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# A system consists of a convex lens and a concave mirror placed at a distance of x from the lens. Focal length $f_1$ of convex lens in 10 cm and focal length $f_2$ of mirror is 60 cm. If an object is placed at a distance 20 cm from the lens and it is found that the final image coincides with the object position, then what must be the distance 'x'

$(a)\;60\;cm \\ (b)\;40\;cm \\ (c)\;20\;cm \\ (d)\;10\;cm$

Can you answer this question?

Since the object is placed 20 cm from the lens it is at a distance 2 f from the lens.
The image formed will be at a distance $2f$ ie 20 cm from the lens at  0 '.
So if the concave mirror is placed at this position , the 1st image will be at the pole of the mirror so it will reflect symmetrically and the final image will be at 0 itself.
$\therefore x=20\;cm$
Hence c is the correct answer.
answered Jan 22, 2014 by
edited Jul 28, 2014 by meena.p