Measuring the Speed of Light: Interesting Thing of the Day

Fun with mirrors and math

From ancient times, astronomers and other thinkers wondered how fast light moved; for a long while, conventional wisdom held (reasonably enough) that it traveled instantaneously.Early EstimatesFrom ancient times, astronomers and other thinkers wondered how fast light moved; for a long while, conventional wisdom held (reasonably enough) that it traveled instantaneously. Galileo described (and possibly performed) an experiment in which two subjects stood about a mile apart, with a third person observing them both from a distance.

The first person uncovered a lantern, and as soon as his partner a mile away saw the lantern’s light, he uncovered his lantern.

The third person’s job was to measure the time between when he saw the first light and the second light; Galileo then intended to use that amount of time, along with the distances between the participants, to calculate the speed of light. Unfortunately, the test was inconclusive, because the delay was too short to be measured accurately. Even Galileo admitted it was more a test of response time than a measurement of the speed of light.

All he could conclude from the experiment was that light traveled at least 10 times faster than sound.Over the following centuries, several astronomers made inferential estimates of the speed of light based on observations of the movements of planets and stars. Some of these estimates were quite shrewd, sophisticated, and (it would later turn out) fairly accurate, but they were unsatisfying because they required educated guesses about astronomical speeds and distances and could not be reproduced in a laboratory.

So in the middle of the 19th century, two French scientists started investigating the problem independently, each arriving at a novel way to make the measurement with readily available equipment.Wheels and MirrorsIn 1849, Armand Fizeau sent a beam of light through a rotating wheel with a large number of teeth around the outside. A mirror on the other side reflected the beam each time a gap appeared in the path of the light.

Fizeau realized that if the wheel rotated fast enough, the return beam would be blocked by the next tooth as it came around. So he varied the speed of the wheel until the reflected beam disappeared, performed a bit of math, and got a result of 315,000 km/second (195,732 miles/second)—certainly in the ballpark.

Meanwhile, Foucault was working on a different but equally clever technique, which he demonstrated the following year. Foucault’s method was to shine a sharply focused beam of light onto a rotating mirror, and from there onto a fixed mirror. Once the light hit the fixed mirror, it bounced back onto the rotating mirror and then back toward the source. But because the mirror was rotating, the angle at which it was positioned had changed slightly by the time the beam made its return trip.

Consequently, the reflected beam did not line up precisely with the original. Foucault could easily measure the angle between the original light source and the reflected beam, and along with known constants (the distances between the various surfaces and the speed of the mirror’s rotation), it was a matter of a few straightforward calculations to convert that small angle into a representation of speed.

Using this technique, Foucault produced a measurement of 298,000 km/second (185,167 miles/second), which is shockingly close to the modern measurement of 299,792 km/second (186,282 miles/second), keeping in mind that the latter figure applies only in a vacuum; light travels more slowly in air.

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