Question

A solid transparent sphere has a small opaque dot at its centre. When observed from outside, the apparent position of the dot will be

• A. closer to the eye than the actual position.
• B. farther away from the eye than its actual position.
• C. same as its actual position.
• D. independent of the refractive index of the sphere.

Answer 1

Answer: (C), (D)

The correct options are
C same as its actual position.
D independent of the refractive index of the sphere.

We apply the lens formula considering the refractive indices of the medium involved.

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

Substituting the values of the physical quantities given,

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

This gives, $\frac{1}{v}=\frac{1}{-R}$

Thus, the image will be formed in the same position and it is independent of the value of the refractive index $\mu$.