Expressions for the group velocity

AI Thread Summary
The discussion focuses on deriving expressions for group velocity, starting with the fundamental equation g = dw/dk and exploring various forms, including g = v + k(dv/dk) and g = v - λ(dv/dλ). The user seeks assistance in using the equation g = v - λ(dv/dλ) to derive a specific expression involving the wavelength in vacuum, λ'. The challenge lies in manipulating the equations to arrive at g = v[1 - 1/(1 + (v/λ')(dλ'/dv))]. Participants are encouraged to provide insights or methods to achieve this derivation. The conversation emphasizes the complexity of the derivation process and the need for collaborative problem-solving.
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Homework Statement


Okay so I've been deriving various expressions for the group velocity starting with

g=dw/dk

then g=v+kdv/dk

also g=v-lambda dv/dlambda (*)

then finally g=c/u(1+lambda/u (du/dlambda))

Ok so finally I am asked to use equn (*) to derive the following expression

g=v[1-1/(1+(v/lambda')(d lambda'/dv))

where lambda' is the wavlength in vacuum..


not sure how to do it..any help would be great thanks

Homework Equations





The Attempt at a Solution

 
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