Definition:Speed of Light
Physical Law
The speed of light, and that of other electromagnetic waves (in a vacuum) is a physical constant.
Information cannot travel faster.
Symbol
- $c$
The symbol for the speed of light is $c$.
Its $\LaTeX$ code is c .
Dimension
The speed of light has the dimension $\mathsf {L T^{-1} }$.
Units
The SI unit for the speed of light is given as metres per second: $\mathrm {m \, s^{-1} }$
The CGS unit for the speed of light is given as centimetres per second: $\mathrm {cm \, s^{-1} }$
Value
The value of the speed of light in a vacuum is:
| \(\ds c\) | \(=\) | \(\ds 299 \, 792 \, 458\) | $\mathrm {m \, s^{-1} }$ | \(\quad\) (exact) | ||||||||||
| \(\ds \) | \(=\) | \(\ds 2 \cdotp 99792 \, 458 \times 10^{10}\) | $\mathrm {cm \, s^{-1} }$ | \(\quad\) (exact) |
The speed is smaller through a medium
Also known as
The speed of light is also seen referred to as velocity of light.
However, it can be argued that speed of light is better, as in this context we are concerned only with the magnitude of that velocity.
Sometimes the words in vacuo are added, which is Latin for in a vacuum.
Historical Note
Until the $1983$ definition of the metre as exactly $\dfrac 1 {299 \, 792 \, 458}$ of the distance travelled by light in $1$ second, the speed of light has been the subject of measurement.
This measurement has been accomplished to greater and greater accuracy over the course of history.
| Date | Technique | Value $(\mathrm {km} \, \mathrm s^{-1})$ | Tolerance | Error | |
|---|---|---|---|---|---|
| $1675$ | Ole Christensen Rømer and Christiaan Huygens | observing the moons of Jupiter | $220 \, 000$ | $-27 \%$ | |
| $1729$ | James Bradley | aberration of light | $301 \, 000$ | $+0 \cdotp 40 \%$ | |
| $1849$ | Armand Hippolyte Louis Fizeau | toothed wheel | $315 \, 000$ | $+5 \cdotp 1 \%$ | |
| $1862$ | Jean Bernard Léon Foucault | rotating mirror | $298 \, 000$ | $\pm 500$ | $−0 \cdotp 60 \%$ |
| $1907$ | Rosa and Dorsey | EM constants | $299 \, 710$ | $\pm 30$ | $−280$ ppm |
| $1926$ | Albert Abraham Michelson | rotating mirror | $299 \, 796$ | $\pm 4$ | $+12$ ppm |
| $1950$ | Essen and Gordon-Smith | cavity resonator | $299 \, 792 \cdotp 5$ | $\pm 3 \cdotp 0$ | $+0 \cdotp 14$ ppm |
| $1958$ | K.D. Froome | radio interferometry | $299 \, 792 \cdotp 50$ | $\pm 0 \cdotp 10$ | $+0 \cdotp 14$ ppm |
| $1972$ | Evenson et al. | laser interferometry | $299 \, 792 \cdotp 4562$ | $\pm 0 \cdotp 0011$ | $−0 \cdotp 006$ ppm |
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $2^{86243} - 1$
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): speed of light
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): wave
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): speed of light
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): wave
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): constant (in physical laws)
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): speed of light