importance of measuring speed of light

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Why is it important to measure speed of light? 


Speed of light possesses very important role for studying various phenomena, such as wave nature of light, reflection, refraction, relativity, electromagnetism etc., in Physics. The major importance of measuring velocity of light are mentioned as below:

1. Since the electromagnetic wave travels with speed of light, the wavelength(`\lamda`) of electromagnetic radiation is related to speed of light(c) as,

 `\lamda \times \nu = c`  ------------ (1), f  is frequency of wave.

2. The speed of light is used to find energy equivalence of mass(m) in accordance with Einstein's mass-energy relation, 

  `E= m c^2` ------------ (2)

           To learn more about Why the speed of light is there in `E= m c^2` ?, Click Here.

3. The speed of light is used to determine relativistic mass of a particle whose rest mass is `m_o` and speed is v. The relation for relativistic mass is, 

`m = \frac{m_o}{\sqrt{1 - \frac{v^2}{c^2}}}` ------------ (3)

4. Measuring speed of light in vacuum (air medium) enables us to know to highest possible speed of a particle in accordance with the relativistic mass relation.

5. The speed of light enables of us determine the energy and momentum of wave.

`E = h \nu = \frac{hc}{\lamda}` --------(4), where `\nu = \frac{c}{\lamda}` from (1)

and momentum, ` P = \frac{E}{c} = \frac{h \nu}{c}` --------(5).




6. The speed of light in medium and in vacuum enables us to determine the refractive index of medium by the relation, 

`\mu = \frac{c}{v}` --------(6)
 where v is speed in medium and c is speed in vacuum.

Actually, refractive index ={speed of refracted ray}/{speed of  incidence ray}

                                         = {speed of light in medium}/{speed of light in vacuum}.

Refractive index is the term mostly used in physical phenomena such as refraction of light, dispersion of light. The process of bending of light ray at the boundary of two media when light travels from one medium to another is called refraction of light, as shown in fig.1. 




The dispersion of light can simply be understood as splitting of a single white ray of light into seven different colors when it passes through a small angled prism, shown in fig.2.
For small angled prism, the deviation of incident light is given as, 

`\delta = A (\mu - 1)` -------------(7)

where `\mu` is refractive index of prism and A angle of prism.
This relation is very important in optics.

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