Relation between group velocity and phase velocity

unscientific
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Homework Statement



k2mnp1.png



Homework Equations





The Attempt at a Solution


2hg8yt1.png


Is my initial assumption wrong?
 
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unscientific said:

Homework Statement



k2mnp1.png



Homework Equations





The Attempt at a Solution


2hg8yt1.png


Is my initial assumption wrong?

No, it's right.
 
rude man said:
No, it's right.

But I seem to be missing out on a 1/vph term..
 
unscientific said:
But I seem to be missing out on a 1/vph term..

You asked if you initial assumption was right. I did not check all your work. Will try later.
 
You wrote dk/dw = (2pi/0)dn/dw.

However, k depends on more than w:
dk = ∂k/∂w dw + ∂k/∂n dn

So 1/vg = dk/dw = ∂k/∂w + ∂k/∂n dn/dw
= n/c + (w/c) dn/dw
Etc.
 

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