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 surface of sphere?

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

Answer 1

Answer: (C)

$\frac{R}{\mu-1}$

Answer 2

For an object placed at the first principal focal point of a sphere, rays become parallel after the first refraction. These parallel rays then refract at the second surface, converging at the second principal focal point. For a sphere, the principal focal length from the surface is $f = \frac{R}{\mu-1}$. If the object is placed at this distance from the first surface, the image will be formed at the same distance from the second surface, and it will be real (since $\mu > 1$).