What will happen if the refractive index of lens is less than unity?

Question

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?

Answer 1

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.