For a refraction acquisition of a three$-$layered model, with upper$-$layer velocity of $5$ km$/$s$,$ middle$-$layer velocity of $12$ km$/$s$,$ bottom$-$layer velocity of $13$ km$/$s$,$ and layer thicknesses of $600$ m $($upper layer$)$ and $500$ m $($middle layer$),$ calculate the critical distance for the interface between middle and bottom layers.