I just love Snell’s Law.
It relates to something simple in our childhood experience, when we put a pencil in a class of water and the pencil looked magically bent from the refracted light. Then when you find out why when you’re older, it just keeps getting more awesome and seemingly magical, because it’s as if the light ‘seeks out’ the fastest path going through a faster medium (e.g. air) and then a slower medium (e.g. water): the light takes a bent path that goes a little farther in the fast air, and through a shorter amount of water that it has to swim through more slowly. That’s known as Fermat’s Principle.
That math is simple, except for one bit of baby (1st semester) calculus at the end, but if you don’t know calculus, no problem, and that’s just one small step. And you can think about it as a roller coaster, that you want to find the point at the bottom of the hill, that minimum point where the roller coaster is flat; and doing the calculus trick of taking a derivative and setting it to zero is just a way to find that lowest point at the bottom of the roller coaster dip. And in this case, the bottom of that curve is the path that takes the shortest time for the light to travel. Other than that, the math is simple and clear. I just think this is one of the most elegant formulas that describes a cool real-life experience and has such a pretty and simple result.
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