Question 186 of 295

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

A$2.6m$ from the mirror, realB$1m$ from the mirror, virtualC$1m$ from the mirror, realD$2.6m$ from the mirror, virtual

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Answer: (D) $2.6m$ from the mirror, virtual

For ${I}_{1}$ applying lens formula
$\begin{matrix}\dfrac{1}{{v}_{1}}-\dfrac{1}{-1}=\dfrac{1}{0.5} \\ \end{matrix}$
${v}_{1}=1$
For ${I}_{2}$ applying condition of plane mirror
for final image (${I}_{3}$) again applying lens formula
$\dfrac{1}{{v}_{3}}-\dfrac{1}{-3}=\dfrac{1}{0.5}$
${v}_{2}=\dfrac{3}{5}$
The distance of final image from mirror
$D=\dfrac{3}{5}+3$
$D=2.6$
The image will be real (but it is given virtual in answer)