GR8677 #3



Alternate Solutions 
swimjk89 20100321 11:31:13  I'm not sure if I am right here, but according to (http://www.microwaves101.com/encyclopedia/phasevelocity.cfm)
where and are the relative permittivity and permeability. Since
these two equations would imply for this problem that . I think that this would make sense if dealing with monochromatic light.  

Comments 
tHulk 20120519 10:45:19  What is this equation called for ? I can't seem to find it in any of my text books.
tHulk 20120519 11:11:20 
Oh I see it comes from Maxwell's equations. http://en.wikipedia.org/wiki/Maxwell's_equations#With_neither_charges_nor_currents

  livieratos 20111107 07:30:34  hmm you got me confused... i thought the speed of an em wave was always the phase velocity. what does group velocity have to do with anything?   swimjk89 20100321 11:31:13  I'm not sure if I am right here, but according to (http://www.microwaves101.com/encyclopedia/phasevelocity.cfm)
where and are the relative permittivity and permeability. Since
these two equations would imply for this problem that . I think that this would make sense if dealing with monochromatic light.
swimjk89 20100321 11:32:29 
I forgot to say this means the answer would be (D)

  rehab 20091027 18:13:50  the answer must be (B )otherwise groub velocity will exceed the speed of light from this realtion vp=c^2/vg and that ,of course, impossible!!rn
flyboy621 20101109 20:07:51 
The relation does not always hold.

ngendler 20151020 21:54:15 
The group velocity can exceed the speed of light. Information is carried only at the phase velocity. For example, consider the following scenario: you shine a laser at the moon, and move the point to the right. If you measure the \"speed\" of the laser point, you might get a value greater than the speed of light, but that\'s okay because no new information was transmitted.

  smokwzbroiplytowej 20081022 19:18:33  Not _exactly_ related to this problem, but Wikipedia has a nice applet showing the difference between group and phase velocity:
http://en.wikipedia.org/wiki/Group_velocity
  blue_down_quark 20080802 09:10:29  I think the answer is incorrect. The question doesn't ask 'what is light's velocity ?' it instead asks 'what is light's PHASE VELOCITY? '. Phase velocity can actually be larger than c . The equation for phase velocity is = . I think the correct answer is B . for more information see : http://en.wikipedia.org/wiki/Phase_velocity
wangjj0120 20080820 20:59:02 
but when is the equation v_pv_g = c^2 valid?
To integrate this equation, we realize that
only when the light propagate in the air and wave guide (or plasma) have the dispersion relation which corresponds to this equation.

zaijings 20090403 08:22:28 
I am also confused when the problem asks about the phase velocity.

segfault 20090822 21:06:49 
I think when dealing with a signal of a single frequency (e.g., blue light), it only makes sense to talk about the phase velocityyou can't construct a "group" or wavepacket out of a single frequency signal.

jchys 20100202 20:38:17 
If you look at the section carefully, it says that
"any particle that has MASS (according to special relativity) phase velocity of matter waves always exceeds c"
photons obviously has no mass.

alemsalem 20100920 03:51:17 
the refractive index is always defined in terms of v_p and it's equal to (Ke * Km)^0.5 where Ks are the relative permittivity and permeability.

misbah 20141205 02:13:46 
i agree with kittle 's book view

  erc 20051104 09:11:07  I don\'t know anything about this, so maybe about to make a fool of myself...
But, to be consistent, I think the and should each lose the power?
Thanks.
yosun 20051104 15:10:14 
erc: thanks for the typo note. The extra squared sign on the c's and v's have been removed. (you can also check it by dimensional analysis. the units for permeability and permittivity are given on the table of info included with the exam)

  erc 20051104 09:09:06 
rehab 20091027 18:30:09 
the answer must be (B )otherwise groub velocity will exceed the speed of light from this realtion vp=c^2/vg and that ,of cource, impossible!!

 

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