Question

An object$\left(O\right)$ is placed at a distance $20\text{cm}$ from a convex mirror. If a plane mirror is also kept at a distance of $12\text{cm}$ from the same object as shown, image$\left(I\right)$ formed by plane mirror is at the same point at which image is produced by the convex mirror. The focal length of the convex mirror is

• A. $5\text{cm}$
• B. $6\text{cm}$
• C. $7\text{cm}$
• D. $8\text{cm}$

Answer 1

The correct option is A $5\text{cm}$

For plane mirror,
Object distance $=$ Image distance
Thus, plane mirror will form image $12\text{cm}$ behind itself.


Since, convex mirror and plane mirror forms the images at the same point.
So, $v=+(12+12-20)=+4\text{cm}$
$u=-20\text{cm}$
From mirror formula,
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{4}-\frac{1}{20}=\frac{1}{f}$
$\Rightarrow \frac{1}{f}=\frac{1}{5}$
$\Rightarrow f=5\text{cm}$