(Optics disguised as mechanics) In the bottom half of the cartesian plane (y < 0) the potential energy is UB and in the top half it is UT (both are constants). A particle with y < 0 is headed toward the the top half-plane with an initial kinetic energy TB at angle ϕB relative to the y axis. At what speed and angle ϕT does it emerge into the upper half of the plane? Discuss the relationship to Ibn Sahl's (aka Snell's) law that you remember from your elementary E&M class (PHYS119 if at UNC).