Question

A thin equiconvex lens of reflective index 3/2 is placed on a horizontal plane mirror as shown in figure. The space between the lens and mirror is filled with a liquid of refractive index 4/3 It is found that when a point object is placed 15 cm above the lens on its principal axis, the object coincides with its own image.

The radius of curvature of the convex surface is

(a)  10 cm

(b)   15 Cm

(c)   20 cm

(d)  25 cm

Answer 1

Correct option  (1)   25 cm

Explanation :

For the object to coincides with its image, rays must fall on mirror in a direction to it. So object must be at focus of lens. 

x = 1

x = 3/2

μ = 4/3

1/f = n₂ - n₁/R₁ + n₃ - n₂/R₂

_{1/15 = 4/6R}

_{R = 15 x 2/3}

_{R = 10 cm}