Fraso / nomograms

Optics

Thin lens

Object and image distance against focal length.

A thin lens nomogram: three vertical scales, s (50 to 5000) on the left, f (25 to 2500) in the middle and s′ (50 to 5000) on the right. A straight line laid across any two scales cuts the third at the value that satisfies 1/f = 1/s + 1/s′.505560708010012015020030050010005000smm505560708010012015020030050010005000s′mm25273035405060801001402005002500fmm

Readings

mm
mm
mm

Drag the red line, or type into any two boxes — the third is solved. The marked box is the one being solved for.

Print at 100% scale, then check the 100 mm bar with a rule before trusting a reading.

Why this one is an instrument

The same reciprocal geometry as resistors in parallel, which is not a coincidence — they are the same equation wearing different units, and putting the two instruments side by side makes that visible in a way the algebra does not. Useful for bellows, enlargers, and any close-up work where the image distance stops being negligible.

Equation
1/f = 1/s + 1/s′
Ranges
s 50–5000 mm · s′ 50–5000 mm
Reading
Any two values fix the third. Outside the printed ranges the instrument stops being valid — that is what the end marks are for.

These are drawn from the stated equation and nothing else. Where an equation is itself an approximation — hyperfocal distance and tap drill sizes both are — the instrument inherits that approximation exactly, no better and no worse.