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# Phase velocity of EM radiation in free space Watch

1. (i) What is the phase velocity of EM radiation in free space?

(ii) What is its group velocity?

Are the solutions below correct?

Using the definition as per this page:
http://physicsdaily.com/physics/Phase_velocity

(i) Vp = (C^2) / Vg

(ii) Vg = (C^2) / Vp
2. (Original post by little pixie)
(i) What is the phase velocity of EM radiation in free space?

(ii) What is its group velocity?

Are the solutions below correct?

Using the definition as per this page:
http://physicsdaily.com/physics/Phase_velocity

(i) Vp = (C^2) / Vg

(ii) Vg = (C^2) / Vp
your solutions imply that Vg=Vp (and I think Vp=c for E/M radiation in free space which comes out of the wave equation).

So starting from Vp=w/k and Vg=dw/dk

w=kVp so Vg=Vp+kdVp/dk

since k=2pi/wavelength (let wavelength=l I'm LaTex illiterate)

Vg=Vp-ldVp/dl

for E/M radiation in a refractive index 'n' Vp=c/n

so Vg=(c/n)(1+(l/n)(dn/dl)) in a vacuum n=1=constant across all w/l as non-dispersive I think

so Vp=Vg=c and everyone is happy

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