Question

A narrow pencil of parallel light is incident normally on a solid transparent sphere of radius r. What should be the refractive index if the pencil is to be focussed

(a) At the surface of the sphere,

(b) At the centre of the sphere.

Answer 1

v = 2r, $u=-\infty$

${\mu }_2=\mu$ (let)

${\mu }_1=1$

$\frac{\mu }{v}-\frac{1}{\infty }=\frac{\mu -1}{r}$

$\frac{\mu }{2r}=\frac{\mu -1}{r}$

$\Rightarrow \mu =2\mu -2,\mu =2$

(b) For this case v = r

So, $\frac{\mu }{r}=\frac{\mu -1}{r}$

$\Rightarrow -1=0$ not possible.