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 real image at the same distance from the sphere?

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

Answer 1

Answer: (B)

As $P_{1}O=P_{2}I$, therefore, the rays must pass through the sphere in a direction parallel to the optic axis, as shown in the figure.

Now, for first refraction at $A$ from rarer to denser medium,
$-\frac{{\mu }_1}{u}+\frac{{\mu }_2}{v}=\frac{{\mu }_2-{\mu }_1}{R}$
$\Rightarrow -\frac{1}{u}+\frac{\mu }{\infty }=\frac{\mu -1}{R}$
$\therefore u=-\frac{R}{(\mu -1)}$
or $|u|=\frac{R}{(\mu -1)}$