What is meant by power of a lens? What does its sign (+ve or -ve) indicate? State its S.I. unit. How is this unit related to focal length of a lens?

The power of a lens is a measure of the degree of convergence or divergence of light rays falling on it.

The (diverging lens) concave lens has negative focal length hence its power is negative. Thus the negative sign of power indicates the type of lens.

The SI unit of lens is diopter, denoted by D. One diopter is the power of a lens whose focal length is 1 metre.