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When light goes from a more dense medium to a less dense medium, it bends away from the normal, as in the image

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When light goes from a less dense medium to a more dense medium it bends towards the normal, as in the pic

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But is it possible that light turns all the way around the normal? I think it should be possible as it doesn't violate fermat's principle, or does it? (see the image that follows)

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NOTE(1): I have specified the interface in pic 3 so as to show that this is not a case of total internal reflection
NOTE(2): please explain in regards to fermat's principle, as you would to a person just been introduced to ray optics

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For positive refractive indices, it will violate the conservation of momentum (which is used to derive Snell's law).

Also it would violate Fermats principle as there would be a more direct path (eg any normal incidence connecting two opposite points on the path).

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  • $\begingroup$ +1 I was just going to mention the conservation law that leads to Snell's law. $\endgroup$
    – user196418
    May 24, 2019 at 12:03
  • $\begingroup$ Not sure how metamaterials get around this. Potentially they are only negative in the one axis. $\endgroup$
    – Paul Childs
    May 24, 2019 at 12:08
  • $\begingroup$ Would you please explain in detail? $\endgroup$
    – Amritansh Joshi
    May 24, 2019 at 14:59
  • $\begingroup$ arxiv.org/pdf/physics/0502054.pdf $\endgroup$
    – Paul Childs
    May 24, 2019 at 22:35
  • $\begingroup$ Or see wikipedia for Snell's law $\endgroup$
    – Paul Childs
    May 24, 2019 at 22:36
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No, this is not possible. Light basically takes the path that requires the least number of wavelengths to get from one point to another (this is a special case of the principle of least action. The wavelength changes according to the material the ray of light is traversing, but it is always a positive number. In the case you suggest, there are always trajectories for which the wavelength count will be smaller than for the one you propose; for example, taking a straight line joining the two ends of the trajectory you propose would give a lower wavelength count, although it would likely not be optimal.

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