What is the Group Velocity of Infrared Radiation in a Dispersive Medium?

[nathangrand]

Infrared radiation, of wavelength λair = 1um in air, travels through a
dispersive medium with refractive index n = 1.4505 and with
dn/dλair = -0.01 per um at this wavelength. Calculate the speed at which the
radiation carries information.

So know that

c/n = λf

radiation carries information at group velocity dw/dk

can also show that dw/dk = c/(n + w(dw/dn))

but don't know where to go from here

feel http://en.wikipedia.org/wiki/Group_velocity has some useful expression in alternative expressions but need to be able to show, and can't

 

[bm0p700f]

w is angular frequency. In the other expression are formula needed to calculate w. The convert dn/d(lambda) into dw/dn.

 

[nathangrand]

how?

 

[bm0p700f]

Take at look at the link you posted in the other expressions sections. It all there.

 

[nathangrand]

I know the expressions are there, I just can't fiddle around with the differetiation