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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 -4.0 cm 2.0 cm -2.0 cm |
-4.0 cm |
The correct answer is Option (2) → -4.0 cm
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
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