Question

A convex lens (of focal length $20cm)$ and a concave mirror, having their principal axes along the same lines, are kept $80cm$ apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of $30cm$ to the left of the convex lens, its image remains at the same position even if the concave mirror is removed. The maximum distance (in cm) of the object for which this concave mirror, by itself would produce a virtual image would be :

Answer 1

Answer: 10

For lens

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
or $\frac{1}{v}-\frac{1}{-30}=\frac{1}{20}$
$\therefore v=+60cm$
According to the condition, image formed by lens should be the centre of curvature of the mirror, and so
$2f’=20$ or $f’=10cm$