A convex lens of focal length ' f ' m forms a real, inverted image twice in size of the object. The object distance from the lens in metre is

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For a real and inverted image, the magnification $m$ is negative. Given that the image is twice the size of the object, $m = - 2$ .

Using the formula for magnification:
$m = \frac{v}{u} = - 2 \Rightarrow v = - 2 u$

Using the lens formula:
$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$

Substituting $v = - 2 u$ into the lens formula:
$\frac{1}{- 2 u} - \frac{1}{u} = \frac{1}{f}$

$\frac{- 1 - 2}{2 u} = \frac{1}{f}$

$\frac{- 3}{2 u} = \frac{1}{f}$

$u = - 1.5 f$

The object distance from the lens is the magnitude of $u$ , which is $1.5 f$ .

Answer: 1.5 f

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