Question

Refractive index of a rectangular glass slab is $\mu =\sqrt{3}$. A light ray from air is incident at an angle of ${60}^{\circ }$ is displaced laterally through $2.5\text{cm}$. Distance travelled by the light in the glass slab will be

• A. $4\text{cm}$
• B. $5\text{cm}$
• C. $6\text{cm}$
• D. $7\text{cm}$

Answer 1

The correct option is B $5\text{cm}$

The path of refracted ray in slab has been shown in the figure.


We know that, by Snell's law,
$\mu =\frac{\sin i}{\sin r}$
$[$when first medium is air$]$
$\Rightarrow \sqrt{3}=\frac{\sin {60}^{\circ }}{\sin r}$
$\Rightarrow \sin r=\frac{1}{2}$
$\Rightarrow \frac{BC}{AB}=\frac{1}{2}$
$[$in $△$ABC$]$
$\Rightarrow AB=2BC=2\times 2.5=5\text{cm}$

Why this question? It highlights the importance of lateral displacement of a light ray while passing through a transparent medium like glass slab. Tips: Focus on geometry of ray diagram and apply Snell's law at interface.