My toddler asked me "how does rainbow happen", and I would like to give a pedagogical explanation of the relation of photon frequency, its color, and the way different frequencies are bent in a drop of water.

However, I wouldn't want to create the wrong mental image, so I'd like it to be a "closest to correct" explanation, without invoking any math. So I thought we do something like this using crayons:

Photon frequencies from red to violet

Fig.1 Poorly drawn waveforms representing photons with frequencies from red to violet

But is there a "toddler intuitive" explanation of dispersion without math (i.e. without the need for Snell's law)? I am aware the photon is absorbed and re-emitted several times, so this process simply works a bit "slower" for higher frequencies?

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    $\begingroup$ When it comes to dispersion, I suggest you show your toddler what happens with water as it encounters a single slit. $\endgroup$ – Mikael Fremling Aug 21 '17 at 15:15
  • $\begingroup$ @MikaelFremling: Thanks, sorry if I don't get you though. :) Do waves on the other side behave differently based on water frequency? $\endgroup$ – Lou Aug 21 '17 at 15:19
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    $\begingroup$ The concept of "photon" is completely unnecessary here, and a clear overkill -- to understand such a concept you need to understand quantum field theory. Classical electrodynamics, and even geometric optics, should suffice here. $\endgroup$ – AccidentalFourierTransform Aug 21 '17 at 15:19
  • $\begingroup$ @AccidentalFourierTransform: well, it wouldn't be anything more than "a tiny packet of light". I wanted to introduce it that way since it then explains how tiny atoms start jiggling more when struck by that "packet", or how atoms emit these tiny packets again, and it takes a bit more time to emit packets which have a higher frequency. I don't know, there are never-ending "why" questions which seemed to necessitate at least the basic principes: 1) everything is made of perpetually jiggling tiny atoms and 2) the light that we see comes in tiny packets which can make these atoms jiggle even more. $\endgroup$ – Lou Aug 21 '17 at 15:25
  • $\begingroup$ I didn't plan on bringing particle-wave duality of course, these tiny waves are supposed to be "tiny blocks of light" in a way (like a really tiny snake travelling through space, not an infinitely long snake). $\endgroup$ – Lou Aug 21 '17 at 15:26

As already mentioned in several of the comments, you do not really need more than geometrical optics to explain the rainbow. Nevertheless I suppose it will be quite difficult to explain Snell's law to your kid. However, a small demonstration might be quite insightful, so I suppose the best way to explain it and to have some fun together (on a rainy day perhaps) is to do a little experiment! Using a water filled flask as a model for a single drop of rain and a slide projector, you can generate a rainbow. See for instance the information on this site or Google for "Florence's Rainbow".


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