Question

A transparent sphere of radius $R$ and refractive index $\mu$ is kept in air. At what distance from the surface of the sphere should a point object be placed so as to form a real image at the same distance from the other side of sphere?

• A. $R/\mu$
• B. $\mu R$
• C. $\frac{R}{\mu -1}$
• D. $\frac{R}{\mu +1}$

Answer 1

The correct option is C $\frac{R}{\mu -1}$

Given: A transparent sphere of radius R and refractive index $\mu$ is kept in air.

To find the distance from the surface of the sphere at which a point object should be placed so as to form a real image at the same distance from the other side of sphere.

Solution:

Using the equation:

$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$

For refraction at the first surface of the sphere,

(Air to glass)

if $x$ is the distance from the surface of the sphere at which a point object should be placed

Then,

$\frac{\mu }{\infty }-\frac{1}{(-x)}=\frac{\mu -1}{R}⟹x=\frac{R}{\mu -1}$

is the distance from the surface of the sphere at which a point object should be placed so as to form a real image at the same distance from the other side of sphere