Question

If the speed of light in glass is $2\times {10}^{8}m/s$, and that in air is $3\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$, calculate the refractive index of glass with respect to air?

Answer 1

Step-1: Given

Speed of the light in the glass, $\nu =2\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

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

Step-2: Formula

Refractive index is calculated by the given formula,

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

Step-3: Refractive index of glass with respect to air

$$\begin{gathered} n=\frac{Speedoflightinair\left(c\right)}{Speedoflightinanymedium\left(\nu \right)} \\ \Rightarrow n=\frac{3\times {10}^8{\displaystyle \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.}}{2\times {10}^8{\displaystyle \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.}} \\ \Rightarrow n=1.5 \end{gathered}$$

Hence, the Refractive index of glass with respect to air is $n=1.5$.