Measuring the speed of light

In 1849 Hippolyte Fizeau timed light over a round trip of about 17 km with a spinning wheel of 720 teeth.

Is light instant?

Switch on a lamp and the room seems to fill with light at once. For a long time many thinkers, including Johannes Kepler and René Descartes, took the speed of light to be infinite, as the American Physical Society notes in its history of the measurement. Galileo was among the first to doubt it. In 1638 he described an experiment in which two people with covered lanterns stand far apart: the first uncovers his lantern, and the second uncovers hers the moment she sees the light. Timing the gap should give the speed. OpenStax notes that such early attempts only showed that light is extremely fast, perhaps instantaneous.

It is easy to see why the lantern test failed. With the lanterns 5 km apart, the light covers 10 km there and back in about 33 millionths of a second, far less than the fraction of a second it takes a person to react. To catch light in the act you need either enormous distances or very fast timing. The first success used enormous distances.

Rømer and the moons of Jupiter

In the 1670s the Danish astronomer Ole Rømer was timing the eclipses of one of Jupiter’s moons as it passed behind the planet. OpenStax describes what he noticed: the moon’s average orbital period, measured from Earth, seemed to change depending on whether the Earth was moving toward Jupiter or away from it. When the Earth was farther away the eclipses came late, and when it was nearer they came early. He concluded that the light was taking time to cross the changing distance. A value calculated from his 1676 data, OpenStax says, is 2.26 × 10⁸ m/s, about 25% below today’s figure, mainly because the size of the Earth’s orbit was not well known then. The important point was that light has a finite speed.

Wheels and mirrors on Earth

The first measurement made entirely on the ground came from Hippolyte Fizeau in 1849. He sent a beam of light through the gaps of a spinning toothed wheel to a mirror 8633 m away and back. At a slow spin the returning light passed through the same gap. As the wheel sped up, a point came where the light that left through a gap came back to find a tooth in the way, and the light seen by the observer dimmed. The wheel had 720 teeth. The light first vanished at 12.6 turns per second, when a tooth had moved into the gap’s place; at twice that speed, 25.2 turns per second, it showed again through the next gap, so the light’s round trip took the time for the wheel to move on by one gap. That gives 2 × 8633 m × 720 × 25.2 per second ≈ 313 000 km/s, about 4.5% too high.

Léon Foucault replaced the wheel with a rotating mirror. Light bounced off the spinning mirror to a fixed mirror and back, and in the meantime the rotating mirror had turned slightly, so the returning beam was shifted by a small measurable angle. In 1862 he obtained 298 000 km/s, within 0.6% of the modern value, using mirrors only about 20 m apart. With the same kind of apparatus he and Fizeau had also shown, around 1850, that light travels more slowly in water than in air, as the wave theory of light predicted. Albert Michelson refined the rotating-mirror method for decades; OpenStax describes his set-up with a fixed mirror 35 km away, and his 1926 result was 299 796 km/s, about 12 parts per million too high.

From measuring c to defining it

By the 1970s lasers with very stable frequencies let scientists measure the frequency and the wavelength of the same light and multiply them, since c = fλ. NIST describes how Ken Evenson’s group in Boulder obtained 299 792 456.2 ± 1.1 m/s, a hundred times more accurate than before. The limit was no longer the measurement of light but the definition of the metre itself, then based on light from krypton atoms. So in 1983 the General Conference on Weights and Measures turned the problem around and defined the metre as the length of the path travelled by light in a vacuum in 1/299 792 458 of a second. Since then the speed of light has been exactly 299 792 458 m/s by definition, and distance is measured with clocks.

A few numbers put the speed in perspective. Light from the Sun, about 149.6 million km away, takes 499 seconds, a little over 8 minutes, to reach us. A laser pulse sent to a reflector on the Moon, 384 400 km away on average, returns about 2.56 seconds later.