Question

A luminous 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 of curvature $10cm$ be placed in order to have an inverted image of the object coinciding with image formed by lens?

• A. $12cm$
• B. $30cm$
• C. $50cm$
• D. $60cm$

Answer 1

The correct option is C $50cm$

For the lens,
$\frac{1}{v}=\frac{1}{f}+\frac{1}{u}=\frac{1}{20}-\frac{1}{30}=\frac{1}{60}$
$v=60cm$.
To have an inverted image of the object, coincident with it, image should tend to form at centre of curvature of convex mirror.

Therefore, distance of convex mirror from the lens $=60–10=50cm$.