Question

A spherical surface of radius r seperates two media of refractive indices u1 and u2 respectively. When a parallel beam is incident from medium a along the axis, the focal length is f1. When a parallel beam is incident from medium b along the axis, the focal length is f2. Then f1/f2 is a) u1/u2 b) u2/u1 c) u1u2/(u1-u2)^2 d) (u1-u2)^2/u1u2

Answer 1

x =  [(μ2 + μ1) / R ] / (μ2 - μ1)

Explanation:

μ2 /v - μ1/u  = μ2 - μ1 / R

Let v = x and u = -x as the object and image are equidistant from the medium.

 μ2 /v - μ1/u  = μ2 /x - μ1/(-x)  

    = μ2 /x + μ1/x

x =  [(μ2 + μ1) / R ] / (μ2 - μ1)