A particle of mass m1 with initial laboratory velocity u1 collides with a particle of mass m2 at rest in the LAB system. The particle m1 is scattered through a LAB angle ψ and has a final velocity v1, where v1 = v1 (ψ). Find the surface such that the time of travel of the scattered particle from the point of collision to the surface is independent of the scattering angle. Consider the cases
(a) m2 = m1,
(b) m2 = 2m1, and
(c) m2 = ∞. Suggest an application of this result in terms of a detector for nuclear particles.