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
34−12=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+1u⟹1f=112+1(−36)⟹1f=3−136⟹f=18cm
And we know the radius of curvature, R=2f=2×18=36cm