Question

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

• A. $2.6\text{m}\text{from the mirror, real}$
• B. $1\text{m}\text{from the mirror, virtual}$
• C. $1\text{m}\text{from the mirror, virtual}$
• D. $3.66\text{m}\text{from the mirror, virtual}$

Answer 1

The correct option is D $3.66\text{m}\text{from the mirror, virtual}$

Focal length of the convex lens, $f=0.5\text{m}$
Object is at $2f$ so, image $\left(I_1\right)$ will also be at $2f$.
Image of $I_1$ i.e $I_2$ will be $1\text{m}$ behind mirror.
Now $I_2$ will be object for lens.

$\therefore u=(-1)+(-1)+(-1)=-3\text{m}$
Using lens formula, $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{v}=\frac{1}{f}+\frac{1}{u}=\frac{1}{+0.5}+\frac{1}{-3}\frac{3-0.5}{1.5}=\frac{5}{3}=1.66\text{m}$
Hence, distance of image from mirror
$=2+1.66=3.66\text{m}\text{and real.}$