A luminious object is placed at a distance of $30cm$ from the convex lens of focal length $20cm$. On the other side of the lens, at what distance from the lens a convex mirror of radius curvature $10cm$ be placed in order to have of radius an inverted image of the object coincident with it

The correct option is B $50cm$
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f};\frac{1}{v}-\frac{1}{-30}=\frac{1}{20}\Rightarrow v=60cm$

$\begin{array}{c}\text{coincidence is possible when the}\\ \text{image is formed at the center of}\\ \text{curvature of the mirror. only then}\\ \text{the rays refracting through the}\\ \text{lens will fall normaly on the}\\ \text{convex mirror and retrate their}\\ \text{path to form the image at}0\text{.}\\ \text{so, the distance between}\\ \text{lens \& mirror}=60-10\\ =50cm\\ \text{option}c\text{is correct.}\end{array}$