light momentum

[flyerpower]

So, photons have zero rest mass, but they never stand still so they have momentum at the speed of light, i quite understand that, and i think it can be derived from this:

http://upload.wikimedia.org/math/d/2/d/d2dec44ba56c41a31b4d334b144b51d6.png
http://upload.wikimedia.org/math/9/c/3/9c3f2777ac6cb5f4c9c1edc647c68311.png

If we plug in v=c in the gamma factor then it turns out that light has some momentum p=(0*c)/0 which is a constant.
But c is the speed of light in vacuum, what if light travels through a medium in which light travels slower than c, then p=(0*v)/gamma, where gamma is not 0 so p=0.

What is going wrong here?

[HallsofIvy]

What's wrong with that is that 0/0 is NOT equal to 1. It does not exist; you cannot divide by 0.
As for non-vacuum, it isn't quite right to say that the speed of light is slower. More precisely, light moves at the speed of light (in vacuum) between atoms, is absorbed by an atom, then, a tiny time later, is ejected from the atom so that the average speed through the material is slower.

[Doc Al]

So, photons have zero rest mass, but they never stand still so they have momentum at the speed of light, i quite understand that, and i think it can be derived from this:

http://upload.wikimedia.org/math/d/2/d/d2dec44ba56c41a31b4d334b144b51d6.png
That formula only applies to massive particles, for which the speed v is always less than c. For photons, momentum is given by p = E/c (where E is the energy).

[flyerpower]

What's wrong with that is that 0/0 is NOT equal to 1. It does not exist; you cannot divide by 0.

If we plug x=1 in (x-1)/(x^2-1) = 0/0, if we plug in x=0.9 it returns ~0.52, and for x=1.1 it returns ~0.47, and if we want the defined value for that when we plug x=1, we reduce the expression to 1/(x+1) which gives 0.5, so it's a constant. Wouldn't it work in that case too?

[pervect]

I've found a number of interesting-sounding papers on the topic of the momentum of light in a refractive medium. Frustratingly, I can't access them in their entirety. Amongst what I found are:

"The momentum of light in a refractive medium" , Peierls, two papers
http://rspa.royalsocietypublishing.org/content/347/1651/475.abstract http://www.jstor.org/pss/79058 http://www.jstor.org/pss/79317

Also, a more recent http://prl.aps.org/abstract/PRL/v104/i7/e070401 (and a physicsworld.com article citing it that was .... not very well written.)

Peierls makes the interesting observation that it's not only light that caries the momentum when an electromagnetic wave travels through a medium - motion of the atoms in the medium (or of the medium itself in the continuum approximation) are also generated, in particular acoustic waves (which I assume could also considered to be phonons).

It'd be nice to see a full treatment of the problem that was accessible.

[add]http://www.opticsinfobase.org/aop/abstract.cfm?uri=aop-2-4-519 also looks interesting.