Question

A ray of light falls on a transparent sphere with centre at $C$ is shown in Fig.
The ray emerges from the sphere parallel to line $AB$. The refractive index of the sphere is

• A. $\sqrt{2}$
• B. $\sqrt{3}$
• C. $3/2$
• D. $1/2$

Answer 1

Answer: (B)

$\sqrt{3}$

Deviation by a sphere is $2(i-)$
Here, deviation $\delta ={60}^{\circ }=2(i-r)$
or $i-r={30}^{\circ }$
$\therefore r=i-{30}^{\circ }={60}^{\circ }-{30}^{\circ }={30}^{\circ }$
$\therefore \mu =\frac{\sin i}{\sin r}=\frac{\sin {60}^{\circ }}{\sin {30}^{\circ }}=\sqrt{3}$.