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  4. In order to obtain a real image of magnification 2 using a converging lens of focal length 20 cm, where should an object be placed?

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Q. In order to obtain a real image of magnification $2$ using a converging lens of focal length $20\, cm$, where should an object be placed?

AFMCAFMC 2004

Solution:

$ \text{Magnification = }\frac{\text{image distance}}{\text{object distance}} $
$ \therefore M=-\frac{v}{u}=2 $
$ \Rightarrow v=-2u $
Also from lens formula for focal length $ f,v $ as image distance and $u$ as object distance, we have
$ \frac{1}{f}=\frac{1}{v}=\frac{1}{u} $
Putting $ f=20\,cm,$
$v=-2u, $ we get
$ \frac{1}{20}=-\frac{1}{2u}-\frac{1}{u} $
$ \Rightarrow \frac{1}{20}=-\frac{1-2}{2u} $
$ \Rightarrow u=-30\,cm $