Question

if a convex lens having focal length 'f' is cut into two halfs along its diameter.The focal length of each half is?​

Answer 1

Along the diameter” is too ambiguous to make the answer unique. At least we know, from the assumption that a diameter exists, that the lens is round.

The plane of the circumference contains every diameter. Cutting the lens along that plane produces two plano-convex lenses, unless the original lens was already plano-convex (i.e. flat on one side). The focal length of each half can be calculated if we assume either that both faces of the original have the same curvature, or that the original is plano-convex.

It is also possible to cut the lens along a diameter and perpendicular to the plane of its circumference. In that case, each half has the same focal length as the original.