Measuring the Speed of Light

In one line: In 1849 Hippolyte Fizeau sent a beam of lamplight through the gaps of a wheel with 720 teeth, out to a mirror ~8.6 km away on Montmartre and back — and by spinning the wheel fast enough that a returning flash was eclipsed by a tooth, he traded an unmeasurable interval of time for a countable number of teeth, and clocked the speed of light on Earth for the first time.

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The world then

By the mid-nineteenth century the speed of light was known to be finite and enormous. Two centuries earlier Ole Rømer had caught it lagging — the eclipses of Jupiter's moons ran early or late as the Earth swung nearer to or farther from Jupiter, so light plainly took time to cross the gap. (Rømer showed the finitude and gave a travel time; Huygens was the first to turn it into a numerical speed. Bradley's stellar aberration later sharpened the astronomical value.) But every estimate lived in the heavens. On the ground, light seemed to arrive the instant it left — it crosses a kilometre in a few millionths of a second, faster than any clock, shutter, or reflex of the era could resolve.

The question

Could the speed of light be measured entirely on Earth — over a known stretch of countryside you could pace out yourself — with no appeal to astronomical distances?

The design

Fizeau's shutter was a wheel with 720 teeth, spun so its gaps opened and closed hundreds of times a second. A lamp was focused through a single gap; the thin beam ran from Suresnes to a mirror on Montmartre — about 8.6 km each way, ~17 km round trip — and back through the same wheel. The trick: turned slowly, the light leaves and returns through the same gap and you see it, bright. Spin the wheel faster and, while the beam is away on its long flight, the wheel turns just enough that a tooth swings into the gap's place — the returning beam strikes the tooth and vanishes. That first blackout is the measurement: at it, the wheel advanced by one gap→tooth step during the round trip. The first eclipse came at ~12.6 turns per second.

The result

Three numbers — 720 teeth, ~12.6 rev/s at the eclipse, and the ~17 km round trip — fix the flight time at a few hundred-thousandths of a second, an interval no clock of the day could catch. Distance divided by that flicker of time gives ≈ 313,000 km/s (his figure, reported in old French lieues; conversions run 313,000–315,000). The modern value is 299,792.458 km/s — so Fizeau, with gears, a mirror, and a lamp, landed within about 4.5% on the first terrestrial try.

What we learned, and why it's beautiful

A fundamental constant had come down from the sky to the surface of the Earth. Within a year Léon Foucault refined the method with a rotating mirror and used it to compare light in air against light in water; light proved slower in water — decisive evidence for the wave theory over the corpuscular one. (The water test is Foucault's, 1850; Fizeau repeated it independently weeks later.) The speed of light only grew more fundamental from there, until in 1983 it was fixed by definition and the metre itself was redefined in terms of it. The beauty is a reframing: the interval was impossibly short, so Fizeau stopped trying to measure time and measured teeth and gaps instead — letting mechanical rotation do what no clock could, and making an invisible flash into something you could watch appear and vanish.

Sources

Full claim-by-claim evidence is in references.md. Primary anchors:

• H. Fizeau, Sur une expérience relative à la vitesse de propagation de la lumière, Comptes Rendus 29 (1849) 90–92 (original-paper translation + figures via Skulls in the Stars).
• Wikipedia: Fizeau's measurement of the speed of light in air · Foucault's measurements of the speed of light · Rømer's determination of the speed of light · Speed of light (1983 CGPM). Linda Hall Library · Britannica.

Accuracy note: Rømer showed light's speed is finite (a travel time); Huygens first computed a number — the script never puts a km/s figure on Rømer. Fizeau's result is quoted qualitatively ("about 313,000," "within a few percent") because his original lieue figure converts to anywhere from 313,000 to 315,000 km/s. The air-vs-water / wave-theory test is Foucault's rotating-mirror work (1850), not the 1849 toothed wheel — the episode credits Foucault, not Fizeau, and does not conflate it with Fizeau's separate 1851 aether-drag interferometer.