## Dr. Ahmed G. Abo-Khalil

Electrical Engineering Department

## Speed of light

The speed of light in vacuum, usually denoted by c, is a universal physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time. In imperial units this speed is approximately 186,282 miles per second.

According to special relativity, c is the maximum speed at which all energy, matter, and information in the universe can travel. It is the speed at which all massless particles and associated fields (including electromagnetic radiation such as light) travel in vacuum. It is also the speed of gravity (i.e. of gravitational waves) predicted by current theories. Such particles and waves travel at c regardless of the motion of the source or the inertial frame of reference of the observer. In the Theory of Relativity, c interrelates space and time, and also appears in the famous equation of mass–energy equivalence E = mc2.[2]

The speed at which light propagates through transparent materials, such as glass or air, is less than c. The ratio between c and the speed v at which light travels in a material is called the refractive index n of the material (n = c / v). For example, for visible light the refractive index of glass is typically around 1.5, meaning that light in glass travels at c / 1.5 ≈ 200,000 km/s; the refractive index of air for visible light is about 1.0003, so the speed of light in air is about 90 km/s slower than c.

In most practical cases, light can be thought of as moving "instantaneously", but for long distances and very sensitive measurements the finite speed of light has noticeable effects. In communicating with distant space probes, it can take minutes to hours for a message to get from Earth to the spacecraft or vice versa. The light we see from stars left them many years ago, allowing us to study the history of the universe by looking at distant objects. The finite speed of light also limits the theoretical maximum speed of computers, since information must be sent within the computer from chip to chip. Finally, the speed of light can be used with time of flight measurements to measure large distances to high precision.

Ole Rømer first demonstrated in 1676 that light travelled at a finite speed (as opposed to instantaneously) by studying the apparent motion of Jupiter's moon Io. In 1865, James Clerk Maxwell proposed that light was an electromagnetic wave, and therefore travelled at the speed c appearing in his theory of electromagnetism. In 1905, Albert Einstein postulated that the speed of light with respect to any inertial frame is independent of the motion of the light source, and explored the consequences of that postulate by deriving the special theory of relativity and showing that the parameter c had relevance outside of the context of light and electromagnetism. After centuries of increasingly precise measurements, in 1975 the speed of light was known to be 299,792,458 m/s with a measurement uncertainty of 4 parts per billion. In 1983, the metre was redefined in the International System of Units (SI) as the distance travelled by light in vacuum in 1299,792,458 of a second. As a result, the numerical value of c in metres per second is now fixed exactly by the definition of the metre.

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