The Camera Obscura

The oldest camera: a dark room with a single pinhole. Rays from the scene outside cross at the hole and paint an inverted, left–right reversed image on the back wall. No lens — just geometry. Magnification m = v/u. Drag the hole size and find the sweet spot: too big blurs by geometry, too small blurs by diffraction. The optimum is the classic d _opt = √(2.44·λ·v).

Pinhole & geometry

Hole ø d 0.50 mm

Image depth v 150 mm

Scene distance u 3.0 m

Object height H 1.20 m

Wavelength λ 550 nm

Readout

Look

Geometric blur grows with the hole: B_geo = d·(u+v)/u. Diffraction grows as it shrinks: B_diff = 2.44·λ·v/d. Their quadrature sum has one minimum — the marked optimum. The self-test proves m, the image height, and that the analytic d_opt equals the numeric minimiser to machine precision.