Snell's law proof using springs
This is a supplement to the Brachistochrone video, proving Snell's law with a clever little argument by Mark Levi.
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So, in my video with Steve Strogatz about the brachistochrone, we reference this thing called Snell's Law. It's the principle in physics that tells you how light bends as it travels from one medium into another, where its speed changes. Our conversation did talk about this in detail, but it was a little bit too much detail, so I ended up cutting it out of the video. So what I wanted to do here is just show you a condensed version of that, because it references a pretty clever argument by Mark Levi, and it also gives a sense of completion to the brachistochrone solution as a whole. Consider when light travels from air into water. The speed of light is a little bit slower in water than it is in air. And this results in the beam of light bending as it enters the water. Why? There are many ways that you can think about this, but ...
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So, in my video with Steve Strogatz about the brachistochrone, we reference this thing called Snell's Law. It's the principle in physics that tells you how light bends as it travels from one medium into another, where its speed changes. Our conversation did talk about this in detail, but it was a little bit too much detail, so I ended up cutting it out of the video. So what I wanted to do here is just show you a condensed version of that, because it references a pretty clever argument by Mark Levi, and it also gives a sense of completion to the brachistochrone solution as a whole. Consider when light travels from air into water. The speed of light is a little bit slower in water than it is in air. And this results in the beam of light bending as it enters the water. Why? There are many ways that you can think about this, but ...
