Fizeau's Toothed Wheel
Chop light into pulses, send them to a far mirror, and spin until the returning light hits a tooth.
Lesson at a glanceShow the key points
- Light passes through a gap of a toothed wheel, travels D to a mirror and back.
- Speeding up the wheel, the image first vanishes when the next tooth arrives in the time 2D/c.
- A tooth replaces a gap after turning π/n: so c = 2Dnω/π = 4Dnν (21.1) for n teeth, ν revolutions per second.
- Fizeau used D = 8.6 km. Drawbacks: dim image, and kilometres of open space.
In 1849 Hippolyte Fizeau timed light over a 17-kilometre round trip using nothing faster than a spinning gear wheel.
The apparatus
Light from a source is reflected by a half-silvered glass plate and focused at the rim of a toothed wheel. Light passing through a gap is made into a parallel beam by a lens, travels several kilometres (8.6 km in Fizeau’s experiment), and is focused by another lens onto a mirror at its focal plane. It returns along the same path to the wheel. If it finds a gap, it passes through the glass plate to an observer looking through a telescope.
The eclipse
Spinning the wheel chops the light into bursts. At low speed the image flickers. As the wheel speeds up, a speed is reached where, in the time light takes to go to the mirror and back, the wheel turns so that the next tooth sits where the gap was. Every burst then returns to a tooth, and the image disappears completely.
With n teeth, a tooth replaces the neighbouring gap after the wheel turns by π/n. At angular speed ω this takes (π/n)/ω, during which light covers 2D:
A wheel with 500 teeth is 8.0 km from the mirror. At what rate does the image first vanish?
- 1A toothed wheel chops light into pulses that travel D to a mirror and back.
- 2The image first vanishes when a tooth replaces a gap during the round trip.
- 3c = 4Dnν.
- 4Drawbacks: dim image, needs kilometres of space.
Check yourself
Keep exploring
Hand-picked videos, simulations and readings that explain this idea from a different angle.