# A convex lens (of focal length 20 cm) and a concave mirror, having their principal axis along the same lines, are kept 80 cm apart from each other. the concave mirror is to the right of the convex lens, its image remains at the same position even if the concave mirror is removed. The maximum distance of the object for which this concave mirror, by itself would produce a virtual image would be:Option 1)30 cmOption 2)25 cmOption 3)10 cmOption 4)20 cm

using lens formula

$\frac{1}{V}-\frac{1}{-30}=\frac{1}{20}$

$\Rightarrow v=60 cm$distance of this Image from mirror is 20 cm.

As per given condition Image should be form, at centre of circle of mirror

so, $20 cm=2 f_{m} \\ \Rightarrow f_{m}=10 cm$

Thus , Maximum distance =10 cm

Option 1)

30 cm

Option 2)

25 cm

Option 3)

10 cm

Option 4)

20 cm

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