# What's the relationship between velocity factor and refractive index?

Wikipedia on velocity factor explains:

For optical signals, the velocity factor is the reciprocal of the refractive index.

On refractive index, Wikipedia also has an explanation of refractive indexes less than 1, which mean a phase velocity greater than $c$, but does not violate causality because phase velocity doesn't carry information. OK, fine. It even discusses negative refractive indexes, and while I haven't really absorbed what this means intuitively, I'll believe such materials can exist.

But now going back to the original statement, this would imply that there are materials with a velocity factor greater than one, or a negative velocity factor. I can't quite get my head around that.

Is this true? I'm not sure exactly what is meant by "for optical signals". Am I making an incorrect assumption somewhere?

## 1 Answer

Refractive index, as a number, actually varies with the frequency of the EM wave, so when someone quotes it as just some number (like: water's refractive index is n=1.33) usually it means in the optical frequency range ("for optical signals"). I suspect that is what's going on here.

As to VF being greater than one or negative, I don't think I can explain anything in a way that you won't find elsewhere. I will say that it's absolutely no different, from a 'thinking about it' point of view, than refractive index being less than one or negative, so there at least are not new problems to ponder. Look up "negative index of refraction" or "metamaterials".

• The wikipedia article on Negative Index Materials states that a material with a negative refractive index reverses the direction of wave propogation, so there's your negative VF. – Sean Dec 9 '14 at 16:54
• So is it then accurate to say that velocity factor describes the phase velocity, and velocity factor is exactly equal to 1/n? – Phil Frost Dec 9 '14 at 17:25
• I'd never heard of the velocity factor, but AFAICT it's 1/n. (the wiki gives is as 1/sqrt(permitivity) add magnetic susceptibility (or what ever the name is) and that's velocity ala Maxwell.) – George Herold Dec 10 '14 at 2:54