# Gain medium and the speed of light

I am currently studying optics, and when taking a closer look at refractive indices, I stumbled across gain mediums. On Wikipedia it states that gain mediums can have a refractive index of $n<0$. But how can this be? According to $v_{ph}=\frac{c}{n}$ the wave would have to propagate faster than the speed of light. Doesn’t this clash with the assumption no information can travel faster than the speed of light?

• Can you add a link to what you have read? – eranreches Nov 18 '17 at 17:59
• @eranreches sure, just added it – BluNova897 Nov 18 '17 at 18:07
• It's $k<1$. This is the imaginary part of $n$. – Andrei Geanta Nov 18 '17 at 18:14
• @Arthur It clearly states that n can be smaller than one though. – BluNova897 Nov 18 '17 at 18:27
• @BluNova897, Yes, $n$ can be smaller than $1$, but the refractive index measures the phase velocity of light, which does not carry information. So there is not contradiction with special relativity. – Andrei Geanta Nov 18 '17 at 18:33