The Eikonal approximation is a method for calculations involving the scattering of waves, and so it is used in many kinds of physics physics like optics/E&M, as well as quantum mechanics, and quantum field theory. The Eikonal approximation corresponds to the limit where ray optics (geometric optics) is valid, where we are mostly concerned with the change in the phase of the wave more so than it's trajectory. These topics are usually discussed in a graduate class on E&M or QM, e.g. in Jackson or Sakuai.