Phase velocity of EM radiation in free space

AI Thread Summary
The phase velocity (Vp) and group velocity (Vg) of electromagnetic radiation in free space are both equal to the speed of light, denoted as c. The equations Vp = (C^2)/Vg and Vg = (C^2)/Vp are valid, but they cannot be simplified to Vp = c and Vg = c without confirming that Vp equals Vg. In free space, the speed of electromagnetic waves does not depend on frequency, which means phase and group velocities are the same. The discussion emphasizes the importance of recognizing that Vp and Vg can differ in other contexts where wave speed is frequency-dependent.
ZedCar
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Homework Statement



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

(ii) What is its group velocity?


Homework Equations





The Attempt at a Solution



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

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

(ii) Vg = (C^2)/Vp
 
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ZedCar said:

Homework Statement



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

(ii) What is its group velocity?
They are the same: c

AM
 
Andrew Mason said:
They are the same: c

AM

So is the eqn which I have referred to, and used for my solution, the incorrect one to use on this occasion?

Thanks
 
ZedCar said:
So is the eqn which I have referred to, and used for my solution, the incorrect one to use on this occasion?
The equation is correct: VpVg = c^2 ; Vp=Vg=c

AM
 
Thank you.
 
Andrew Mason said:
The equation is correct: VpVg = c^2 ; Vp=Vg=c

AM

Since, as you have above Vp=Vg=c, does that mean I can further reduce the two solutions I had in my original post from

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

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

to

(i) Vp = c

(ii) Vg = c
 
ZedCar said:
Since, as you have above Vp=Vg=c, does that mean I can further reduce the two solutions I had in my original post from

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

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

to

(i) Vp = c

(ii) Vg = c
You cannot conclude that Vp = c from the equation: VpVg=c2. You would have to know that the phase velocity of light in a vacuum is equal to the group velocity.

A difference between phase velocity and group velocity occurs if the speed of a wave is frequency dependent. But the speed of em waves in a vacuum do not depend on frequency.

AM
 
Andrew Mason said:
You cannot conclude that Vp = c from the equation: VpVg=c2. You would have to know that the phase velocity of light in a vacuum is equal to the group velocity.

Yes, of course. That's a silly mistake to have made.

Thanks again.
 
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