### 3.4 Image positions and magnifications

The lens equation (6) can be re-formulated in the case of a single point lens:
Solving this for the image positions one finds that an isolated point source always produces two
images of a background source. The positions of the images are given by the two solutions:
The magnification of an image is defined by the ratio between the solid angles of the image and
the source, since the surface brightness is conserved. Hence the magnification is given as
In the symmetric case above, the image magnification can be written as (by using the lens equation):
Here we defined as the “impact parameter”, the angular separation between lens and source in units of
the Einstein radius: . The magnification of one image (the one inside the Einstein
radius) is negative. This means it has negative parity: It is mirror-inverted. For the
magnification diverges. In the limit of geometrical optics, the Einstein ring of a point source has infinite
magnification!
The sum of the absolute values of the two image magnifications is the measurable total magnification :
Note that this value is (always) larger than
one!
The difference between the two image magnifications is unity: