A classic experiment, explained

Suppose you send a loved one on a small errand. Take out the trash. If you are concerned about his or her propensity to dawdle, it’s easy to calculate his or her average speed to acquire solid evidence. Just take the distance to the curb, multiply by 2 to account for the “to” and “from” portions of the trip. Divide this result by the total time it took and you’ll get the average speed. (If the result is comparable to the land speed of a box turtle, you are in the clear to berate your loved one.) In 1849, Armand Fizeau used this same principle to calculate the speed of light directly: He reflected light off of a mirror a fixed distance away and timed the round trip. This was the first measurement of the speed of light on Earth.

While Fizeau used the same method to calculate the speed of light, it wasn’t quite so easy. Light zooms by with a speed many times faster than a person could even hope to muster. So if you sent light back-and-forth from your house to the curb, the event would happen too quickly for you to measure with your stopwatch. One thing Fizeau realized was that in order to have any chance at measuring the speed, the distance traveled would have to be as great as possible in order to maximize the time. Fizeau chose two hilltops about 8.5 km apart, resulting in 17 km total distance. (For the Francophile reading this, they were hills near Paris, and one was Montmartre.)

However, even though this distance was large, a stopwatch still couldn’t handle the timing job. Ironically, the watchmakers of the 19th century inspired an elegant solution: it is easy to rotate a cog at a fixed rate. A cog was positioned between the light source and the mirror. The light beam was positioned to go through the gap between two teeth. If the cog is still, the beam can travel to the mirror, bounce off, come back through the same gap, and be projected onto a screen. Now imagine turning the cog at a steady rate. The beam goes through the gap. Suppose the cog rotates halfway to the next gap in the time it takes the light to travel back. The returning beam is then blocked by the tooth next to the original gap, resulting in a dark projection. Suppose you increase the turning rate so that the cog rotates fully to the next gap. Then the returning beam will sail back through untouched, and the projection will be bright.

Fizeau used this exact logic to make his measurement. He varied the rotation rate of the cog and looked at the intensity of projected light on the screen. The brightest projection meant the rotation rate was in its sweet spot: the cog had moved exactly from one gap to the next in the time it took the light to return. The rotation rate that corresponded to the brightest projection was 25.2 rotations per second, or about 0.04 seconds per rotation. The particular cog he used had 720 teeth. So the time it took the light to travel out of one gap and go back through the next was 0.04 seconds / 720 ~ 0.000055 seconds, truly incredible precision for that time! He divided the known distance by this time, and managed to get the speed of light to within 5% of today’s accepted value.

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