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  4. A convex lens of focal length 30 cm produces 5 times magnified real image of an object. What is the object distance ?

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Q. A convex lens of focal length $30\, cm$ produces $5$ times magnified real image of an object. What is the object distance ?

WBJEEWBJEE 2011Ray Optics and Optical Instruments

Solution:

We have a lens of focal length $30\, cm$ that produces $5$ times magnified real image. So, we have
$\frac{1}{5 u}-\left(\frac{1}{-u}\right)=\frac{1}{30}$
Hence, $\frac{1}{5 u}+\frac{1}{u}=\frac{5+1}{5 u}=\frac{1}{30}$
So, $u=36 \,cm$