When an object is placed 20 cm from a complex lens then a real image is formed 30 cm from the lens. Where should the object be placed so that a real image of the same size is formed by the lens.

Object should be placed 24 cm from the lens.

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Object should be placed 34 cm from the lens.

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Object should be placed 14 cm from the lens.

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Object should be placed 30 cm from the lens.

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Solution

The correct option is A Object should be placed 24 cm from the lens.
$\frac{1}{v} - \frac{1}{u} = \frac{1}{f} ⟹ \frac{1}{30} - \frac{1}{- 20}$
On solving we get $f = 12 c m$
Now $m = - 1$
$\frac{v}{u} = - 1, v = - u$

$\frac{1}{12} = \frac{1}{- u} - \frac{1}{u} = \frac{- 2}{u}$

$u = - 24 c m$
Object should be placed 24 cm from the lens.

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When an object is placed 20 cm from a complex lens then a real image is formed 30 cm from the lens. Where should the object be placed so that a real image of the same size is formed by the lens.

The correct option is A Object should be placed 24 cm from the lens.1v−1u=1f⟹130−1−20On solving we get f=12cmNow m=−1vu=−1, v=−u112=1−u−1u=−2uu=−24cm Object should be placed 24 cm from the lens.