A luminous object is placed at a distance of $30 c m$ from the convex lens of focal length $20 c m$ . On the other side of the lens, at what distance from the lens a convex mirror of radius of curvature $10 c m$ be placed in order to have an upright image of the object coincident with it?

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$50 c m$

$12 c m$

$30 c m$

$60 c m$

answer is C.

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Detailed Solution

For the lens,

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}; \frac{1}{v} - \frac{1}{- 30} = \frac{1}{20} \Rightarrow v = 60 cm$

Coincidence is possible when the image is formed at the centre of curvature of the mirror. Only then the rays refracting through the lens will fall normally on the convex mirror and retrace their path to form the image at $O .$ So, the distance between lens and mirror $= 60 - 10 = 50 c m .$