The Speed of Light

The Speed of Light

Early attempts to measure the speed of light, such as those made by Galileo, determined that light moved extremely fast, perhaps instantaneously. The first real evidence that light traveled at a finite speed came from the Danish astronomer Ole Roemer in the late 17th century. Roemer had noted that the average orbital period of one of Jupiter’s moons, as measured from Earth, varied depending on whether Earth was moving toward or away from Jupiter. He correctly concluded that the apparent change in period was due to the change in distance between Earth and Jupiter and the time it took light to travel this distance.

From his 1676 data, a value of the speed of light was calculated to be \(2\text{.}\text{26}×{\text{10}}^{8}\phantom{\rule{0.25em}{0ex}}\text{m/s}\) (only 25% different from today’s accepted value). In more recent times, physicists have measured the speed of light in numerous ways and with increasing accuracy. One particularly direct method, used in 1887 by the American physicist Albert Michelson (1852–1931), is illustrated in this figure. Light reflected from a rotating set of mirrors was reflected from a stationary mirror 35 km away and returned to the rotating mirrors. The time for the light to travel can be determined by how fast the mirrors must rotate for the light to be returned to the observer’s eye.

A schematic of early apparatus used by Michelson and others to determine the speed of light. As the mirrors rotate, the reflected ray is only briefly directed at the stationary mirror. The returning ray will be reflected into the observer's eye only if the next mirror has rotated into the correct position just as the ray returns. By measuring the correct rotation rate, the time for the round trip can be measured and the speed of light calculated. Michelson’s calculated value of the speed of light was only 0.04% different from the value used today.

The speed of light is now known to great precision. In fact, the speed of light in a vacuum \(c\) is so important that it is accepted as one of the basic physical quantities and has the fixed value

\(c=2\text{.}\text{99792458}×{\text{10}}^{8}\phantom{\rule{0.25em}{0ex}}\text{m/s}\approx 3\text{.}\text{00}×{\text{10}}^{8}\phantom{\rule{0.25em}{0ex}}\text{m/s,}\)

where the approximate value of \(3\text{.}\text{00}×{\text{10}}^{8}\phantom{\rule{0.25em}{0ex}}\text{m/s}\) is used whenever three-digit accuracy is sufficient. The speed of light through matter is less than it is in a vacuum, because light interacts with atoms in a material. The speed of light depends strongly on the type of material, since its interaction with different atoms, crystal lattices, and other substructures varies. We define the index of refraction \(n\) of a material to be

\(n=\cfrac{c}{v},\)

where \(v\) is the observed speed of light in the material. Since the speed of light is always less than \(c\) in matter and equals \(c\) only in a vacuum, the index of refraction is always greater than or equal to one.

That is, \(n\ge 1\). This table gives the indices of refraction for some representative substances. The values are listed for a particular wavelength of light, because they vary slightly with wavelength. (This can have important effects, such as colors produced by a prism.) Note that for gases, \(n\) is close to 1.0. This seems reasonable, since atoms in gases are widely separated and light travels at \(c\) in the vacuum between atoms. It is common to take \(n=1\) for gases unless great precision is needed. Although the speed of light \(v\) in a medium varies considerably from its value \(c\) in a vacuum, it is still a large speed.

Index of Refraction in Various Media