The particle distribution in phase space near the loss cone of a stable mirror machine is determined by an asymptotic analysis based on the smallness of λ, the ratio of transit time between mirrors to mean collision time. Away from the loss cone, the solution is obtained by averaging over a bounce motion. Near the loss Cone, i.e., within a distance scaling as λ1/2, the governing equations are converted into a Wiener-Hopf equation along a boundary line in phase space whose solution yields the desired distribution. It is found that the ratio of plasma density in the mirror throat to central density scales as λ3/4 while the ratio of external density to central density scales as λ. For typical reactor conditions, these ratios correspond to densities of 1011 cm−3 and 108, respectively. Since the distance over which this drop occurs scales as λ1/2 times the local magnetic scale length, it is necessary to re-examine the reflection of unstable plasma waves in the neighbourhood of the mirrors.