A curved surface of radius R separates two medium of refractive indices ${\mathrm{\mu }}_1\text{ and }{\mathrm{\mu }}_2$ as shown in figure 

Choose the correct statement(s) related to the virtual image formed by object O placed at a distance x, as shown in figure.

$\frac{{\mathrm{\mu }}_2}{\mathrm{V}}-\frac{{\mathrm{\mu }}_1}{\mathrm{u}}=\frac{{\mathrm{\mu }}_2-{\mathrm{\mu }}_1}{\mathrm{R}}$

$\Rightarrow \frac{{\mathrm{\mu }}_2}{\mathrm{V}}+\frac{{\mathrm{\mu }}_1}{\mathrm{X}}=\frac{{\mathrm{\mu }}_2-{\mathrm{\mu }}_1}{\mathrm{R}}$

$\Rightarrow \frac{{\mathrm{\mu }}_2}{\mathrm{V}}=\frac{{\mathrm{\mu }}_2-{\mathrm{\mu }}_1}{\mathrm{R}}-\frac{{\mathrm{\mu }}_1}{\mathrm{x}}\Rightarrow \mathrm{V}=\frac{{\mathrm{\mu }}_2\mathrm{Rx}}{\left({\mathrm{\mu }}_2-{\mathrm{\mu }}_1\right)\mathrm{x}-{\mathrm{\mu }}_1\mathrm{R}}$

V should be +ve for real image and -ve for virtual image. Real image forms in ${\mathrm{\mu }}_2$ and virtual image forms in ${\mathrm{\mu }}_1$only.

A) If ${\mathrm{\mu }}_2>{\mathrm{\mu }}_1$ then V may be +ve or -ve i.e., the image may be real or virtual depending
upon the values of x and R. 

B) If x> R,V can be +ve or -ve depending upon the value of ${\mathrm{\mu }}_2 \mathrm{and} {\mathrm{\mu }}_1$