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  4. An object placed at a distance of 16 cm from a convex lens produces an image of magnification m (m > 1). If the object is moved towards the lens by 8 cm then again an image of magnification m is obtained. The numerical value of the focal length of the lens is

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Q. An object placed at a distance of $16 \,cm$ from a convex lens produces an image of magnification $m (m > 1)$. If the object is moved towards the lens by $8 \,cm$ then again an image of magnification $m$ is obtained. The numerical value of the focal length of the lens is

WBJEEWBJEE 2013Ray Optics and Optical Instruments

Solution:

Linear magnification, $m=\frac{f}{f+u}$
As given that magnification is same for both cases this is possible if the two different values of $u$ are of opposite sign. i.e., $\quad \frac{f}{f-16}=\frac{-f}{f-8}$
$\Rightarrow 16-f=f-8$
$\Rightarrow 2 f=24$
or $f=12\,cm$