The lens shown is equiconvex having refractive Index. 1.5. In the situation shown the final image of object coincides with the object. The region between lens and mirror is now filled with a liquid of Rrefractive Index 2.Then find the separation between O & image formed by convex mirror.

Case-I
Radius of curvature of lens is 20 cm
Image formed by convex lens should be at centre of curvature of mirror
$\begin{array}{l}\frac{1}{\mathrm{V}}+\frac{1}{30}=\frac{1}{20}\\ \frac{1}{\mathrm{V}}=\frac{1}{20}-\frac{1}{30}\Rightarrow \mathrm{V}=60\mathrm{cm}\end{array}$
Radius curvature of mirror should be 40 cm.
Case-II
$\begin{array}{l}\frac{2}{{\mathrm{V}}_1}+\frac{1}{30}=\frac{1.5-1}{20}+\frac{2-1.5}{-20}\\ \Rightarrow \mathrm{V}=-60\end{array}$
So for convex mirror u = - 80
$\frac{1}{\mathrm{V}}-\frac{1}{80}=\frac{1}{20}$
V = 16 cm
Seperation between object and this image O = 66 cm