  A realistic magnetic dipole has complex effects on a charged particle near
the entrance and exit of the magnet, even with a constant and uniform magnetic
field deep within the interior of the magnet. To satisfy Maxwell's equations,
the field lines near either end of a realistic magnet are significantly more
complicated, yielding non-trivial forces. The effects of this fringe field are
calculated to first order, applying both the paraxial and thin lens
approximations. We find that, in addition to zeroth order effects, the position
of a particle directly impacts the forces in the horizontal and vertical
directions.
