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 upright image of the object coincident with it?

• A. $60cm$
• B. $50cm$
• C. $30cm$
• D. $20cm$

Answer 1

The correct option is B $50cm$

The given situation can be shown as

Here, $u=OC=-30cm$

$f=20cm$

By using, $\frac{1}{v}=\frac{1}{f}+\frac{1}{u}$

$=\frac{1}{20}-\frac{1}{30}=\frac{1}{60}$

$\Rightarrow v=60cm$

To obtain upright image of $O$ at $O$ itself

$v=O{C}_1=x+10$

$\Rightarrow x=v-10=60-10=50cm$.