Question

Find the refractive index of a medium if the speed of light in that medium is $2.25\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$?

Answer 1

Step-1: Given

Speed of the light in a medium, $\nu =2.25\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Speed of the light in the vacuum, $c=3\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Step-2: Formula

Refractive index is given by the following formula,

Refractive index, $n=\frac{Speedoflightinvacuum\left(c\right)}{Speedoflightinanymedium\left(\nu \right)}$

Step-3: Refractive index of a medium

$$\begin{gathered} n=\frac{Speedoflightinvacuum\left(c\right)}{Speedoflightinanymedium\left(\nu \right)} \\ \Rightarrow n=\frac{3\times {10}^8{\displaystyle \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.}}{2.25\times {10}^8{\displaystyle \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.}} \\ \Rightarrow n=1.33 \end{gathered}$$

Hence, the Refractive index of the medium is $n=1.33$