Why is Diffraction dependent upon wavelength?

[Ray12]

I've searched online and on the forum but still can't find an explanation or mechanism behind why diffraction is dependent upon wavelength.

For example, assume a water wave that diffracts around a small boat (smaller than the wavelength). The degree of diffraction decreases as the boat gets bigger, until being nil when the boat is larger than the wavelength.

Why is this? Is it just an empirical observation that's taken as an axiom or is there an explanation for this?

(Note: any explanations can involve Newtonian Mechanics and Vector Calculus, as I am already familiar with them.)

 

[M Quack]

Check out Huygens' Principle. From that it should be clear why different wavelengths produce different diffraction patterns.

 

[Ray12]

Check out Huygens' Principle. From that it should be clear why different wavelengths produce different diffraction patterns.

I checked out the Huygen's-Fresnel Principle, but can't say I fully understood it (For example, what's the mechanism behind the secondary wavelets? Or are they just a useful model, not necessarily real?

Also FYI, for me to really "get" something, I like to have a mechanical visualization of it. I would prefer a mechanical explanation if possible, one in which the wave effect can be seen to be a result of Newton's laws.

I'll give an example of the mechanical visual analogy I'm using to try to understand it, but which seems flawed as it doesn't make clear the dependence upon wavelength.

Consider a fixed post of a pier. A plane wave approaches the fixed post. The plane wave impacts the post, and in accordance with Newton's 3rd law, is reflected (and due to the post being fixed, analogous to throwing a tennis ball at a wall and having it bounce back).

The two sides of the now cut plane wave reach the other side of the post. They, being higher than the water behind the fixed post and having a greater gravitational potential, fill it in, causing the wave to bend around the object.

In this mechanical visual analogy, it is not apparent what wavelength has to do with it and that I guess is my main difficulty.

What exactly about my visual model is flawed and is it salvageable? Or I am completely barking up the wrong tree with this model?

 

[M Quack]

The secondary wavelets are just a model. In general, there are many many ways to describe a physical reality mathematically. Huygens principle is one mathematical way to describe waves.

Once you accept that waves can be described or "seen" this way, then Huygens principle is actually very graphic and easy to visualize and interpret. Draw some concentric rings on a transparency, for example alternating red (for maxima) and green (for minima). Make an addtional one for a plane wave if you like. The distance from a red ring to another red is the wavelength. Make 3 or 4 of these slides, all with the same wavelength. Then put the centers on the surface of the obstacle, where new wavelets are generated. Where red lines cross you get a maximum, where green lines cross you get a minimum.

Looking at a wave like a sheet of paper that you throw at something and that then wraps around the obstacle is wrong. You will never get the right result that way.

 

[ProTerran]

Why diffraction is wavelength dependent? Well, it boils down to the uncertainty principle. IMO it's very neat way of explanation of this phenomena (although UP doesn't have much in common with Newtonian mechanic, its still very intuitive to visualize what is going on).