# What will happen if the refractive index of lens is less than unity? [duplicate]

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?

• @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 $n < 1$. 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 ($$n\approx 1.5$$).
• 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.
• 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. Oct 26 '18 at 8:02