# Group velocity information

1. Jan 5, 2012

### 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

2. Jan 5, 2012

### bm0p700f

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

3. Jan 5, 2012

how?

4. Jan 5, 2012

### bm0p700f

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

5. Jan 5, 2012

### nathangrand

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

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