Hello candidate,

Here is the complete reason behind by the radius of curvature is infinity for some bodies- If the radius of the sphere is infinite, so the radius of the curvature of the plane mirror is infinite.

Hence, the focal length of any mirror is twice the radius of curvature so the focal length of the plane mirror is also infinite which makes the radius of curvature equal to infinite.

Hope you found it helpful. If you have any other queries feel free to post it here!!