# Optics can enlighten

A lens can be manufactured using a circular glass plate of constant thickness, which in this case is 'd', provided the refractive index 'n' of the material is not a constant, but rather a function of the radial distance from the center of the plate, 'r'. Now by a not-so-complex derivation, the function n(r) comes out as, n(r) = n(0) - a.f(r), where n(0) and 'a' are positive constants. What is f(r)?