# B Behind the laws of reflection

1. Mar 17, 2016

### vin300

I think this may have been done before. So people are aware of the geometry of reflection. If I go beyond, I try to say that if light can pump electrons, it is absorbed, if it merely polarizes, it gives rise to an alternating dipole supposed to be polarizing the region around in all directions, but specular reflection is precise and follows the laws of reflection, does it mean, that this strengthens the particle behaviour of light that is "forced" by the surface?

2. Mar 17, 2016

### blue_leaf77

No, specular reflection need not be associated with any kind of particle-like phenomena. The fact that the reflected light has their wavefronts reverted relative to those of the incoming one is merely due to the flatness of the surface.

3. Mar 17, 2016

### sophiecentaur

Are you implying that it should be looked upon like 'rebounding' particles? The answer to that is no.
When a plane wave hits a flat surface (the easiest example) the wave excites a 'large' area of the surface and the result is another wave, that comes off at an angle according to the laws of reflection. In condensed matter, the bulk of the matter acts, rather than just one atom at a time. You can look at it as another example of Diffraction in which the resulting pattern is due to the whole reflector. The contributions from the whole plane of the reflector will add up only in the appropriate direction. If the reflector is only small, then there will be an imperfect pattern. A circular reflector will produce an Airey Disc just like a lens and some energy will emerge off-axis.
Introducing photons would be 'possible' because there is always that approach open to you but it doesn't help in calculating the result and it is no closer to 'what really happens'.

4. Mar 17, 2016

### vin300

It is supposed to imply that the secondary wave, although omnidirectional, due to interference along a line, has construction along the line.

5. Mar 17, 2016

### sophiecentaur

In order for that to happen in your model, it is necessary that every photon-electron interaction must take exactly the same amount of time or the "interference along the line" will fail to propagate a new, perfect wave front. In fact, the time taken for this interaction is not fixed and the multiple interactions will become diffuse and not produce a specular reflection - or a coherent deviated ray to follow the laws of refraction at an interface either.
This is a personal theory and I don't think you can come up with any good reference to support it.
The diffuse electrons at a metal surface are all in slightly different energy conditions and that is why you can't expect your model to work. Why would you want to deviate from the wave model which actually explains things very well?

6. Mar 17, 2016

### vin300

I meant something like this There is spherical radiation.

7. Mar 18, 2016

### sophiecentaur

That's an excellent diagram to base this discussion on. It is an example of Huygens construction, which is a classical approach to wave behaviour. It was never an attempt to describe what is actually going on, afaik. It was a way of looking at things in order to predict a result; that's certainly the way it is regarded these days, when it is used (and it often is). The way it works assumes that each of the sources of the spherical wavelets is coherent. This is what accounts for the constructive interference in the forward direction only.
And that's as far as it is useful, i'm afraid.
If you try to hop on board with a sort of quantum theme, it will actually show you where the idea is wrong because you cannot validly mix classical and quantum ideas in this way. As I have already said, for the model to work with absorption/emission of individual photons by electrons (which are the yellow dots in your diagram?), the re-emitted wavelets have to be all in step (coherent). If you take two different electrons and imagine them absorbing a photon and re-emitting it, they will each take a different amount of time over the process because the delay is random. Those neat little wavelets which, in the diagram have all originated in perfect order, will not be like that. There will no longer be a resultant coherent wave front but a set of random, short lived wave fronts, aiming in many different directions.
Has that convinced you?

8. Mar 18, 2016

The angle of incidence=angle of reflection for a regular array of atoms at the surface is the "zeroth" order maximum if you consider the surface to be a reflection type diffraction grating. On a related item, in Bragg scattering, the angle of incidence=angle of reflection condition results in constructive interference, along with the atoms in (parallel layers of) crystal planes that constructively interfere with a Fabry-Perot type interference. Both conditions need to be satisfied to get a Bragg peak.

9. Mar 19, 2016

To add to the above post of Bragg scattering as being also a Fabry-Perot type interference, that means that the wavelength $\lambda$ must be such that $m \lambda=2nd \cos(\theta)$ (where d is the distance between crystal planes and m is an integer) must apply along with the angle of incidence=angle of reflection in order to get a Bragg peak in the reflectivity of the incident beam. In some of the more detailed treatments of Bragg scattering, the individual atoms in the crystal are treated as an array of scatterers (e.g. Huygens sources) that must all constructively interfere to obtain a Bragg peak in the reflectivity.

Last edited: Mar 19, 2016
10. Mar 19, 2016

### sophiecentaur

You can also get specular reflections from amorphous solids (and liquids of course) and such reflections are not wavelength dependent as with Bragg reflections.
The OP has made an invalid connection between Huygens and QM and that, I think accounts for his/her problem with the model applied to the phenomenon.

11. Mar 19, 2016

The comments I made were more intended to add to the follow-on discussion than the OP. It actually turned into a rather healthy physics discussion even though the OP gets off to a slow start.

12. Mar 19, 2016

### sophiecentaur

I have read similar ideas before on PF and they come fairly naturally from the simple Hydrogen Atom theory, which doesn't transfer easily to solids however tempting it seems. As you say, it's "healthy".

13. Mar 26, 2016

### vin300

Long ago, I think I had read about something called a single photon emitter. It is an idea used to do away with multiple wavefronts coming together. As I remember, even in this case, there was the same old diffraction grating. How could there be interference without many simultaneous waves?

14. Mar 27, 2016

### sophiecentaur

You are making the assumption that 'one photon = one wavelet'.

Last edited: Mar 27, 2016