Question

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

• A. $\frac{R}{\mu }$
• 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 the air.

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

Solution:

Using the equation,

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

For the refraction at the first surface of the sphere,

(air to glass)

$\frac{\mu }{\infty }-\frac{1}{-x}=\frac{\mu -1}{R}$, Here $x$ is the distance of point object from the sphere, as shown in above fig.

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

Hence the object should be placed this distance from the surface of the sphere in order to get real image.