Question

If a ray of light enters a glass prism(as shown in the figure) of a refractive index of 1.5, then the speed of light inside the prism will be

• A. $0.2\times {10}^{8}m{s}^{-1}$
• B. $2\times {10}^{9}m{s}^{-1}$
• C. $2\times {10}^{7}m{s}^{-1}$
• D. $2\times {10}^{8}m{s}^{-1}$

Answer 1

The correct option is D

$2\times {10}^{8}m{s}^{-1}$

Step 1: Given data

Refractive index of the prism ($\mu$) = $1.5$

Speed of light in vacuum $c=3\times {10}^{8}m{s}^{-1}$

Step 2: Finding the speed of light inside the prism

We know,

$$\begin{gathered} Refractiveindexofprism\left(\mu \right)=\frac{Speedoflightinvacuum\left(c\right)}{Speedoflightinprism\left(v\right)} \\ \Rightarrow Speedoflightinprism\left(v\right)=\frac{Speedoflightinvacuum\left(c\right)}{Refractiveindexofprism\left(\mu \right)} \end{gathered}$$

$\nu =\raisebox{1ex}{$c$}\!\left/ \!\raisebox{-1ex}{$\mu $}\right.$

$$\begin{gathered} \nu =\frac{3\times {10}^8}{1.5} \\ \nu =2\times {10}^{8}m{s}^{-1} \end{gathered}$$

So, the speed of light in a prism is $2\times {10}^{8}m{s}^{-1}$.

Hence, option (d) is correct.