  We prove a gravitational lensing theorem: the magnification of a source of
uniform brightness by a foreground spherical lens is mu =1+pi(2R_E^2-R_L^2)/A,
where A is the area of the source and R_E and R_L are the Einstein radius and
size of the lens projected into the source plane; this provides an accurate
approximation to the exact magnification for R_L^2,R_E^2 << A. Remarkably, this
result is independent of the shape of the source or position of the lens
(except near the edges). We show that this formula can be generalized to
include limb-darkening of a circular source by simply inserting the
surface-brightness at the position of the foreground object (divided by the
average surface-brightness of the star). We also show that similar formulae
apply for a point-mass lens contained in a shear field and mass sheet, and for
an ensemble of point masses as long as the Einstein radii are much smaller than
the source size. This theorem may be used to compute transit or microlensing
lightcurves for which the foreground star or planet has a size and Einstein
radius much smaller than the background star.
