What is the speed of light?

In physics, the speed of light in a vacuum is a fundamental physical constant. It is denoted by the letter $c,$ called constant. The exact value of speeds of light is 299,792,548 meters per second (300,000 km/s). The value is accurate, because, it is fixed by the international convention. A meter is defined as the distance traveled by the light in a vacuum in $\frac{1}{299 792 548}$ seconds. The speed of light is measured by the SI unit m/s. In general, the speed of light is measured by the value $3\times {10}^8$m/s.

Major role in physics

The speed at which the light travels in a vacuum is unbiased for both the source and inertial frame of reference of the observer. This was postulated by the physicist, Albert Einstein, by observing the theory of electromagnetism of Maxwell. Also, there was no evidence for the luminiferous aether, that is, the medium for the propagation of light where the electromagnetic field exists.

The Einstein theory of general relativity explains the consequences of the invariance of c, with the assumption that the law of physics is the same in all the inertial frames of reference of the observer. Of all the consequences, one of them is, c is the speed at which all the massless particles and waves must travel in a vacuum.

The relativity theory has many absurd and analytical implications, which include, mass-energy relationship, length contraction, and time dilation. The factor is known as the Lorentz factor at which the length contracts and time dilates. It is given by,

$\gamma =\frac{1}{\sqrt{1-{\displaystyle \frac{v^2}{c^2}}}}$

From the Einstein theory of relativity, the energy of a particle with rest mass m, speed v is given by $E=\gamma m{c}^2.$ When the speed of the particle v tends to zero, $\gamma$ equals one, and the equation becomes $E=m{c}^2.$ The Lorentz factor tends to infinity when the speed v approaches c, and it takes an infinite quantity of energy to accelerate the particle with mass to the speed of light.

Measurement

There are several methods to the measurement of the speed c. One of the ways is to calculate the actual speed at which the light wave propagates, by using astronomical and earth-based setups. It can also be found by using physical laws. Some of them are,

Astronomical measurements

Ole Rømer made the first quantitative estimate of the speed of light by using astronomical measurements in 1676. Outer space is an exact space for measuring speed because of its large scale and perfect vacuum. One astronomical unit (AU) is defined as the average distance between the earth and the sun.

$1 AU=1.49\times {10}^8 km$

Time of flight  

This method of measuring the speed of light is to measure the time needed for light to travel to a mirror at a known distance and back. Fizeau-Foucault apparatus is working on this principle. It was developed by the physicists Hippolyte Fizeau and Leon Foucault. This setup includes a beam of light that passes through a mirror which is kept at 8 km away. The beam travels into the cogwheel when it travels from the source to the mirror. At a certain time of rotation, the beam strikes the tooth and does not come out of the wheel. By calculating the distance, the number of teeth on the wheel, rate of rotation, the speed of light can be measured.

Interferometry

Interferometry is a technique used to find the wavelength of electromagnetic radiation for calculating the speed. A monochromatic beam of light of known frequency is divided into two and the two beams follow two different paths and then recombine. By observing the interference pattern, and measuring the change in path length, the wavelength is determined. It is calculated from the equation,

$c=\mathrm{\lambda f}$

An example of interferometry is the Michaelson-Morley interferometer.

Propagation of light

In physics, light is defined as an electromagnetic wave. The classical characteristics of the electromagnetic waves are explained using Maxwell’s equations. These equations predict that the speed of light c travels in a vacuum is related to the distributed capacitance and vacuum inductance, and it is known as the electric constant ${\epsilon }_0$ and magnetic constant${\mu }_0$. It is given by,

$c=\frac{1}{\sqrt{{\epsilon }_0{\mu }_0}}$
The light mentioned here is the visible light in the electromagnetic spectrum. The difference between visible light and another light in the spectrum is the magnitude of its wavelength. The wavelength of any wave is described by its frequency and speed of light and it is given by the equation,

$c=\lambda \nu$
In quantum physics, the electromagnetic field is explained by using quantum electrodynamics. In this theory, light is defined as quanta of the field, which is called photons. Here, photons are massless particles which travel at the speed of light in a vacuum.

In a medium

Generally, in physics, a medium is defined as a material that transfers energy or light from one particle to another. In a medium, the light does not travel at a speed that is equal to c. But light travel at different speeds in different medium. The speed at which a crest and trough of the wave propagate is called phase velocity. A signal with a finite speed extent which is a pulse of light propagates at a different speed. The largest area of the pulse is called the group velocity and its earliest part travels at front velocity.

When a light wave travels from one medium to another medium, the phase velocity is used to determine how the light propagates in the medium. It is also known as the refractive index. The refractive index of the medium is defined as the ratio of the light speed to the phase velocity.

$\mu =\frac{c}{v}$

Where, $\mu$ is the refractive index.

c is the speed of light which is a constant.

$\nu$ is the phase velocity.

The refractive index of the material relies on the light’s frequency, intensity, polarization, propagation direction. For example, the refractive index of air is 1.003. And for the denser materials such as water, glass, it is around 1.3 to 1.5. For exotic materials, such as Bose-Einstein condensates near absolute zero, the speed of light is only a few meters per second.

Practical uses of the speed of light

The speed of light is used for communications and distance measurements.

• In supercomputers, the speed of light sets a limit for how fast the data can be sent between the processors.
• In spaceflights, the communication between earth and spacecraft are not instant. Receiving and transferring signals from astronomical sources can take a longer time. It takes 13 billion light-years to travel to earth from distant galaxies.
• Astronomical distances are measured in light-years. It is defined as the distance traveled by light in one year. For example, in Proxima Centauri, the star closest to the earth is 4.2 light-years away from earth.
• The radar system uses the speed of light to measure the distance to a target using transit time, that is time taken by a radio wave pulse to return after being reflected by the target. The distance of the target is half the round-trip transit time multiplied by the speed of light.

Context and Applications

This topic is one of the basic topics in physics, for all the graduates and postgraduates, especially for Bachelors of Science (physics).

Practice Problems

Question 1: The speed of light is denoted by_____.

a. c

b. s

c. k

d. f

Answer: The correct option is a.

Explanation: The speed of light is denoted by the symbol c, which means constant.

Question 2: Photons travel at speed of_____.

a. Wave

b. Light

c. Sound

d. Air

Answer: The correct option is b.

Explanation: The photons are massless particles, which travel at the speed of light in a vacuum.

Question 3: The frequency of green light $6.26\times {10}^{10}Hz$. Determine its wavelength. The speed of light is $3\times {10}^{8}m/s.$

$$\begin{gathered} a.5\times {10}^{-3} m \\ b.6\times {10}^{-3} m \\ c.12\times {10}^{-4} m \\ d.3\times {10}^{-3} m \end{gathered}$$

Answer: The correct option is a.

Explanation:

Frequency $\nu =6.26\times {10}^{10}Hz$

Speed $c=3\times {10}^{8}m/s$

Hence, the wavelength is calculated as,

$$\begin{gathered} c=\nu \lambda \\ \lambda =\frac{c}{\nu } \\ \lambda =\frac{3\times {10}^8}{6.26\times {10}^{10}} \\ \lambda =4.79\times {10}^{-3}m \\ \lambda =5\times {10}^{-3}m \end{gathered}$$

Question 4: Calculate the speed of light in water. The refractive index of water is 1.33.

$$\begin{gathered} a.3.89\times {10}^{8}m/s \\ b.1.36\times {10}^{8}m/s \\ c.2.25\times {10}^{8}m/s \\ d.5.4\times {10}^{8}m/s \end{gathered}$$

Answer: The correct option is c.

Explanation:

Refractive index of water=1.33

Speed of light, c=$3\times {10}^{8}m/s$

The light speed in water is found from the formula,

$$\begin{gathered} \mu =\frac{c}{v} \\ v=\frac{c}{\mu }=\frac{3\times {10}^8}{1.33} \\ \nu =2.25\times {10}^8 m/s \end{gathered}$$

Question 5: The Einstein mass-energy equivalence is expressed by the formula_____.

$$\begin{gathered} a. E=mc \\ b.E=m^{2}c \\ c.E=m^2{c}^2 \\ d.E=m{c}^2 \end{gathered}$$

Answer: The correct option is d.

Explanation: Einstein's mass-energy equivalence is the most famous equation, $E= m{c}^2$. It is defined as the energy equals mass times the speed of light squared. This equation also explains that energy and mass are interchangeable.