  The standard theory of weak gravitational lensing relies on the infinitesimal
light beam approximation. In this context, images are distorted by convergence
and shear, the respective sources of which unphysically depend on the
resolution of the distribution of matter---the so-called Ricci-Weyl problem. In
this letter, we propose a strong-lensing-inspired formalism to describe the
lensing of finite beams. We address the Ricci-Weyl problem by showing
explicitly that convergence is caused by the matter enclosed by the beam,
regardless of its distribution. Furthermore, shear turns out to be
systematically enhanced by the finiteness of the beam. This implies, in
particular, that the Kaiser-Squires relation between shear and convergence is
violated, which could have profound consequences on the interpretation of weak
lensing surveys.
