Is the law of optical reflection true?

The reflection of light from a dielectric interface follows well-known optical principles, such as the equality of the angles of incidence and reflection, as well as Snell's law of refraction. These laws hold precisely when considering the behavior of a single plane wave at an optical interface. However, real optical beams, which have finite spatial and angular extents, exhibit deviations from these idealized laws. Specifically, reflected beams can undergo spatial displacements and angular deflections, collectively referred to as beam shifts. The Goos–Hänchen shift displaces the beam in a direction perpendicular to the plane of incidence, while the Imbert–Fedorov shift introduces a transverse displacement for circularly polarized light. These effects arise from the angular dispersion of the reflection coefficients and from the spin–orbit interaction of circularly polarized light. These shifts can be described using classical electromagnetism; however, this paper presents the theory behind these shifts using a highly compact quantum mechanical formulation. The shifts are small, only a fraction of the wavelength of light. By applying the weak measurement technique known from quantum mechanics, these shifts can be significantly enhanced. We introduce an experimental setup that allows such amplified shifts to be easily measured, even in student laboratories.