minutes)

Set the camera at the viewpoint you chose. Level it with the spirit level before anything else, and record the reading. Fit the shift and record s in millimetres. Read the illuminance, write the computed exposure and its bracket, and note the time and the sun’s rough bearing relative to the facade. Only then expose.

Stage 2 — The low view with shift, and its bracket (40 minutes)

Three sheets: the computed time, one stop over, one stop under. Between them, re-read the light. A cloud arriving between sheet one and sheet three is not a nuisance, it is a logged datum, and it is the reason the session log has a row every fifteen minutes whether or not you exposed.

While the shutter is open, stand where you can see the camera and the pavement. Do not stand in the frame; on a three-minute exposure you would be a substantial part of it.

Stage 3 — The second focal distance (30 minutes)

Same building, second frame fitted. Two things change together and the log must separate them: the angle of view falls (117° to 68° across the diagonal, going from 50 mm to 120 mm), and the exposure rises by (120/50)² = 5.76, which is 2.53 stops. If your first exposure was 83 seconds, this one is eight minutes. Move back far enough to keep the composition and record the new distance.

Stage 4 — Process everything together (40 minutes)

Developer 1 minute at 20 °C, stop about 10 seconds, fixer 30 seconds, wash. Process the session as a batch, so that differences between the sheets are differences you made outdoors.

Stage 5 — Measure the verticals (20 minutes)

Lay tracing paper over the dry negative. Draw the two outer vertical edges of the building with a rule. Measure the separation at the top of the building and at the bottom, and compute the ratio. That ratio is the assessment, and the tilt table above converts it back into the angle you actually had the camera at.

Expected observations

• The sky will be white and featureless, and the building’s brickwork darker than you expect. Blue-sensitive paper does that. It is the nineteenth-century look, and on this subject it is often an asset: a white sky is a clean field against which a roofline reads as a silhouette.
• The corners will be dark, and at 50 mm on 4 × 5 paper they will be dark by around four stops. With shift, the top corners will be visibly darker than the bottom ones. Both are predicted.
• The verticals will not be perfect. A ratio of 0.95 top to bottom means about 1.2° of residual tilt, which is a level read carelessly or a tripod head that crept.
• The people will not be there. A pedestrian walking past at ordinary speed is present at any one point in the frame for as long as it takes to walk their own width — under half a second — which in a three-minute exposure is a quarter of one per cent of the light. Even someone who stops and stands for twenty seconds of a four-minute exposure changes that patch by about a tenth of a stop, which you will not find. The movement assignment does this properly.
• The foreground will be softer than the building. Expected: b = d(1 + f/u), so at 0.3 m on a 50 mm camera the blur is 1.17 d against 1.00 d at the far end of the street.

Reading the session log

The log stops being paperwork on this page and starts being the explanation.

Lay the rows out in time order and put the judged density of each sheet beside its computed time and its measured illuminance. Three patterns are worth looking for.

1. A drift in one direction across the session. Usually the sun moving, and the log’s illuminance column will show it. If the density drifts and the illuminance does not, suspect the developer.
2. A step where nothing changed. Almost always a plate swapped without recording it, or a frame reseated. The pinhole register is the place to check.
3. A sheet that is right when the arithmetic says it should be wrong. Keep it and mark it. Over a season these are the rows that move your effective speed, and the portfolio review will collate them.

The critique

One paragraph per view, written before you show anybody, following the critique sequence:

1. Intention. What did you write down, and which clauses happened?
2. Optics. Measure the vertical convergence and state the tilt it implies. Compare the corner density with the cos⁴ figure for your focal distance and shift.
3. Exposure. Which bracket sheet survived, and what does the session log say about why?
4. Tone. Where did the three-stop scale run out — in the sky, in the shadowed side, or in a dark doorway you did not think about?
5. Time. What moved through and what did the negative record of it?
6. Composition. Did the foreground anchor do the job you predicted from m = f/u, or did it simply take up the bottom third?
7. The two views together. What did the second focal distance gain, and what did it lose? Say it as an exchange, with the angle-of-view numbers in it.

Troubleshooting

What you see	Likely cause	What to do
Verticals converge although you levelled the camera	Level read against a sloping pavement, or a tripod head that crept during a long exposure	Level against the camera’s own machined face, and re-check after tightening
Verticals converge outwards, wider at the top	The camera was tipped down, which happens when a ground-level camera rests on an uneven flag	Shim the front of the camera and re-level
Top of the sky much darker than the bottom	Correct and predicted: the shift asymmetry	Reduce the shift, or move to a longer focal distance where the asymmetry is a third the size
The whole frame darker at one edge, not gradually	Not falloff — a light leak, or the shift carrier fouling the image	Repeat Part VI’s leak test with the shift set
Building tiny in the frame	m = f/u did what it always does; a 20 m building at 20 m on a 50 mm camera images 50 mm tall	Longer frame, or a closer viewpoint, and recompute the exposure for the new N
A pale wash across the lower half	Flare from the sun outside the frame, or from a bright pavement	Shade the pinhole with a card held clear of the field; check the interior blacking
Everything thin, sky included, on a bright day	Metered the shadowed side of the street rather than the lit facade	Read the illuminance at the surface the picture is about

Clean-up, storage and disposal considerations

Trays emptied developer, stop, fixer, with the fixer into the labelled silver-bearing container. Negatives dried face-up and sleeved flat, labelled to the log row. The tracing-paper vertical overlays are part of the submission and are stored with the negative.

Disposal. Used developer and stop carry no silver; used fixer does, and it is collected rather than discharged because of the silver-thiosulfate complexes it contains. Local regulations govern, and they differ between authorities even within the United Kingdom.

What to submit

• One selected negative and its working positive, from the low viewpoint with shift.
• The second view at the other focal distance, negative and positive.
• The tracing overlay with the verticals drawn and the top-to-bottom ratio written on it.
• The session log, complete, including the rows where you exposed nothing.
• Two critique paragraphs, one per view.

Further work

• The tilt series. Same building, same viewpoint, four sheets at 0°, 5°, 10° and 15° of tilt, measured on a level. Plot the measured convergence against the predicted narrowing from the table. It is a fifteen-minute experiment that settles the geometry for good.
• The shift series. Same building, shift at 0, 10, 20 and 30 mm, and read the corner densities against the table. This is also the cleanest measurement of how much worse than cos⁴ your own plate actually is.
• The same building at the same hour on two dates. Six weeks apart, the sun’s elevation at a given clock time will have moved several degrees, and the shadows on the facade will be measurably different. The log is what makes that comparison possible.