Within the axiomatic framework of Time-Field Theory (TFT), we present a complete, self-contained derivation of Snell's law of refraction using only the fundamental axioms of local intrinsic velocity conservation and Fermat's principle established in TFT. We introduce the time-field representation of optical media, identify the direct correspondence between refractive index and the scalar time field γ, and carry out a variational derivation for light propagation across a planar discontinuous interface. The standard Snell's law is obtained as a direct mathematical consequence, without invoking electromagnetic theory, boundary conditions by hand, or auxiliary assumptions. We further rewrite Snell's law in its pure TFT form using the time field, and unify gravitational light deflection and optical refraction under a single dynamical principle: the stationary path of the TFT optical path δ∫ds/γ=0. This work demonstrates that geometric optics constitutes a direct, natural corollary of TFT, establishing a unified description for light propagation in gravitational fields and optical media.
Huowang Huang (Wed,) studied this question.
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