An object of length 2.0 cm is placed at a distance of 1.5 f from a concave mirror where f is the magnitude of the focal length of the mirror. The length of the object is perpendicular to the principal axis. The length of the image will be

-4.0 cm

The correct answer is Option (2) → -4.0 cm

Object distance = $u = 1.5f = \frac{3}{2}f$

Mirror formula: $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$

$\frac{1}{v}=\frac{1}{f}-\frac{1}{u}=\frac{1}{f}-\frac{2}{3f}=\frac{1}{3f}$

$v=3f$

Magnification: $m=-\frac{v}{u}=-\frac{3f}{\frac{3}{2}f}=-2$

Image length: $h'=m\times h=-2\times 2=-4\text{ cm}$

The length of the image is $-4\text{ cm}$ (image is inverted with magnitude $4\text{ cm}$).