An object is placed at a distance of $25\text{cm}$ from the convex mirror and a plane mirror is set such that the image formed by the two mirrors coincide. The plane mirror is placed at $20\text{cm}$ from the object. The radius of curvature of the convex mirror will be

The correct option is D $75\text{cm}$
The image formed by the plane mirror will be at $20\text{cm}$ behind the plane mirror. Thus, the image will be at $(20-5=15\text{cm})$ behind the convex mirror.
For the given convex mirror,
$u=-25\text{cm},v=+15\text{cm}$
Using mirror formula,
$\frac{1}{15}-\frac{1}{25}=\frac{1}{f}$
$\Rightarrow \frac{1}{f}=\frac{2}{75}$
$\Rightarrow f=\frac{75}{2}\text{cm}$
So, radius of curvature,
$R=2f=75\text{cm}$
$\begin{array}{c}\text{Why this question ?}\\ \text{Such question are commonly asked in}\\ \text{the competitive exams. It puts your understanding of image}\\ \text{formation (plane + spherical mirror) to a test.}\end{array}$