# The momentum of a photon

1. Apr 20, 2004

### tozhan

i have a question that'll really test your minds...or not....

Im still just getting to grips with some of this physics stuff but i cant work this out.

If light travels through an object it takes longer to pass through than in a vacuum right? now if heard this is because the photons are absorbed and reemitted by each particle of matter that they encounter. However this would mean that their momentum must somehow be conserved (the photons all carry on is the same direction until they leave the object).

How is this 'direction' conserved? my problem is that ive been taught that momentum is the product of mass times velocity. but if a photon has no mass it cant then have momentum! im sure its explainable and that i just dont understand enough quantum mechanics yet to answer it myself.

If you think you can help, post away!?!?

Last edited: Apr 21, 2004
2. Apr 21, 2004

Staff Emeritus
A photon of frequency $$\nu$$ has momentum $$h\nu$$ in the direction it is going, where h is Planck's constant. Einstein discovered this in the course of explaining the photoelectric effect, for which he got the Nobel prize.

It is not true that in advanced physics momentum is only defined by mass times velocity.

3. Apr 21, 2004

### Gokul43201

Staff Emeritus
Actually, p = hv / c. But in any case, the momentum of a photon passing through some material will not be conserved.

All materials absorb some fraction of the photons that pass through them, so these photons lose all their momentum (and energy, which goes into heating up the material). The fraction of photons absorbed depends on a property of the material called its absortion coefficient, A.

Then, some of the photons get reflected by the material - bouncing back is clearly a changing of direction - depending on it's reflection coefficient, R.

The rest of the photons (this fraction is proportional to the transmission coefficient, T=1-R-A) pass clean through the material, but even these photons have their monentum altered, because they are refracted by the material. They come out in a different direction than they go in. That's why light bends through water or glass, and the angle of deviation depends on the refractive index of the material, which is also defined as the ratio of the speed of light in vaccum to that in the material.

4. Apr 21, 2004

### turin

I would add that the photons either maintain their momentum because they don't at all interact or they completely lose their identity once they interact. It is the momentum of the entire system (beam of photons + bulk of material) that is conserved, not necessarily the momentum of an individual photon, which may not even exist after the process.

5. Sep 25, 2004

### chifos

what dose this mean dose a photon have momentum?

6. Sep 25, 2004

### danitaber

Chifos:
I refer you back to Self-Adjoint's post and Gokul's response directly below it.

A photon does, indeed, have momentum, although defined in a different way.

In dealing with conservation of "___blank___" issues, however, one looks at the whole system and does not zero in on a single item, which is just paraphrasing Turin's post.

Does this clarify it a bit, Chifos?

7. Sep 26, 2004

### reilly

The idea of an electromagnetic momentum predates QM. That is, Poynting's Thrm of classical E&M shows that an electromagnetic field has both energy and momentum, which contribute to the total conserved energy and momentum. And, for the field, energy is directly proportional to momentum's magnitude, that is it is the same as that of a particle of zero mass.(In fact, you use Poynting's thrm to do just this.) Classical/symmetry/invariance considerations really force the photon's zero mass.
Regards,
Reilly Atkinson

8. May 4, 2010

### sah-sah

what is correlate the orbital angular momentum of photon with polarization EM wave?