# Phase velocity of EM radiation in free space

1. May 16, 2013

### ZedCar

1. The problem statement, all variables and given/known data

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

(ii) What is its group velocity?

2. Relevant equations

3. The attempt at a solution

http://physicsdaily.com/physics/Phase_velocity

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

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

2. May 17, 2013

### Andrew Mason

They are the same: c

AM

3. May 17, 2013

### ZedCar

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

Thanks

4. May 18, 2013

### Andrew Mason

The equation is correct: VpVg = c^2 ; Vp=Vg=c

AM

5. May 18, 2013

### ZedCar

Thank you.

6. May 19, 2013

### ZedCar

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

7. May 19, 2013

### Andrew Mason

You cannot conclude that Vp = c from the equation: VpVg=c2. You would have to know that the phase velocity of light in a vaccum 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

8. May 19, 2013

### ZedCar

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

Thanks again.