Any discussion of wave-particle duality has to include the famous two-slit experiment! This is one that's pretty easy to replicate at home (well, part of it, anyway) and it's cool to see the interference pattern demonstrating the wave property of light!
There are several good ways to do this demonstration: this one here is clear and easy to follow.
You can also look at diffraction patterns using these instructions here.
Light viewed through a diffraction grating
For a clear visual demonstration of how interference effects make patterns, you can use these printable moiré patterns. I love moiré patterns—my dad had a whole book of them where you moved one film on top of another to create those strange moving shapes. They can be very beautiful and elaborate. The idea is really the same as the interference you get with waves of light: two superimposed peaks create darker patches, a peak and a trough superimposed cancel each other out. A good explanation is here.
To make these moiré patterns, I just printed off several pdf files from this site onto transparency film (this kind worked great for my printer). When you move and rotate the different patterns on top of each other, you get various beautiful moiré effects.
Here's a short video of how the patterns change as you move them around. So pretty!
We also talked about thin-film interference, or iridescence. This page has a good explanation of why iridescence occurs in soap bubbles, peacock feathers, etc., and this article discusses the same effect.
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