Do you agree that refraction isn't limited to Snell's law?

While Snell's law, named after Willebrord Snellius, explains how light bends at a sharp boundary between two media with different refractive indices (n₁ and n₂), the bending of light within a medium where the refractive index varies smoothly is described by a more general principle: d/ds (n(r) * dr/ds) = ∇n(r) which involves the gradient of n(r). This differential equation, related to Fermat's principle, was developed through the work of scientists like Augustin-Jean Fresnel and Huygens. So, wouldn't you say that refraction encompasses both the boundary rule of Snell and the more general behavior described by this general principle?
3 Replies
RonK
RonK2mo ago
there is no gradient law when it comes to refraction. See snell's law.
Joseff
Joseff2mo ago
Refraction within just air doesn't "bend" light nearly as much as you see with a pensil in a glass of water... That's specifically the reason as to why you guy's believe it's possible, for refraction, to bend over a curve to make objects obstructed by physical curve visible, that your side requires... In just air, refraction makes "the path of light" wavy and distorted. It doesn't"bend" anything! Because the gradient isn't constant nor homogeneous, which means instead of a straight line, you have a mess of zig zags... For lack of a better description! At this point, it's willfull ignorance to properly understand how refraction works or subconcious misdirections... One or the other, because i'm Just describing how refraction actually works...
indio007
indio0072mo ago
the model and the law are not equivalent. Is n sin θ conserved along light path? Mahdiyar Noorbala and Reza Sepehrinia Department of Physics, University of Tehran, Tehran, Iran. P.O. Box 14395-547 Abstract Snell’s law states that the quantity n sin θ is unchanged in refraction of light passing from one medium to another. We inquire whether this is true in the general case where the speed of light varies continuously within a medium. It turns out to be an instructive exercise in application of Snell’s law and Fermat’s principle. It also provides good pedagogical problems in calculus of variations to deal with the subtleties of a variable domain of integration and inclusion of constraints. The final result of these exercises is that, contrary to an initial expectation, the answer to the question in the title is negative. https://arxiv.org/pdf/1604.05106.pdf/

Did you find this page helpful?