Question

The speed of light in air is\[3\times {{10}^{8}}\,{m}/{s}\;\]. Calculate the speed of light in glass. The refractive index of the glass is 1.5.

Answer 1

Hint: The formula that defines the relation between the refractive index, the speed of light in air and the speed of light in the medium should be used to solve this problem. The speed of light in the air by the speed of light in the medium equals the refractive index of the medium.

Formula used:
\[n=\dfrac{c}{v}\]

Complete step-by-step solution:
From the given information, we have the data as follows.
The speed of light in air is\[3\times {{10}^{8}}\,{m}/{s}\;\]. The refractive index of the glass is 1.5.
The formula that defines the relation between the refractive index, the speed of light in air and the speed of light in the medium should be used to solve this problem. The speed of light in the air by the speed of light in the medium equals the refractive index of the medium.
The mathematical representation of the same is given as follows.
\[n=\dfrac{c}{v}\]
Where ‘n’ is the refractive index, ‘c’ is the speed of light in air and ‘v’ is the speed of light in the medium.
Represent the above equation in terms of the speed of light in the medium.
\[v=\dfrac{c}{n}\]
Substitute the values of the speed of light in air and the refractive index of the glass in the above formula.
\[\begin{align}
  & v=\dfrac{3\times {{10}^{8}}}{1.5} \\
 & \Rightarrow v=\dfrac{3\times {{10}^{8}}}{{}^{3}/{}_{2}} \\
 & \Rightarrow v=\dfrac{2\times 3\times {{10}^{8}}}{3} \\
 & \therefore v=2\times {{10}^{8}}\,{m}/{s}\; \\
\end{align}\]
\[\therefore \] The speed of light in glass for the speed of light in air being\[3\times {{10}^{8}}\,{m}/{s}\;\]and the refractive index of the glass being 1.5 is \[2\times {{10}^{8}}\,{m}/{s}\;\].

Note: The speed of light in the air equals the speed of light in the medium when the refractive index of the medium equals unity. The speed of light in the air is constant. The unit of the speed of light is a meter per second. So, the unit of the speed of light should be represented in meters per second.