# First Lab Measurement of Light Speed

Since 1983, the speed of light has been defined as exactly 299,792,458 m/s (often rounded to 3×108 m/s). It’s a fundamental constant of Nature usually represented by “c” and is light’s speed as measured in a vacuum. Light will travel around 30% slower when it passes through transparent substances like water and glass, and almost 60% slower when passing through a diamond. The slowdown occurs because light interacts electromagnetically with atoms of the substance.

These days we have sensitive electronic and optical instruments that make measuring the speed of light possible in a high school physics lab. But the first attempts to measure its speed were crude by comparison. It’s interesting history nonetheless, and worth looking at to appreciate what it took to get the first rough estimates.

The first recorded attempt was made by Galileo in the early 1600s. He used two shuttered lanterns placed on distant hilltops. The plan was, Galileo would open his lantern and start a timer. When his assistant on the other hill saw the light he’d open his lantern. When Galileo saw the light from the other lantern he’d stop the timer and then divide the total distance (back and forth) by the elapsed time to get speed (v=d/t). Problem was, the best timer Galileo had was his own pulse, and given the distance between the two hills the total travel time for light was only around 0.000005 seconds. Human reaction speed just wasn’t fast enough. Galileo believed the speed of light was finite, but had to conclude his experiment wasn’t good enough to measure its speed.

The first measurement that actually succeeded was based on astronomical observations. In 1667 Ole Rømer was studying the moons of Jupiter making charts of when the moons would pass behind the planet. He noticed that when Earth and Jupiter were farther apart the moons were delayed and reasoned that, because of the great distances involved, it might be that the light just took longer to get here. The distances between the planets were not known very accurately back then, so when he did the v=d/t calculation he came up with 2.4×108 m/s — about 20% too low. But he could claim proof that the speed of light was finite.

The first attempt to measure the speed of light in a laboratory was done by Armand Fizeau in 1848–49. His device was functionally similar to the one in the animation but physically more complicated. Instead of using astronomical distances to get measurable times, he used rapidly spinning optical components to act as a “clock” of sorts to measure extremely small time intervals. The value he obtained for the speed of light was 313,274,304 m/s — about 4.5% too high but not that far off.

In the animation, the two holes in the rotating discs are offset from each other by half a rotation. When the rotation speed becomes fast enough, the slice of the laser beam that gets through the first hole will also make it through the second hole and trigger the detector. Until that speed is reached the beam is blocked by the solid part of the disc. Now the speed of light can be calculated by:

• The time for one rotation is: t=1/f ⇒ the time for half a rotation is: t=1/2f (with f measured in RPS).
• If the distance between the discs is “d” then: v=d/t ⇒ c=d/2f.

In Fizeau’s experiment, there was a single “disc” and a mirror separated by 8633 meters. The mirror reflected the light back to his eye, which was the “detector.” And of course, he didn’t have a laser but used a bright focused carbon arc light source. The calculations were essentially the same as those above. Later scientists refined Fizeau’s method, eventually approaching the modern accepted value for c to within 0.2%.

Next Week in Sky Lights ⇒ Transits of Venus and Mercury