[Relativity FAQ] - [Copyright]

Original by Philip Gibbs 23 December 1997

How is the speed of light measured?

The speed of light in vacuum c is not measured. It has an exact fixed value when given in standard units. Since 1983 the metre has been defined by international agreement as the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second. This makes the speed of light exactly 299,792.458 km/s. Since the inch is defined as 2.54 centimetres, the speed of light also has an exact value in non-metric units. This definition only makes sense because the speed of light in vacuum is constant; 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.

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 as would be expected if c is finite. Now we know that light is just too fast for the lag to be noticeable. Galileo doubted that light speed is infinite and described an experiment to measure its speed by covering and uncovering lanterns observed at a distance of a few miles. We don't know if he really attempted the experiment, but again c is too high for such a method to work.

The first successful measurement of c was made by Olaus Roemer in 1676. He noticed that the time between the eclipses of the moons of Jupiter was less as the distance away from Earth is decreasing than when it is increasing. 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 changes. He obtained a value 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: The apparent displacement of stars due to the motion of the Earth around the Sun. He observed the star Draconis and found that its apparent position changed during the year. All stellar positions are affected equally in this way. This distinguishes the effect from parallax which affects nearby stars more noticeably. A useful analogy to help understand aberration is to imagine the effect of motion on the angle at which rain falls. If you stand still in the rain when there is no wind it comes down vertically on your head. If you run through the rain it appears to come at you from an angle and hit you on the front. Bradley measured this angle for starlight. 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 on Earth was by Armand Fizeau in 1849. He used a beam of light reflected from a mirror 8km away. The beam passed through the gaps between teeth of a rapidly rotating wheel. The speed of the wheel was increased until the returning light passed through the next gap and could be seen. Then c was calculated to be 315,000 km/s. Leon Foucault improved on this a year later by using rotating mirrors and got the much more accurate answer 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 from the magnetic permeability and electric permitivity 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 employed to improve accuracy further. It soon became necessary to correct for the refractive index of air. In 1958 Froome had the 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 kept ahead of the accuracy in measurements of the speed of light. Then the point was 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.

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
1973 Evanson 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