Question

The largest distance of the image from a convex mirror of focal length $10cm$ can be

• A. $20cm$
• B. infinite
• C. $10cm$
• D. depends on the position of the object

Answer 1

Answer: (C)

For a real object, in case' of a convex mirror, the images formed between the pole and focus.
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{v}=\frac{1}{f}-\frac{1}{u}$
$\frac{1}{v}=\frac{u-f}{uf}$
$\Rightarrow v=\frac{uf}{u-f}=\frac{f}{1-\left(\frac{f}{u}\right)}$
As $u$ is -ve for a real object, $f$ is +ve for convex mirror,
$v=\frac{f}{1+\left(\frac{f}{u}\right)}\Rightarrow |v|<|f|\cdot s$