Question

A ray Of light takes ${10}^{-9}$ second to cross a glass slab of refractive index 1.5. The thickness of the slab will be

• A. 0.1m
• B. 0.2m
• C. 0.3m
• D. 0.4m

Answer 1

The correct option is B 0.2m

$\begin{array}{c}\text{We know,}\\ n=\frac{c}{v}\\ n\to \text{refractive index of medium}\\ c\to \text{speed of light in vacuum}\end{array}$

$\begin{array}{c}\therefore \\ 1.5=\frac{3\times {10}^8}{v}-\left(i\right)\\ \text{also,}v=\frac{d}{t}\end{array}$

$\therefore v=\frac{d}{{10}^{-9}}={\mathrm{10}}^{9}d-\left(ii\right)$

$\begin{array}{c}\text{from}\left(i\right)\text{and}\left(ii\right)\\ 1.5=\frac{3\times {10}^8}{{10}^{9}d}\Rightarrow d=\frac{3\times {10}^8}{1.5\times {10}^9}\\ \Rightarrow d=0.2m\end{array}$