Confused by Notation: Need Help Understanding c!

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SUMMARY

The discussion centers on the notation of 'c' in the equation for group velocity and phase velocity, specifically the equation Group velocity x Phase velocity = c². Participants clarify that 'c' typically represents the speed of light in a vacuum, while other velocities are denoted as 'v'. It is established that in free space, both phase and group velocities can equal 'c', but in media, group velocity can be less than 'c'. The equation's interpretation varies depending on the context, but it is generally accepted that 'c' refers to the speed of light.

PREREQUISITES
  • Understanding of wave mechanics and velocity concepts
  • Familiarity with the speed of light and its significance in physics
  • Knowledge of group velocity and phase velocity definitions
  • Basic grasp of notation used in physics equations
NEXT STEPS
  • Research the concept of group velocity and phase velocity in wave theory
  • Study the implications of electromagnetic wave propagation in different media
  • Explore the phenomenon of Electromagnetically Induced Transparency (EIT)
  • Review derivations and applications of the equation Group velocity x Phase velocity = c²
USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics, and educators seeking to clarify the notation and concepts related to group and phase velocities.

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Homework Statement



I'm just confused by notation in this question, because the textbook I use has different notation than my course notes and now I'm just not sure what anything means.

Homework Equations



Group velocity x Phase velocity = c^2

The Attempt at a Solution



What is c in this case? Is it the speed of light, or some other velocity?
I know it's a really stupid question...

Ta for any help though.
 
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Well, I assume that it is the speed of light. But really, the equation is not true in general.
Yes, photons move at c in free space, so phase velocity is c in free space (but inside midiums, the speed would get lower.).
However, the group velocity, could actually be lower than c. even 0. Just for reference, this is called EIT.
So if it is someother speed, well, normally it would be denoted as v, instead of c. c is normally reserved for the speed of light, or constant.
I guess what the most important part of this equation is that group velocity and phase velocity are the same in most of the cases: so if it is light, then it is c^2; if it is something else, then it is v^2. It is kinda open interpretation.
 
According to Wikipedia it is indeed the speed of light. I've never seen that particular equation before myself, but the derivation on Wikipedia looks reasonable...
 

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