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
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → -4.0 cm
-
Object height ($h$): $+2.0$ cm
-
Object distance ($u$): $-1.5f$
-
Focal length: $-f$
Using the mirror formula: $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$
$\frac{1}{v} + \frac{1}{-1.5f} = \frac{1}{-f}$
$\frac{1}{v} = -\frac{1}{f} + \frac{2}{3f}$
$\frac{1}{v} = \frac{-3 + 2}{3f} = -\frac{1}{3f}$
$v = -3f$
Finding Image Length ($h'$)
Magnification ($m$) is given by: $m = -\frac{v}{u} = \frac{h'}{h}$
$-\left(\frac{-3f}{-1.5f}\right) = \frac{h'}{2}$
$-(2) = \frac{h'}{2}$
$h' = -4.0$ cm