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OK – I think I’ve got it now.  Why is the sky blue? – or at least, why is it that low wavelengths are scattered more than high wavelengths?

I don’t know if kids do this at school in New Zealand, but when I was at primary school one of the games we played involved a skipping rope laid out on the ground which two people (one at each end) waggled. Their waggling created waves down the skipping rope. This, as I recall, was entirely incidental to the game, which didn’t need a waggling skipping rope at all, but it did make it more eyecatching. Now, to get the wave to go down the rope, the waggling back and forth is important. You can’t just pick up one end and move it at constant speed – all that will happen is that you’ll end up towing the rope behind you. Neither can you move one end then stop (a constant displacement) The rope will change its shape, sure, but no wave will go along it. What you need to do is to accelerate the end – backwards and forwards.

Likewise with electromagnetic waves (of which visible light is just a small subset). To radiate power, we need to take electric charge, and accelerate it. The greater the acceleration, the more it radiates.

When a wave hits a small particle (like a dust particle) it moves the electrons in the particle backwards and forwards a bit. The higher the frequency of the wave, the quicker the electrons accelerate, first one way, then the other, and so the more the particle radiates the energy of the wave. Blue light has higher frequency (lower wavelength) than red, so more of its energy gets scattered in this manner.

And there you have it. No maths, just skipping ropes. If you reckon you can do better, go for it.