Speed of light

The speed of light in vacuum, $c$, is the same for every observer and every wavelength. Since 1983 its value has been fixed by definition: the meter is the distance light travels in 1/299,792,458 of a second, so

exactly. A nanosecond of light travel is 29.98 cm, a microsecond about 300 m. Light takes 1.28 s to reach the Moon at its mean distance and 499 s, 8.3 minutes, to arrive from the Sun at one astronomical unit.

In materials

In a transparent material the wave crests move at the phase velocity $c\mathrm{/}n$, where $n$ is the refractive index: about 225,000 km/s in water ($n$ = 1.333), 197,600 km/s in N-BK7 glass at 587.6 nm ($n$ = 1.5168) and 86,000 km/s in silicon at 1550 nm ($n\approx 3.48$). A pulse or any signal travels at the group velocity $c\mathrm{/}{n}_g$, set by the group index, which is usually one to two percent higher than $n$ in glasses and much higher in waveguides and near resonances. In standard optical fiber that is about 204,200 km/s, 4.90 µs per kilometer; the speed of light in fiber entry covers latency and hollow-core fiber.

"Slow light" experiments reduce the group velocity to meters per second in atomic vapors and cold atoms by exploiting very steep dispersion, and photonic crystal waveguides reach group indices of tens to hundreds; none of this changes $c$ or lets a signal outrun it.

Measurement history

Ole Rømer estimated the speed from the timing of Jupiter's moon Io in 1676. Fizeau (1849) and Foucault (1862) measured it on the ground with a toothed wheel and a rotating mirror, and Michelson refined the rotating-mirror method to a few parts in 10⁵ by the 1920s. By the 1970s laser frequency and wavelength measurements had pinned it to about 1 m/s, limited by the realization of the meter itself, which is why the meter was redefined in terms of $c$ rather than the reverse.

In practice

Photonics uses $c$ constantly: to convert between wavelength and frequency ($\nu =c\mathrm{/}\lambda$; see wavelength, frequency and wavenumber), to turn round-trip times into distances in reflectometry and lidar (15 cm of range per nanosecond of round trip in air), and to compute the free spectral range of a cavity, $c\mathrm{/}(2n_{g}L)$.

The wavelength calculator applies λ = c/ν in vacuum and in a medium of chosen refractive index.

References: BIPM, The International System of Units (SI brochure), 9th ed. (2019); CODATA recommended values of the fundamental physical constants (NIST); E. Hecht, Optics, 5th ed. (Pearson, 2017), Ch. 3.