GREPhysics.NET: GR8677 #72

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kpb
2009-12-18 12:55:18

Refractive index= C/V
group velocity is always less than C, so refractive index is less than one. But phase velocity can be more than C, hence refractive index can be greater than one. so the result E makes sence. For better explanation, please see the link below.

http://www.mathpages.com/home/kmath210/kmath210.htm

kpb
2009-12-18 13:20:28

Please ignore the above explanation.
Refractive index= C/V, group velocity is always less than C, so refractive index is greater than one. But phase velocity can be more than C, hence refractive index can be less than one. so the result E makes sence. For better explanation, please see the link below. http://www.mathpages.com/home/kmath210/kmath210.htm

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gliese876d
2008-10-17 11:37:38

I have to say I just laughed out loud at the "imaginary mass" choice :)

neon37
2010-11-03 12:29:03

yea me too, now I'm wondering if there is any deeper meaning to this other than a mere pun.

acukierm
2013-10-18 20:08:13

Actually this answer does kind of make sense. If n<1, then since $v=\frac{c}{n}$ , it seems like the velocity of the photons is greater than c. Recall that for a massive object, $E=\gamma mc^2$ . But $\gamma$ = $\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$ . So if v>c, then $\gamma$ is imaginary! And since $E$ must be real, that implies that $m$ is imaginary. Of course photons have zero mass so this is all nonsense, but this answer is actually the most plausible of all the other wrong ones.

Objects that travel faster than c are called tachyons. Laugh all you want, but a lot of string theorists believe that tachyons do exist, and that they have imaginary mass.

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nitin
2006-11-16 12:10:49

No! The group velocity $v_g$ cannot be greater than c, and it is not $v_g$ which is "at work in the equation n=c/v". Concerning the latter, if $v=v_g$ , then we have

$n_g=\frac{c}{v_g}$ ,

which is called the "group index", and which is NOT the commonly known refractive index $n$ . Instead, $n$ is defined with respect to the phase velocity $v_p=\frac{\omega}{k}$ .

prismofmoonlight
2007-10-28 13:21:58

To clear things up, the index of refraction n=c/v_phase. rnrnn<1 does not violate the theory of relativity, which says that no information-carrying signal can propagate faster than c, because it is v_group that describes the velocity of the transmitted information.

prismofmoonlight
2007-10-28 13:22:43

That's just supposed to be n<1 in the second line.

temujin
2008-10-28 15:31:02

speed of light in a material is less than c; so, the group velocity in the medium can be greater than the the speed of light (for that medium).

Jeremy P
2008-11-04 10:53:01

nitin is right.rnrn $V_{group}$ carries information and so cannot travel faster than $c$ rnrn $V_{phase}$ carries no information and is greater than $c$ rnrnuse $n=\frac{c}{V_{p}}$ to arrive at n<1

Setareh
2011-10-27 01:43:48

I do agree with the guys who believe this is the phase velocity which can be faster than the speed of light. We also got familiar with this fact in electromagnetic and optics..

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globalphysics
2006-10-29 22:19:21

Shouldn't it be n<1 for the 4th line?

zeper
2011-08-07 08:10:14

yes it must have been n<1

zeper
2014-09-18 03:53:50

correction: no it is true in the answer.....n>1 so vc why? this was the question.

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