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Lens Maker's Formula

Find the posi...

Question

Find the position of an object when placed in front of a concave mirror of a focal length 20 cm produces a virtual image twice the size of the object.

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Solution

Given f=-20cm m=+2 because the image is virtual and erect.

$- \frac{v}{u} = 2$ $v = - 2 u$

$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$

$\frac{1}{- 20} = \frac{1}{u} - \frac{1}{2 u}$

$\frac{1}{- 20} = \frac{1}{2 u}$

$2 u = - 20$
$u = - 10 c m$
so the object is placed at a distance of 10cm from the mirror.

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