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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.
A. Object should be placed $24\,cm$ from the lens
B. Object should be placed $34\,cm$ from the lens
C. Object should be placed $14\,cm$ from the lens
D. Object should be placed $30\,cm$ from the lens

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Last updated date: 01st Mar 2024
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Hint: In order to solve this question, you must be aware about the relationship between the distance of an image (v), the distance of an object (u), and the focal length (f) of the lens. This is given by a formula known as Lens formula. It is applicable for convex as well as concave lenses.

Complete step by step answer:
It is given that, when $u = - 20$ cm $v = 30$ cm
We know that;
$\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$ (Lens formula)
$\dfrac{1}{f} = \dfrac{1}{{30}} - \dfrac{1}{{ - 20}}$
We get, $f = 12$ cm
Now, $m = - 1$(Image formed is of the same size as that of the object)
$\dfrac{v}{u} = - 1$
$v = - u$
Using lens formula,
$\dfrac{1}{{12}} = \dfrac{1}{{ - u}} - \dfrac{1}{u}$
$\therefore u = - 24$ cm
Therefore, the object should be placed 24 cm from the lens.

Hence, option A is correct.

Note: A convex lens is employed in microscopes and magnifying glasses to converge all incoming light rays to a particular point. It is also used in cameras. The various types of lenses are also used in the correction of certain defects of the eye.
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