# Can light have a phase velocity faster than c?

1. Jun 5, 2008

### redtree

Can an electromagnetic wave have a phase velocity greater than c? Is the phase velocity of a photon always c?

As far as I understand, the phase velocity of all massive particles (particles with rest mass) is greater than c.

2. Jun 5, 2008

### granpa

well neither the group velocity nor the phase velocity is always c.

the group velocity can be greater than c.
not sure whether the phase velocity can be greater than c.

3. Jun 5, 2008

### yuiop

As I understand it, the group velocity of a light wave is thought to be the velocity at which information is transmitted. The phase velocity of light in a medium is generally less than the speed of light in a vacuum but in some rare circumstances the phase velocity can be greater than c but it is generally thought that the rate information can be transmitted never exceeds c over any reasonable distances. Confusingly the group velocity can also exceed c in certain rare circumstances but it still claimed information transmission does not exceed c in those conditions.

The velocity of a particle in a medium can exceed the phase velocity of c in the same medium and in those circumstances Cerenkov radiation is given off. I am not sure of the universal truth of your last statement about the phase velocity of massive particles.

This Wikipedia article http://en.wikipedia.org/wiki/Phase_velocity does support your statement.

Last edited: Jun 5, 2008
4. Jun 10, 2008

### cesiumfrog

And if you understood why (say derived from the assumption that a particle of definite momentum is identified with a packet of waves that have no preferred frame), you know that the phase (and group) velocity of any zero-rest-mass particle in vacuum is c.

But in medium? Phase velocity is given simply by refractive index, and commonly exceeds c (n<1). For sufficiently pathological media, even group velocities can take any value. Next question?

5. Jun 10, 2008

### yuiop

OK, next question(s).

Given that in a medium the phase velocity of light and the group velocity of light can both exceed c and the signal velocity of light (transfer of energy or information) never exceeds c, then

What is the relationship between signal velocity and phase velocity of monochromatic light of wavelength (w) in a medium of phase refractive index (n)?

Is the group velocity of monochromatic light always the same as the phase velocity in a given medium?

Given the equation for group velocity $$v_g = c\left(n-w\frac{dn}{dw}\right)^{-1}$$

and if the refractive index of an optical medium is determined empirically for a given wavelength of light can the refractive index for any wavelength of light in the same medium be determined mathematically without further emperical measurements?