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Question

A point object is placed at a distance of 12 cm on the axis of a convex lens of focal length 10 cm. On the order side of the lens, a convex mirror is placed at a distance of 10 cm from the lens such that the image formed by the combination coincides with the object itself. The focal length of convex mirror is

A
25 cm
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B
50 cm
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C
100 cm
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D
12.5 cm
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Solution

The correct option is A 25 cm
For convex lens u=12 cm,f=10 cm As 1v1u=1f,1v=110112v=60 cm
Now the image of object formed by convex lens is I at a distance of 60cm from lens. For convex mirror Now I, acts as an object form (convex mirror) and forms image I at o itself, means the rays after reflection from the mirror retrace the paths, i.e. these rays incident normally on mirror. This is possible only if I, is at center of curvature
of M . Thus Radius of Curvature R=MI1=50 cm So focal length of Convex mirror =R2=25 cm.

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