Q. A parallel beam of light is incident on a solid transparent sphere of a material of refractive index $n.$If a point image is produced at the back of the sphere, the refractive index of the material of sphere is
A) 2.5
B) 1.5
C) 1.25
D) 2.0
Explanation
(d) The parallel beam of light forms a point image at the back of a sphere of refraction index $n$ as shown in figure.
If $R$ is the radius of sphere,
Then $u = \ \infty$
$v = 2R$ (from figure)
Since,
$\frac{n}{v} - \frac{1}{u} = \frac{n\ - \ 1}{R}$
Putting values, we get
$\frac{n}{2R} = \frac{1}{\infty} = \frac{n - 1}{R}$
$\frac{n}{2R} = \frac{n - 1}{R}$
$n = 2n - 2$
$\therefore n = 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.