Question

A rod of length $10\text{cm}$ lies along the principal axis of a concave mirror of focal length $10\text{cm}$ in such a way that the end closer to the pole is $20\text{cm}$ away from it. Find the length of the image.

• A. $4\text{cm}$
• B. $6\text{cm}$
• C. $5\text{cm}$
• D. $7\text{cm}$

Answer 1

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

The situation is shown in the figure.

The radius of curvature of the mirror is $R=2f=20\text{cm}$.

Thus, the nearer end $B$ of the rod $AB$ is at the centre of the curvature and hence, its image will be formed at $B$ itself.

We shall now locate the image of $A$.

Here,
$u=-30\text{cm}$
$f=-10\text{cm}$

We have,
$\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$

$\text{or},\frac{1}{v}=\frac{1}{f}-\frac{1}{u}$

$\text{or,}$$\frac{1}{v}=\frac{1}{-10}-\frac{1}{(-30)}$

$\text{or,}$ $v=-15\text{cm}$

Thus, the image of $A$ is formed at $-15\text{cm}$ from the pole.

Therefore, the length of the image is $5\text{cm}$.