Question

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

• A. $\mu =\sqrt{2}$
• B. $\mu =\sqrt{\frac{3}{2}}$
• C. $\mu =\sqrt{3}$
• D. $\mu =\sqrt{\frac{5}{2}}$

Answer 1

Answer: (C)

Apply Snell's law at points $A$ and $B$
$1\sin 60^{\circ }=\mu \sin r\dots (i)$
$\mu \sin r=1\sin \varphi \dots (ii)$
Solving equations (i) and (ii), we get $\varphi =60^{\circ }$
Also, $2r+180^{\circ }-\varphi =180^{\circ }$
$2r+180^{\circ }-60^{\circ }=180^{\circ }$
or $2r=60^{\circ }$ or $r=30^{\circ }$
From equation (i), we get $\mu =\frac{\sin 60^{\circ }}{{\sin }^{\circ }}=\frac{\sin 60^{\circ }}{\sin cin30^{\circ }}=\sqrt{3}$