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Question

An object is placed at a distance of 36 cm from a convex mirror. A plane mirror is placed in between so that the two virtual images so formed coincide. If the plane mirror is at a distance of 24 cm from the object, find the radius of curvature of the convex mirror.

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Solution

Given: An object is placed at a distance of 36 cm from a convex mirror. A plane mirror is placed in between so that the two virtual images so formed coincide. If the plane mirror is at a distance of 24 cm from the object,
To find the radius of curvature of the convex mirror.
Solution:
As per the given criteria,
object distance from the convex mirror, u=36cm
distance of plane mirror from the object, d=24cm
So,
The distance of plane mirror from the convex mirror will be
3412=12cm
The image formed by the plane mirror will be at a distance of 24cm from the plane mirror and 12 cm from the convex mirror.
Since both the images should coincide therefore the convex mirror will form image at a distance of 12cm from itself.
Therefore, u=36cm
v=12cm
Applying the lens formula, we get
1f=1v+1u1f=112+1(36)1f=3136f=18cm
And we know the radius of curvature, R=2f=2×18=36cm

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