A convex spherical refracting surface with radius R separates a medium having refractive index `5//2` from air. As an object is moved towards the surface from far away from the surface along the principle axis, its image

Options

A. changes from real to virtual when it is at a distance R from the surface
B. changes from virtual to real when it is at a distance R from the surface
C. changes from real to virtual when it is at a distance `2R//3` from the surface
D. changes from virtual to real when it is at a distance `2R//3` from the surface

Answer

c.

Explanation

`(2.5)/(v)-(1)/(-u)=(2.5-1)/(R)`
`(2.5)/(v)=(1.5)/(R)-(1)/(u)`
`v=(2.5uR)/(1.5u-R)`
`v=oo at 1.5 u-R=0`
`u=(R)/(3)`
For `ult(2R)/(3), v=0`, virtual image
`ugt(2R)/(3),v=0`, real image
So, image is changing from real to virtual at `u=(2R)/(3)`