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unscientific
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Homework Statement
Homework Equations
The Attempt at a Solution
Is my initial assumption wrong?
Relation between group velocity and phase velocity
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SUMMARY
The discussion centers on the relationship between group velocity (vg) and phase velocity (vph) in wave mechanics. Participants confirm the correctness of initial assumptions regarding the equations governing these velocities. The key equation derived is 1/vg = dk/dw = ∂k/∂w + ∂k/∂n dn/dw, which incorporates the refractive index (n) and the speed of light (c). The conversation emphasizes the importance of understanding the dependencies of k on both frequency (w) and refractive index (n).
PREREQUISITES- Understanding of wave mechanics and velocity concepts
- Familiarity with calculus, particularly derivatives
- Knowledge of refractive index and its implications in optics
- Basic principles of dispersion in wave propagation
- Study the derivation of group and phase velocity equations in wave mechanics
- Explore the concept of dispersion and its effects on wave propagation
- Learn about the application of the chain rule in calculus for multi-variable functions
- Investigate the role of the refractive index in optical systems
Students and professionals in physics, particularly those focusing on wave mechanics, optics, and related fields. This discussion is beneficial for anyone looking to deepen their understanding of the relationship between group and phase velocities.
Is my initial assumption wrong?
- #2
rude man
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unscientific said:Homework Statement
Homework Equations
The Attempt at a Solution
Is my initial assumption wrong?
No, it's right.
- #3
unscientific
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rude man said:
But I seem to be missing out on a 1/vph term..
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rude man
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unscientific said:
You asked if you initial assumption was right. I did not check all your work. Will try later.
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rude man
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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.
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.
for d), I am a bit confused. I have two trains of thoughts here
any thoughts on which answer is correct, and why the other one is incorrect? Both seem like valid solutions to me. Or is the question ambiguous?
thanks
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