### 3.1 Lens equation

The basic setup for such a simplified gravitational lens scenario involving a point source and a point lens
is displayed in Figure 2. The three ingredients in such a lensing situation are the source S, the lens L, and
the observer O. Light rays emitted from the source are deflected by the lens. For a point-like lens, there
will always be (at least) two images S_{1} and S_{2} of the source. With external shear – due to
the tidal field of objects outside but near the light bundles – there can be more images. The
observer sees the images in directions corresponding to the tangents to the real incoming light
paths.
In Figure 3 the corresponding angles and angular diameter distances , , are
indicated.
In the thin-lens approximation, the hyperbolic paths are approximated by their asymptotes. In the
circular-symmetric case the deflection angle is given as

where is the mass inside a radius . In this depiction the origin is chosen at the observer. From
the diagram it can be seen that the following relation holds:
(for , , ; this condition is fulfilled in practically all astrophysically relevant situations). With
the definition of the reduced deflection angle as , this can be expressed as:
This relation between the positions of images and source can easily be derived for a non-symmetric mass
distribution as well. In that case, all angles are vector-valued. The two-dimensional lens equation then
reads: