Question

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

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

Answer 1

Answer: (B)

$\sqrt{3}$


Deviation due to first surface(incidence point) on the sphere (i -r)

Deviation due to second surface(leaving point) on the sphere (i -r)

Therefore total deviation $\delta ={60}^{\circ }=(i-r)+(i-r)=2(i-r)$
(or) $i-r={30}^{\circ }$
$\therefore$ $r=i-{30}^{\circ }={60}^{\circ }-{30}^{\circ }={30}^{\circ }$
$\therefore$ $\mu =\frac{sini}{sinr}=\frac{sin{60}^{\circ }}{sin{30}^{\circ }}=\sqrt{3}$