Phase velocity of EM radiation in free space

In summary, the phase velocity and group velocity of electromagnetic radiation in free space are equal and given by the equation Vp = Vg = c, where c is the speed of light in a vacuum. This is because the speed of electromagnetic waves in a vacuum is not dependent on frequency.
  • #1
ZedCar
354
1

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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  • #2
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
 
  • #3
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
 
  • #4
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
 
  • #5
Thank you.
 
  • #6
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
 
  • #7
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
 
  • #8
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.
 

FAQ: Phase velocity of EM radiation in free space

1. What is the definition of phase velocity?

The phase velocity of EM radiation in free space is the speed at which the phase of the wave propagates, or the rate at which the wave's crests and troughs move forward.

2. How is the phase velocity related to the speed of light?

The phase velocity of EM radiation in free space is equal to the speed of light, which is approximately 299,792,458 meters per second in a vacuum. This means that the phase of the wave is moving at the same speed as the wave itself.

3. Can the phase velocity of EM radiation in free space be greater than the speed of light?

No, according to Einstein's theory of special relativity, the speed of light is the maximum speed at which anything can travel. Therefore, the phase velocity of EM radiation in free space cannot exceed the speed of light.

4. How does the phase velocity of EM radiation in free space differ from the group velocity?

The group velocity of EM radiation in free space is the speed at which the overall shape or envelope of the wave propagates, whereas the phase velocity is the speed at which the individual crests and troughs of the wave move. In some cases, the group velocity can exceed the phase velocity, but it can never exceed the speed of light.

5. How is the phase velocity of EM radiation in free space measured?

The phase velocity of EM radiation in free space can be measured using specialized equipment such as interferometers, which measure the phase difference between two waves at different points in space. This measurement can then be used to calculate the phase velocity of the EM radiation.

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