Question

A $10mm$ long awl pin is placed vertically In front of a concave mirror. A $5mm$ long image of the awl pin is formed at $30cm$ in front of the mirror, The focal length of this mirror is

• A. $-30cm$
• B. $-20cm$
• C. $-40cm$
• D. $-60cm$

Answer 1

The correct option is B $-20cm$

It is given that the image is formed $30cm$ in front the mirror.

$\therefore v=-30cm$

Also magnification, $m=\frac{\text{image height}}{\text{object height}}$

$\Rightarrow m=\frac{5mm}{10mm}=\frac{1}{2}$

Again, $m=\frac{v}{u}$

$\therefore \frac{-30}{u}=\frac{1}{2}$

$\Rightarrow u=-60cm$

The mirror formula is given as,

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

$\Rightarrow \frac{1}{f}=\frac{1}{-30}+\frac{1}{-60}$

$\Rightarrow \frac{1}{f}=\frac{-2-1}{60}=-\frac{3}{60}=-\frac{1}{20}$

$f=-20cm$

The correct option is (B)