Does this mean the speed of x ray faster than light in vaccum

[einstein1921]

http://global.britannica.com/EBchecked/topic/495677/refractive-index
refractive index, also called index of refraction, measure of the bending of a ray of light when passing from one medium into another. If i is the angle of incidence of a ray in vacuum (angle between the incoming ray and the perpendicular to the surface of a medium, called the normal; see figure) and r is the angle of refraction (angle between the ray in the medium and the normal), the refractive index n is defined as the ratio of the sine of the angle of incidence to the sine of the angle of refraction; i.e., n = sin i / sin r. Refractive index is also equal to the velocity c of light of a given wavelength in empty space divided by its velocity v in a substance, or n = c/v.

Some typical refractive indices for yellow light (wavelength equal to 589 nanometres [10−9 metre]) are the following: air, 1.0002; water, 1.333; crown glass, 1.517; dense flint glass, 1.655; and diamond, 2.417. The variation of refractive index with wavelength is the source of chromatic aberration in lenses. The refractive index of X-rays is slightly less than 1.0, which means that an X-ray entering a piece of glass from air will be bent away from the normal, unlike a ray of light, which will be bent toward the normal. The equation n = c/v in this case indicates, correctly, that the velocity of X-rays in glass and in other materials is greater than its velocity in empty space.

 

[mfb]

The phase velocity in matter can exceed the speed of light in vacuum. It does not transmit any information, however.
Even the group velocity can do this in some rare circumstances (with high absorption in the material).
The signal speed ("how fast can I transmit data") cannot exceed the speed of light.

In vacuum, all three speeds are the same. In matter, things are more complicated.

 

[cwilkins]

To add to what mfb said, I'm pretty sure the only way you could use the phase velocity to transmit information would be to detect changes in the phase velocity. Those changes will propagate at a speed less than or equal to the speed of light in whichever medium you're considering.

 

[einstein1921]

The phase velocity in matter can exceed the speed of light in vacuum. It does not transmit any information, however.
Even the group velocity can do this in some rare circumstances (with high absorption in the material).
The signal speed ("how fast can I transmit data") cannot exceed the speed of light.

In vacuum, all three speeds are the same. In matter, things are more complicated.

thank you for your answer. "phase velocity in matter can exceed the speed of light in vacuum" .Does this violate special relativity in which the speed of light in vacuum is the limit of speed? why?
PS:why " It does not transmit any information"?

 

[mfb]

Does this violate special relativity in which the speed of light in vacuum is the limit of speed?

No. Special relativity puts a limit on the signal speed.

" It does not transmit any information"?

To get a propagating phase at some point, you need the signal ("information") to arrive (slower than light) first.

 

[Redbelly98]

thank you for your answer. "phase velocity in matter can exceed the speed of light in vacuum" .Does this violate special relativity in which the speed of light in vacuum is the limit of speed? why?
PS:why " It does not transmit any information"?

A picture is worth a thousand words.

Look at the middle-left figure below, where the phase velocity is greater than the group velocity. The red dot indicates the phase velocity, moving along with the peak of a wave.

But the signal or pulse (i.e. the information) is represented by the broad peak enveloping the group of waves. It travels more slowly than the phase velocity, and the blue dot indicates how fast this travels as it moves along with the signal pulse.

(from this web page)

 

[einstein1921]

No. Special relativity puts a limit on the signal speed.


To get a propagating phase at some point, you need the signal ("information") to arrive (slower than light) first.

thank you! what does "velocity of X-rays in glass " mean ? phase velocity or group velocity?
by the way, I don't say about wave packet,I just say plane wave(x ray wave). Does plane wave
have group velocity ?

 

[mfb]

thank you! what does "velocity of X-rays in glass " mean ? phase velocity or group velocity?

There is no single "velocity of [whatever] in glass", that is exactly my point.

by the way, I don't say about wave packet,I just say plane wave(x ray wave). Does plane wave
have group velocity ?

Well, you can still calculate the group velocity, but a plane wave will be independent of that.

 

[einstein1921]

A picture is worth a thousand words.

Look at the middle-left figure below, where the phase velocity is greater than the group velocity. The red dot indicates the phase velocity, moving along with the peak of a wave.

But the signal or pulse (i.e. the information) is represented by the broad peak enveloping the group of waves. It travels more slowly than the phase velocity, and the blue dot indicates how fast this travels as it moves along with the signal pulse.

[PLAIN]http://resource.isvr.soton.ac.uk/spcg/tutorial/tutorial/Tutorial_files/littlewavepackets.gif[/INDENT][/INDENT]
(from this web page)​

Thank you! The equation n = c/v in this case indicates, correctly, that the velocity of X-rays in glass and in other materials is greater than its velocity in empty space. if we consider plane wave,not wave packet, is this correct? I don't understand why the velocity of x ray can surpass light in vaccuum! thank you!​

 

[mfb]

if we consider plane wave,not wave packet, is this correct? I don't understand why the velocity of x ray can surpass light in vaccuum! thank you!

Some specific speed in the description of the plane wave (the phase velocity) is faster than light. This is not the motion of anything! The phase velocity is not restricted in any way - it can even go backwards.