Fizeau's Toothed Wheel

Plate 23 speaks for itself: “Seven hundred twenty teeth, and light was caught.”

The Physics

Fizeau sent light through the gaps of a spinning toothed wheel to a mirror 8.6 km away. At the right spin rate the returning light hit a tooth and the image went dark, timing the round trip.

c = 4 d N f

• c: speed of light, m s⁻¹
• d: wheel-to-mirror distance, m
• N: number of teeth, dimensionless
• f: rotation rate at first eclipse, rev s⁻¹

720 teeth, 8633 m, 12.6 rev/s. Fizeau, 1849: about 315 000 km/s.

Honest caveat: Plugging the rounded 12.6 rev/s into the formula gives about 313 000 km/s; Fizeau's published value was about 315 000 km/s, roughly 5% above today's exact 299 792.458 km/s.

Sources

• H. Fizeau, C. R. Acad. Sci. 29, 90 (1849).

On the poster

Plate 023, “Fizeau's Toothed Wheel”: the pixel-art plate with its slogan “Seven hundred twenty teeth, and light was caught.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.