Why Are Photons Reflected at the Same Angle They Are Absorbed?

[Devils]

I'm starting out with QM (I have a maths degree) and have come up with the following problem to help me understand QM more.

Say we have a mirror lying flat on the ground. We shine a laser from the East on the mirror at say X degrees, to be reflected to the West at X degrees. At the quantum level all we have is photons being absorbed by the reflective coating atoms of the mirror (eg silver), then being re-emitted shortly later.

I'm trying to understand is why the photons are reflected at the same angle they are absorbed. Once the photon is absorbed I can't see how the silver atom "decides" to emit it at the same angle. Is it to do with QED or conservation of momentum? Is there a good book to get me started with this?

 

[ndung200790]

I think that QM is ''wave-particle''(''dual'') physics,then it automatically leads to reflection law of light by ''wave characteristic''.

 

[Cthugha]

This is quite a non-trivial question. Before tackling the quantum problem, it is best to solve the classical problem first. So I assume you are either familiar with the Huygens–Fresnel principle or should read up on it. Constructing reflection using the Huygens-Fresnel principle is not too complicated and it is very instructive to do it once.

Going on to the quantum description, I suppose we are talking about typical metal mirrors and visible light. It is important to note that the reflection is typically not caused by single atoms. These do not really take part in the reflection process. The delocalised conduction electrons are important here. So what you get is a polarization in the mirror material caused by the incident light. The incoming em field causes the conduction electrons to oscillate collectively. This in turn creates secondary light emission. The superposition of the incoming and the reemitted light field will again roughly behave as predicted by the Huygens principle. However, the exact processes happening can get pretty complicated and you need to know material properties and a fair share of solid state physics as the electron dispersion and the allowed transitions become important. A thorough microscopic description is really pretty non-trivial.

 

[Dadface]

One technique is to assume that the reflected photon might take every possible path from a source to a detector and then work out the most probable path.The path that gives the highest probability works out to be the classical path,namely the one that follows the laws of reflection.

Try googling "sum over paths theory"

 

[sym666]

Is there a good book to get me started with this?

Hi, this is the first time I post. English it's not my primary language, I apologize in advance for the certain mistakes I'm going to do. Nice to meet everybody :-)

I've read "QED" by Richard Feynman, which I found I good book, surely you'll find an interpretation for the question you propose. It's divulgative tough and since you have a degree in maths, maybe you want to look for something more technical. Hope it helps
Bye bye

 

[DrChinese]

One technique is to assume that the reflected photon might take every possible path from a source to a detector and then work out the most probable path.The path that gives the highest probability works out to be the classical path,namely the one that follows the laws of reflection.

Try googling "sum over paths theory"

Welcome to PhysicsForums, Devils!

Keep in mind there is experimental support for Dadface's position. What Cthugha says is very good too, clearly one should not think of it as a silver atom absorbing and re-emitting.