3.2 Einstein radius
For a point lens of mass 
, the deflection angle is given by Equation (4). Plugging into Equation (6)
and using the relation 
(cf. Figure 3), one obtains:
For the special case in which the source lies exactly behind the lens (
), due to the symmetry a
ring-like image occurs whose angular radius is called Einstein radius 
:
The Einstein radius defines the angular scale for a lens situation. For a massive galaxy with a mass of
at a redshift of 
and a source at redshift 
, (we used here
= 50 km sec–1 Mpc–1 as the value of the Hubble constant and an Einstein–deSitter universe), the
Einstein radius is
(note that for cosmological distances in general 
!). For a galactic microlensing scenario in
which stars in the disk of the Milky Way act as lenses for bulge stars close to the center of the Milky Way,
the scale defined by the Einstein radius is
An application and some illustrations of the point lens case can be found in Section 4.7 on galactic
microlensing.
), one obtains:
For the special case in which the source lies exactly behind the lens (
