Phase velocity of EM radiation in free space

[ZedCar]

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

 

[Andrew Mason]

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

 

[ZedCar]

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

 

[Andrew Mason]

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

 

[ZedCar]

Thank you.

 

[ZedCar]

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

 

[Andrew Mason]

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

 

[ZedCar]

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.