Deriving Group Velocity with Frequency and Wavelength | Simple Homework Solution

[ramses07]

Homework Statement

so I am asked to derive the group velocity of an equation in terms of its frequency and wavelength, but I am stuck at a simple derivative, which is df/d(1/n) where is the frequency and n is the wavelength.

Homework Equations

the group velocity is dw/dk

The Attempt at a Solution

so i got this far

dw/dk = d(2pif)/d(2pi(1/n)

i canceled out the 2pi since they are constants.

= df/d(1/n) f= frequency, and n = wavelength

but i just can't figure out what to do with this derivative.

 

[vela]

You need to use the chain rule. You may find it easier to see what you need to do when it's written this way:

$$\frac{d\omega}{dk} = \frac{d\omega}{d\lambda}\frac{d\lambda}{dk}$$

 

[hunt_mat]

Normally, you just get the dispersion relation when do your calculations, which gives $$\omega^{2}=f(k)$$