We study the Dirichlet boundary value problem for eikonal type equations of ray
light propagation in an inhomogeneous medium with discontinuous
refraction index. We prove a comparison principle
that allows us to obtain existence and uniqueness of a continuous
viscosity solution when the Lie algebra generated by the coefficients satisfies a Hörmander
type condition. We require the refraction index to be piecewise continuous across Lipschitz hypersurfaces. The results characterize the value function of the generalized minimum time problem with discontinuous running cost.