Pinhole Optics for Makers and Solargraphy
Geometry first: diameter, distance, and diffraction decide sharpness before aesthetics.
A pinhole is a lens-free aperture. Image size scales with focal length (pinhole-to-plane). Sharpness peaks near an optimal diameter for that focal length, larger holes blur geometrically; tiny holes diffract.
Sun safety: never look at the Sun directly, or through a viewfinder, binoculars or a telescope. Aim pinhole cans and cameras by their shadow, not by eye. Any lens pointed at the Sun needs a certified solar filter fitted over the front. Supervise children at all times.
Key relationships
- Focal length (f): box depth.
- Diameter (d): hole size.
- f-number ≈ f / d, larger f/# is dimmer.
- Optimal d ≈ 1.9 × √(f × λ), with λ = 0.00055 mm (550 nm, green light). This is Lord Rayleigh's 1891 result, and it is the rule the calculator and the demo below use. Worked values: f = 50 mm gives 0.32 mm; a 66 mm drink can gives 0.36 mm; 100 mm gives 0.45 mm; 120 mm gives 0.49 mm (about a #10 sewing needle). Other published rules use smaller constants (Petzval about 1.41, Young about 1.56), so treat the optimum as a sweet spot, not a knife edge.
Use the Pinhole Optics Calculator to iterate before cutting foil.
The calculator's cans and papers: the best hole, the f-number, the Sun's trail and how much sky the paper covers.
The calculator these numbers come from, recorded step by step: the default Monster can, the best hole, then a Guyana Milo tin.
Your Milo tin camera is 120 mm from pinhole to paper. Which hole does Rayleigh's rule give?
- About 0.12 mm
- About 0.25 mm
- About 0.49 mm, close to a #10 sewing needle (the right answer)
- About 1.2 mm
1.9 × √(120 × 0.00055) is about 0.49 mm, close to a #10 sewing needle.
Practical trade-offs
| Goal | Bias | |------|------| | Solargraphy detail | Hole close to the optimum (a smaller one only gets softer from diffraction), long total exposure, careful sealing | | Classroom demo / camera obscura | Larger hole, brighter, softer | | Room obscura | Large f, carefully sized aperture |
Field tips (Guyana STEM)
- Foil tears create oval apertures, re-punch.
- Measure depth from foil plane to paper, not outer box wall.
- Tropical cardboard softens, reinforce and reseal after rain season mounts.
Real paper results (soft trails, cloud gaps) look like this west-facing scan:
Photo: Samir Mohammed / AstroPhotosGY.
The blur trade-off
Play with the trade-off below: larger holes blur geometrically; tiny holes diffract; the optimum grows with √focal length. Then cut foil with real millimetres in the calculator.
Blur against hole size: the hole's own blur, diffraction, and Rayleigh's sharpest hole between them.
You want a bright camera obscura for a classroom. Which way do you bias the hole?
- Larger than the optimum: brighter, softer (the right answer)
- Smaller than the optimum: sharper, brighter
- Exactly the optimum: it is always best
- Smaller than the optimum: dimmer, sharper
A bigger hole lets in more light at the cost of geometric blur. Smaller than the optimum is never sharper, because diffraction takes over.