# Why Negative refractive index is negative

$n=\sqrt{\epsilon \mu }$

Negative refractive index happens when permittivity ($\epsilon$) and permeability ($\mu$)of a material is negative. My question is, if permittivity and permeabilitity of a material is negative then the end product, according to the above equation, should be positive. If two negative numbers multiplied should give a positive number. Then why in here two negative numbers ($\epsilon$ and $\mu$) gives a negative refractive index?

-
Remember when you take the square root you can select either the positive or negative answer. –  Chris Oct 5 at 7:24
This explains everything iopscience.iop.org/0038-5670/10/4/R04/pdf/… In fact it is the original paper on the matter. –  Chris Oct 5 at 7:31