  We investigate a two-component model for gravitational lenses, i.e., the
fermion-fermion star as a dark matter self-gravitating system made from two
kinds of fermions with different masses. We calculate the deflection angles
varying from arcseconds to even degrees. There is one Einstein ring. In
particular, we find three radial critical curves for radial magnifications and
four or five images of a point source. These are different from the case of the
one-component model such as the fermion stars and boson stars. This is due to
the fermion-fermion star being a two-component concentric sphere. Our results
suggest that any possible observations of the number of images more than 3
could imply a polytropic distribution of the mass inside the lens in the
universe.
