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Generally the refractive index of any lens is greater than air. My question is what will happen if the refractive index of lens is less than unity?


marked as duplicate by Kyle Kanos, user191954, Yashas, Peter Diehr, Jon Custer Oct 29 '18 at 20:35

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  • $\begingroup$ @Steeven $c$ is only the phase velocity, which can indeed be greater than in the vacuum. $n$ is less than unity for example in metamaterials, plasmas, metals and dielectrics at certain wavelengths. See my question here for a real life example of $n < 1$. $\endgroup$ – ahemmetter Oct 26 '18 at 7:06

Steeven is correct in comments when he says that there are no materials with $n<1$, because this would imply light propagating faster than $c$ in these materials.

However, you can imagine a situation where a "lens" made of a low-index material is embedded in a high-index medium, for example a bubble of water ($n\approx 1.33$) in a body of oil ($n\approx 1.5$).

In this case you should consider what is the "optical" length of the path different rays travel through the lens, depending on their distance from the optical axis. Since a thicker path through the lens results in a shorter optical length, you'll find that convex shapes form converging lenses and concave shapes produce diverging lenses, the opposite of the situation for high-index lenses in air.

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    $\begingroup$ Actually, it is possible for the index of refraction $n$ to be less than 1. $n<1$ for many materials at x-ray wavelengths in the 10's of keV range. And, no, that does not imply faster than light propagation of information according to the equation $n=c/v$ because the $v$ here refers to the phase velocity, which can exceed the speed of light. $\endgroup$ – Samuel Weir Oct 26 '18 at 6:55
  • $\begingroup$ Of course the phase velocity $c$ can be higher than in a vacuum - this happens in plasmas (ionized gases, metals and even most dielectrics near the absorption maximum). Adjusting the arrangement of areas of different $\varepsilon$ and $\mu$ even allows the refractive index to be negative (which corresponds to a backward wave propagation) in the case of metamaterials or even simple transmission lines. $\endgroup$ – ahemmetter Oct 26 '18 at 8:02

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