question_answer

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

A) Changes from real to virtual when it is at a distance of R from the surface

B) Changes from virtual to real when it is at a distance of R from the surface.

C) Changes from real to virtual when it is at a distance no. of \[\frac{2R}{3}\] from the surface

D) Changes from virtual to real when it is at a distance of \[\frac{2R}{3}\] from the surface

Correct Answer: C

Solution :

[c]

Using refraction at spherical surface\[=\frac{2.5}{v}-\frac{1}{u}=\frac{2.5-1}{R}\]

\[\Rightarrow \]   \[\frac{2.5}{v}=\frac{1.5}{R}-\frac{1}{u}\]            \[\Rightarrow \]   \[v=\frac{2.5uR}{1.5u-R}\]

\[v=\infty \] at \[1.5u-R=0\Rightarrow u=\frac{2R}{3}\]

For        \[u<\frac{2R}{3},v<0\] virtual image

\[u>\frac{2R}{3},v>0\] real image