A1 Refereed original research article in a scientific journal
Is the law of optical reflection true?
Authors: Kuusela, Tom A.
Publisher: American Association of Physics Teachers (AAPT)
Publication year: 2026
Journal: American Journal of Physics
Volume: 94
Issue: 2
First page : 133
Last page: 141
ISSN: 0002-9505
eISSN: 1943-2909
DOI: https://doi.org/10.1119/5.0270188
Publication's open availability at the time of reporting: No Open Access
Publication channel's open availability : Partially Open Access publication channel
Web address : https://doi.org/10.1119/5.0270188
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/509031440
Self-archived copy's version: Final draft
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.
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