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

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Homework Help Overview

The discussion revolves around calculating the group velocity of infrared radiation in a dispersive medium, specifically focusing on the relationship between wavelength, refractive index, and angular frequency.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to relate the speed of radiation to its group velocity using various expressions but expresses uncertainty about the next steps. Other participants inquire about the conversion of dn/dλ into dw/dn and seek clarification on the differentiation process.

Discussion Status

The discussion is ongoing, with participants exploring different expressions and seeking guidance on differentiation. Some have pointed to external resources for further clarification, but there is no explicit consensus on the approach to take.

Contextual Notes

Participants are working within the constraints of the problem, which involves specific values for wavelength and refractive index, and are grappling with the mathematical manipulation required to progress.

nathangrand
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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
 
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w is angular frequency. In the other expression are formula needed to calculate w. The convert dn/d(lambda) into dw/dn.
 
how?
 
Take at look at the link you posted in the other expressions sections. It all there.
 
I know the expressions are there, I just can't fiddle around with the differetiation
 

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