How far should an object be held from a concave mirror of focal length 40 cm so as to obtain a real image twice the size of the object?

10 cm

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20 cm

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30 cm

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60 cm

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Solution

The correct option is C 60 cm

Real image is formed i.e, $v < 0$
$m a g n i f i c a t i o n = \frac{- v}{u} = - 2$
$v = 2 u$
$\frac{- 1}{2 u} + \frac{- 1}{u} = \frac{- 1}{f}$
$f = \frac{2 u}{3}$
$u = \frac{3 f}{2} = \frac{3 \times 40}{2} = 60 c m$

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