Eikonal approximation in electromagnetic scattering

Eikonal approximation, which uses the laws of geometrical optics, has been used in the study of scattering theories for over a century. Although eikonal approximation originated in the field of optics and electromagnetism, it has been extensively used in quantum mechanics and quantum field theories in the form of a closely related WKB approximation. Eikonal approximation is an uncontrolled approximation and often fails to give an unambiguous next-to-leading order contribution. The region of validity of eikonal approximation has not been explored well and this motivates us to explore its validity regime. In this work, we revisit the scattering of a monochromatic wave through a weak dielectric sphere to understand the validity of the eikonal approximation in electromagnetism. Scattering of a monochromatic wave through a weak dielectric sphere is exactly solvable and we compare the total cross-section calculated using the exact method with the eikonal approximation. We expect our work will highlight the regime of validity under which eikonal approximation gives a precise next-to-leading order contribution.