Question

A point object is placed at $15\text{cm}$ in front of a convex lens of focal length $10\text{cm}$. Where shall we place a convex mirror of focal length $13\text{cm}$ so that real image and object coincide?

• A. $6\text{cm}$ from lens
• B. $3\text{cm}$ from lens
• C. $4\text{cm}$ from lens
• D. $2\text{cm}$ from lens

Answer 1

The correct option is C $4\text{cm}$ from lens

Using Lens formula
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$;

$\frac{1}{v}=\frac{1}{10}-\frac{1}{15}$

$v=30\text{cm}$.
In order the ray to retrace the path, the ray must be incident normal on the mirror.
Hence, distance of mirror from $I^{\prime }$ should be equal to $R=2f=26\text{cm}$
Distance of mirror from lens should be
$30-26=4\text{cm}$ from lens.