An object of length 2.5 cm is placed at a 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 is:
Answer & explanation
Correct answer: option 3
The focal length F = -f and u = -1.5 f, we have,
$\frac{1}{u}+\frac{1}{v}=\frac{1}{F}$ or $\frac{1}{-1.5f}+\frac{1}{v}=-\frac{1}{f}$
$\frac{1}{v}=\frac{1}{1.5f}-\frac{1}{f}=-\frac{1}{3f}$, v = -3 f
Now, $m = -v/u = -\frac{3f}{1.5f}=-2$
or $\frac{h_2}{h_1}=-2$ or $h_2 = -2h_1 = -5 cm$
The image is 5 cm long. The minus sign shows that it is inverted.