Returning to Classics
Tom Eigelsbach describes the simple elegance of Snell’s Law. Refraction, or the bending of light as it enters a medium where its speed is different, is responsible for the way images form from the lens in our eyes.
Originally shared by Tom Eigelsbach
I just love Snell’s Law.
It relates to something simple in our childhood experience, when we put a pencil in a glass 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.
#scienceeveryday #sciencesunday #math #mathematics #physics
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I do not like Fermat’s principle. It gives too much “intelligence” to something that requires none. Light is not TRYING to get to point B the FASTEST. Light doesn’t make decisions. It is simply the math that if something gets in the way of light’s path that causes it to move slower that it strays from it’s original path and bends based on the angle of incidence.
Yeah, That meaning is back to the future.
Better is to read QED: The Strange Theory of Light and Matter by Richard Feynman. It explains the bending of light from the perspective of quantumelectrodynamics — and it actually makes sense! (Well, as much as QED makes sense…which is not much. 🙂 )
hmmm…. light travels a geodesic. When you toss out time … it makes more sense. see:
and keep in mind that s is the spatial density of two different spaces.
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