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  4. A convex lens of focal length 20 cm produces a real image twice the size of the object. Then the distance of the object from the lens is

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Q. A convex lens of focal length $20 \,cm$ produces a real image twice the size of the object. Then the distance of the object from the lens is

AMUAMU 2002

Solution:

From lens formula $\frac{1}{f}=\frac{1}{v}-\frac{1}{u} \ldots$ (i)
Also magnification $(m)=\frac{v}{u} \ldots$ (ii)
Given, $f=20\, cm , v=2 \,u$
$\therefore $ From Eqs. (i) and (ii), we get
$\frac{1}{20}=\frac{1}{2 u}-\frac{1}{-u}$
$\Rightarrow \frac{1}{20}=\frac{1}{2 u}+\frac{1}{u}$
$\Rightarrow u=30\,cm$