Is Group Velocity Dispersion Infinite for Light in Air?

[Dimani4]

Hey ppl,
I have a question for you.

For the case of light propagation in the air the the group-velocity dispersion parameter D is infinity because the derivative of the group velocity should be a zero (group velocity is constant ; w=ck and Vgroup=dw/dk). Who can explain me this? dispersion parameter is infinity meaning that the pulse will spread very fast. I never thought about that question but maybe I'm wrong. Plz clarify me that point.

formula for D parameter you can find here:
http://en.wikipedia.org/wiki/Dispersion_(optics)

 

[Dimani4]

the question is solved. you can't not turn upside down the second derivative. i.e

a=(Dispersion parameter)=(approx) d2(k)/d2(w)$$\neq$$1/d2(w)/d2(k). here was the problem. in the case of light propagation through the air a should equal to zero.d2()-second derivative=$$\partial$$²

d2(k)/d2(w)=$$\partial$$²k/$$\partial$$²w