Question

A point like object is placed at a distance of $1m$ in front of a convex lens of focal length $0.5$ $m.$A plane mirror is placed at a distance of $2m$ behind the lens. The position and nature of the final image formed by the system is :

• A. $1m$ from the mirror, virtual
• B. $1m$ from the mirror, real
• C. $2.6m$ from the mirror, real
• D. $2.6m$ from the mirror, virtual

Answer 1

Answer: (C)

Object is at $2f$. So image will also be at ' $2f^{\prime }$
$\left(I_1\right)$
Image of $I_1$ will be $1m$ behind mirror.
i.e. $\Rightarrow I_2$
Now $I_2$ will be object for lens.
$\therefore u\Rightarrow -3m$
$f\Rightarrow +0.5m$
$\frac{1}{v}\Rightarrow \frac{1}{f}+\frac{1}{u}$
$\Rightarrow \frac{1}{+0.5}+\frac{1}{-3}$
$v\Rightarrow \frac{3}{5}\Rightarrow 0.6m$
So total distance from mirror $\Rightarrow 2+0.6$
$\Rightarrow 2.6m$ and real image