# when an object is placed at distance of 10 cm from a convex lens its virtual image twice as big as the object is formed calculate the focal length of the lens where to the object should the in front of the same lens so as to form its real image of twice the size

We use formula of magnification for convex lens.

given m = 2, u = 10 cm

$m=-\frac{(-v)}{u}\phantom{\rule{0ex}{0ex}}2=\frac{v}{10}\phantom{\rule{0ex}{0ex}}v=20cm$

For virtual image v is positive.

Calculation for Focal length:

$\frac{1}{f}=\frac{1}{-20}+\frac{1}{10}\phantom{\rule{0ex}{0ex}}f=20cm\phantom{\rule{0ex}{0ex}}$

To get real inverted image object should be placed beyond its focal length.

$m=-\frac{v}{u}=-2\phantom{\rule{0ex}{0ex}}Heremisnegativefortheinvertedimage.$

$\frac{1}{f}=\frac{1}{2u}+\frac{1}{u}\phantom{\rule{0ex}{0ex}}\frac{1}{20}=\frac{1}{2u}+\frac{1}{u}\phantom{\rule{0ex}{0ex}}u=30cm\phantom{\rule{0ex}{0ex}}$

Regards

Vijaya

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