Two objects are equal distances from sphere of radius R & refractive index μ

Question

Two objects are equal distances from sphere of radius R & refractive index \(\mu\) such that the image of one object forms on other object. Find the object distance from the surface of sphere.

(1) \(\frac{R}{\mu}\)

(2) \(\frac{R}{\mu-1}\)

(3) R

(4) \(\frac{R}{\mu + 1}\)

Answer 1

Correct option is : (2) \(\frac{R}{\mu-1}\) 

\(\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}\) 

After first refraction the ray must become parallel to the line joining two objects.

So \(v = \infty\)

\(\Rightarrow 0 - \frac{1}{u} = \frac{(\mu - 1)}{R}\)

\(\Rightarrow |u| = \frac{R}{\mu - 1}\)