Mirrorspin

Mirrorspin, a helmeted knight, aims a spinning mirror and a bright orange beam.

The Physics

In 1862 Léon Foucault measured the speed of light in a laboratory with a rapidly rotating mirror (Comptes rendus 55, 501). Light reflects off the spinning mirror to a distant fixed mirror and back. In the round-trip time the rotating mirror turns a tiny angle, so the returning spot lands slightly displaced. From the displacement, the path length and the spin rate he got c = 298 000 ± 500 km/s, close to the modern value.

Δα = 2ωD/c

• Δα: angle the mirror turns during the round trip (rad); the returning beam is deflected by 2Δα
• ω: angular speed of the mirror (rad/s)
• D: distance to the fixed mirror (m)
• c: speed of light (m/s)

In 1850 the same method showed light is slower in water than in air, against the particle theory.

Honest caveat: The formula is the simplest geometry; turning the spot displacement into an angle needs the lens distances of the real setup. The modern defined value is 299 792.458 km/s. This is a different Foucault experiment from his pendulum.

On the sticker

Mirrorspin holds a round mirror with curved motion lines and a glowing orange beam running from it. Printed text: MIRRORSPIN with the line 298 000 km/s. Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.