Diffraction and Probability Amplitude

[Johnleprekan]

Hi, I would like to understand how diffraction works in layman's terms. Why does a wave entering a corner or a slit (in the case of light) bend?

I found an answer here, but it doesn't make a lick of sense.

http://wiki.answers.com/Q/How_does_diffraction_work

What is a probability amplitude (also in layman's terms) and how does that cause a wave to diffract?

 

[Simon Bridge]

Laymans description that does justice to the process is not available.
The "bending" is an emergent effect ... we actually don't know what happens at the slit or by the corner because as soon as we look there to see, the effect goes away. (because the act of looking messes with what we are looking at.) Basically, light bends because that is what it does... it is of the properties of light that it may be detected within the classical shadow of things.

Here's an accessible attempt:
http://vega.org.uk/video/subseries/8
... see all eight lectures. You need the concepts and background so it's a long sit - fortunately the lecturer is one of the best at this. At the very least it should show you what else you need to read about.

 

[Jano L.]

The answer at wiki is not very accurate. The phenomenon can be explained within classical wave optics.

The wave spreads to all directions basically because all elementary waves are spherical. Together they add and form more complicated front, which can have any shape.

Now, if you have a hole in a desk, the total resulting wave behind it is composed of many such elementary waves, from the source as well as from the desk.

Since the wave front would be planar without the desk, and since the shape of the curved wave front depends on the shape of the hole, it is easy to see that it is the atoms in the desk which contribute with elementary waves such that they result in the going "around the corner."

 

[Johnleprekan]

Thank you.

How do the elementary waves of the desk contribute to the wave front? Are they interacting in some way?

 

[Simon Bridge]

The answer at wiki is not very accurate. The phenomenon can be explained within classical wave optics.

Except that the question is asked in the context of quantum mechanics. You are aware of the failings of classical wave optics when it comes to interference of light?

How do the elementary waves of the desk contribute to the wave front? Are they interacting in some way?

For classical wave optics, you want to look at Huygens construction of wavelets.
executive summary: each point on a wave-front acts as the source of a spherical wavelet - the sum of all these is the observed wave. When there is a barrier of some kind, some of the wavelets get blocked, and cannot contribute to the wave behind the barrier. You can see the effect clearly in water ripples.
[http://www.colorado.edu/physics/phys1230/phys1230_fa01/topic14.html] [http://www.cliffsnotes.com/study_guide/Wave-Optics.topicArticleId-10453,articleId-10442.html ]

It works well to show interference and the penetration of the ray-optics shadow.

In the quantum mechanics description (but bear in mind the limitation of that paper), the most accessible form is still the Feynman lectures from post #2.

It is always possible to give some incomplete description so a layman will nod and feel they understand it - until something shows up to start questions again.

 

[Jano L.]

How do the elementary waves of the desk contribute to the wave front? Are they interacting in some way?

Yes, the atoms in the desk interact with the primary wave from the source. This makes the electric charges in the atoms at the surface of the desk vibrate and they send out new secondary waves. Since these spread spherically from the atoms, they are no longer parallel to the desk. When these secondary waves are added to the primary wave, diffraction pattern results.

Huygens principle Simon is referring to is rather an approximate method to calculate the resulting pattern. In fact the points of the wavefront do not radiate any new waves. Only the atoms in the source and the desk can do that, but the calculations are often more tractable when the Huyghens principle is used.

 

[Simon Bridge]

... if we are going to split hairs, then the interaction for much light is with the electrons in the surface of the material and not whole atoms. But a description at that level is better handled with quantum mechanics.

You also why do you need the desk to radiate to model interference.

 

[Jano L.]

the interaction for much light is with the electrons in the surface of the material and not whole atoms.

The primary EM wave penetrates into all depths and interacts there with everything that has charge. That means nuclei also, although this can be often neglected. New secondary wavefronts are created in these charges. True, atoms deep enough will not be radiating much, but the decay of oscillations with depth is continuous.

You have the same situation even with the Feynman model of probability amplitudes - the "photon" from the source has non-zero probability amplitude going inside the desk and then to the detector.