Feynman’s Lifeguard : Refraction

lifegA girl swimmer is in trouble and the lifeguard has to save her. Naturally, he needs to get to her in the shortest time possible. He can run on the sand faster than he can swim, so he must spend as little time in the water as possible. One possibility is to run along the shore until directly opposite the drowning swimmer, and then swim from there, as in path A. The trouble is that this path is very long. An alternative approach would be to take the shortest  path which is the straight line between him and the drowning girl. However, with this path he spends a fair bit of time swimming. It turns out that the correct path for optimising the time it takes is the one that is a compromise between paths A and B, namely path C in the figure. Given the relative speeds on the sand and in the water, there is a specific angle through which he has to turn or to “refract” in order to have the greatest chance of saving the girl.  Aww. Nice. Thanks to Richard Feynman for this – the guy who made physics look easy.

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