A point object is placed at a distance of $60\text{cm}$ from a convex lens of focal length $30\text{cm}$. If a plane mirror were put perpendicular to the principal axis of the lens and at a distance of $40\text{cm}$ from it, the final image would be formed at a distance of -

The correct option is A $20\text{cm}$ from the plane mirror, it would be a virtual image
Using lens formula for first refraction from convex lens,

$\frac{1}{v_1}-\frac{1}{u}=\frac{1}{f}$

$v_1=?,u=-60\text{cm},f=30\text{cm}$

$\Rightarrow \frac{1}{v_1}+\frac{1}{60}=\frac{1}{30}\Rightarrow v_1=60\text{cm}$


Here $I_1$ is the first image by the lens.

The plane mirror will produce an image at distance $20\text{cm}$ to the left of it.

For second refraction from convex lens,

$u=-20\text{cm},v=?,f=30\text{cm}$

From lens formula,

$\Rightarrow \frac{1}{v}-\frac{1}{(-20)}=\frac{1}{30}\Rightarrow v=-60\text{cm}$

Thus, the final image is virtual and at a distance, $60\text{cm}-40\text{cm}=20\text{cm}$ from the plane mirror.

Hence, option $\left(A\right)$ is the correct answer.