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

The correct option is B $-20$ cm
Given :
Object height 'h' = 10 mm,
Image size h' = 5 mm,
Image distance$v=-30cm,\text{To find: u = ? f=?}\text{From magnification formula m=}\frac{h^{\prime }}{h}=\frac{-v}{u}or\frac{5}{10}=\frac{-30cm}{u}or\frac{-30cm}{u}=\frac{1}{2}oru=-60\text{Now. it can be calculated as follows:}\frac{1}{v}+\frac{1}{u}=\frac{1}{f}or\frac{1}{-30cm}+\frac{1}{-60cm}=\frac{1}{f}or\frac{-2-1}{60}=\frac{1}{f}\frac{1}{f}=-\frac{1}{20cm}orf=-20cm\text{(the negative sign confirms that the calculated}\text{focal length is of a concave mirror).}$