How/why does diffraction occur?

[saim_]

What is the mechanism of diffraction? Let's consider water waves and not light; if we consider water an aggregate of little molecules, why would a chain of molecules moving up and down (the wave) suddenly turn once passed through a slit? I hope I'm clear enough.

 

[sophiecentaur]

The molecules don't "bend". The patterns of waves which are caused by the oscillating movement of the particles is what is bent. No molecules actually go anywhere with an ordinary progressive wave. It's the energy wot moves.

 

[mikeph]

Try to imagine a water wave without diffraction. The surface would be discontinuous and wouldn't make any sense.

 

[sophiecentaur]

Not half. A 'hard edge' at the sides of the wave would be a bit of a novelty!

 

[saim_]

@MikeyW: Yes, that's true; it makes sense that something different should happen once the wave passes through the slit. But, still, I would really like to understand the exact mechanical process. Do you think it is completely intuitive what happens in diffraction such that its mechanical explanation is unnecessary? I feel exactly the opposite and I'm actually starting to believe nobody has really worked it out !

I wish there was some sort of a visualization aid like a java applet that makes waves with small particles interacting and passes them through slits. Is there some such app?

@sophiecentaur: I never said molecules bend or "go" somewhere.

 

[sophiecentaur]

@MikeyW: Yes, that's true; it makes sense that something different should happen once the wave passes through the slit. But, still, I would really like to understand the exact mechanical process. Do you think it is completely intuitive what happens in diffraction such that its mechanical explanation is unnecessary? I feel exactly the opposite and I'm actually starting to believe nobody has really worked it out !

I wish there was some sort of a visualization aid like a java applet that makes waves with small particles interacting and passes them through slits. Is there some such app?

@sophiecentaur: I never said molecules bend or "go" somewhere.

Fair enough about the 'bending'.

But if you can state that you think that nobody has actually worked this out yet you would be prepared to look at some animated simulated package and be convinced by it then you are in the wrong business. Wave theory has been done every which way and backwards by a lot of very able people.
If you want to study this subject and be absolutely sure about it then you really need to be able to understand the solution to the differential equation which is given by the equation of motion of part of the fluid and how the boundary conditions affect the answer. That is the only way to discover the true why and how of waves.
If you haven't understood what you have read here or in books then it's because it may not be as simple as you would like it to be.

Why should the wave 'leak round the corner'? the first bit of the wave that peeps round the side of the gap can't help but spill out sideways because you would have a high spot right next to a low spot - water will flow in that direction, forming a wave as the later bits of the wave emerge from the gap and a trough starts to emerge etc. That's about as noddy an explanation as I can think of. But that's only the same sort of reason that any wave propagates.

 

[saim_]

@sophiecentaur: Thank you for teaching me "the business" and telling me that people have worked on wave theory; where would I be if you hadn't done that.

Why should the wave 'leak round the corner'? the first bit of the wave that peeps round the side of the gap can't help but spill out sideways because you would have a high spot right next to a low spot - water will flow in that direction, forming a wave as the later bits of the wave emerge from the gap and a trough starts to emerge etc. That's about as noddy an explanation as I can think of. But that's only the same sort of reason that any wave propagates.

This was actually helpful; exactly the kind of thing I'm trying to get at. Thanks.

 

[mikeph]

I don't exactly know the answer, was just trying to give a nudge in the right direction, why don't we get discontinuities in the water surface?

One simple suggestion is due to surface tension - the surface of water will tend to evolve to minimise itself without changing the volume of the water. That's why raindrops are spherical - the shape with the minimum surface to volume ratio. So sharp edges are instantly removed and "short-cut" by curves.

This leads to a different approach - water volume is preserved because it is incompressible. This leads to the argument that your basic approach in the first post is wrong - the water molecules don't simply go up and down, because that would imply water is being compressed and stretched. There is also some longitudinal motion forwards and backwards to keep the density of water uniform. So when you consider particle collisions - and the mean free path of a water molecule is very short - the forward/backward motion can easily spread out when a molecule moving forwards hits another molecule in front of it at some angle, and transfers some transverse momentum to it, so the wave spreads in all directions.

 

[sophiecentaur]

@sophiecentaur: Thank you for teaching me "the business" and telling me that people have worked on wave theory; where would I be if you hadn't done that.

Well, your initial approach was that no one knew anything about it. That's just a red rag to a bull, isn't it? Sometimes there just isn't an answer in the exact terms you might want. Glad my arm waving was useful.

 

[sophiecentaur]

water volume is preserved because it is incompressible. This leads to the argument that your basic approach in the first post is wrong - the water molecules don't simply go up and down, because that would imply water is being compressed and stretched. There is also some longitudinal motion forwards and backwards to keep the density of water uniform. So when you consider particle collisions - and the mean free path of a water molecule is very short - the forward/backward motion can easily spread out when a molecule moving forwards hits another molecule in front of it at some angle, and transfers some transverse momentum to it, so the wave spreads in all directions.

It's well known that surface waves on water involve circular motion of the particles. Contrary to what they tell kids in School, water waves are not 'transverse'- they are as much longitudinal on the surface. Just watch a floating ball in the waves when at the beach.

 

[saim_]

@MikeyW: That's a really nice explanation. Thanks. I couldn't have thought to use so many properties of water for the explanation.

...why don't we get discontinuities in the water surface?

Another simpler reason for this would be that we can't really expect there to any isolated vertical stack of molecules in any liquid since its highly unlikely that a small subset of molecules would pile on top of one another in small region in complete equilibrium. It would be like stacking small balls in a vertical position; it very unlikely that they will be in exact alignment to remain in the vertical stack, and, if by some chance they are arranged so, their vibrational motion would throw them off.


I have always thought Huygens principle of secondary wavelets is a very nice model for diffraction but I felt it was an ad hoc explanation to solve problems, replacing the question of "why diffraction occurs" with "why are secondary wavelets produced", but, now I see that it is quite intuitive that a propagating wave has wavelets at each point, at least for material particles, since each disturbance creates a disturbance around it of it own. Its even more apparent if a wavefront is cutoff with an aperture; the disturbances on the sides i.e. closer to the walls of the aperture, will continue moving as before but due to various forces between the particles and their packing it will create similar harmonic motion in a spherical region around it and those newly moving particles will in turn propagate the wave further. So Huygens principle seems to describe the correct mechanism for diffraction in material medium. As for EM radiation or a general scalar field wave, Huygens principle is a mathematical fact.

Awesome reads I found on diffraction and Huygens principle:
http://www.mathpages.com/home/kmath636/kmath636.htm
http://www.mathpages.com/home/kmath242/kmath242.htm