[Physics FAQ] - [Copyright]

Original by Philip Gibbs 1997.





How is the speed of light measured?

Before the seventeenth century, it was generally thought that light is transmitted instantaneously. This was supported by the observation that there is no noticeable lag in the position of the Earth's shadow on the Moon during a lunar eclipse, which would otherwise be expected if c were finite. Nowadays, we know that light moves just too quickly for the lag to be noticeable. Galileo doubted that light's speed is infinite, and he devised an experiment to measure that speed by manually covering and uncovering lanterns that were spaced a few miles apart. We don't know if he ever attempted the experiment, but again c is too high for such a method to give an even remotely accurate answer.

The first successful measurement of c was made by Olaus Roemer in 1676. He noticed that, depending on the Earth–Sun–Jupiter geometry, there could be a difference of up to 1000 seconds between the predicted times of the eclipses of Jupiter's moons, and the actual times that these eclipses were observed. He correctly surmised that this is due to the varying length of time it takes for light to travel from Jupiter to Earth as the distance between these two planets varies. He obtained a value of c equivalent to 214,000 km/s, which was very approximate because planetary distances were not accurately known at that time.

In 1728 James Bradley made another estimate by observing stellar aberration, being the apparent displacement of stars due to the motion of the Earth around the Sun. He observed a star in Draco and found that its apparent position changed throughout the year. All stellar positions are affected equally in this way. (This distinguishes stellar aberration from parallax, which is greater for nearby stars than it is for distant stars.) To understand aberration, a useful analogy is to imagine the effect of your motion on the angle at which rain falls past you, as you run through it. If you stand still in the rain when there is no wind, it falls vertically on your head. If you run through the rain, it comes at you at an angle, and hits you on the front. Bradley measured this angle for starlight, and knowing the speed of the Earth around the Sun, he found a value for the speed of light of 301,000 km/s.

The first measurement of c that didn't make use of the heavens was by Armand Fizeau in 1849. He used a beam of light reflected from a mirror 8 km away. The beam was aimed at the teeth of a rapidly spinning wheel. The speed of the wheel was increased until its motion was such that the light's two-way passage coincided with a movement of the wheel's circumference by one tooth. This gave a value for c of 315,000 km/s. Leon Foucault improved on this result a year later using rotating mirrors, which gave the much more accurate value of 298,000 km/s. His technique was good enough to confirm that light travels slower in water than in air.

After Maxwell published his theory of electromagnetism, it became possible to calculate the speed of light indirectly by instead measuring the magnetic permeability and electric permittivity of free space. This was first done by Weber and Kohlrausch in 1857. In 1907 Rosa and Dorsey obtained 299,788 km/s in this way. It was the most accurate value at that time.

Many other methods were subsequently employed to further improve the accuracy of the measurement of c, so that it soon became necessary to correct for the refractive index of air since c is light's speed in a vacuum. In 1958 Froome obtained a value of 299,792.5 km/s using a microwave interferometer and a Kerr cell shutter. After 1970 the development of lasers with very high spectral stability and accurate caesium clocks made even better measurements possible. Up until then, the changing definition of the metre had always stayed ahead of the accuracy in measurements of the speed of light. But by 1970 the point had been reached where the speed of light was known to within an error of plus or minus 1 m/s. It became more practical to fix the value of c in the definition of the metre and use atomic clocks and lasers to measure accurate distances instead. Nowadays, the speed of light in vacuum is defined to have an exact fixed value when given in standard units. Since 1983 the metre has been defined by international agreement as the distance travelled by light in vacuum during a time interval of 1/299,792,458 of a second. This makes the speed of light exactly 299,792.458 km/s. (Also, because the inch is now defined as 2.54 centimetres, the speed of light also has an exact value in imperial units.) This definition only makes sense because the speed of light in vacuum is measured to have the same value by all observers; a fact which is subject to experimental verification (see relativity FAQ article Is the speed of light constant?). Experiments are still needed to measure the speed of light in media such as air and water.

This table gives some of the best measurements according to Froome and Essen:

Date Author Method Result (km/s) Error 1676 Olaus Roemer Jupiter's satellites 214,000 1726 James Bradley Stellar Aberration 301,000 1849 Armand Fizeau Toothed Wheel 315,000 1862 Leon Foucault Rotating Mirror 298,000 +-500 1879 Albert Michelson Rotating Mirror 299,910 +-50 1907 Rosa, Dorsay Electromagnetic constants 299,788 +-30 1926 Albert Michelson Rotating Mirror 299,796 +-4 1947 Essen, Gorden-Smith Cavity Resonator 299,792 +-3 1958 K. D. Froome Radio Interferometer 299,792.5 +-0.1 1972 Evenson et al. Lasers 299,792.4574 +-0.001 1983 Adopted Value 299,792.458

Sources of information:

Twentieth Century Physics, Vol 2, IOP/AIP press.

Hutchinson Science Library.

The Velocity of Light and Radio Waves, Froome and Essen.