  One of the frontiers for advancing what is known about dark matter lies in
using strong gravitational lenses to characterize the population of the
smallest dark matter halos. There is a large volume of information in strong
gravitational lens images -- the question we seek to answer is to what extent
we can refine this information. To this end, we forecast the detectability of a
mixed warm and cold dark matter scenario using the anomalous flux ratio method
from strong gravitational lensed images. The halo mass function of the mixed
dark matter scenario is suppressed relative to cold dark matter but still
predicts numerous low-mass dark matter halos relative to warm dark matter.
Since the strong lens signal is a convolution over a range of dark matter halo
masses and since the signal is sensitive to the specific configuration of dark
matter halos, not just the halo mass function, degeneracies between different
forms of suppression in the halo mass function, relative to cold dark matter,
can arise. We find that, with a set of lenses with different configurations of
the main deflector and hence different sensitivities to different mass ranges
of the halo mass function, the different forms of suppression of the halo mass
function between the warm dark matter model and the mixed dark matter model can
be distinguished with $40$ lenses with Bayesian odds of 29.4:1.
