What do Lifeguards, Lasers, and Archery Fishing Have in Common?

If you guessed the speed of light then you'd be correct! At least in water that is. In this mathematical exploration we tackle why objects appear distorted when looking into water and show how optimizing the path of travel for a beach lifeguard relates to how light optimizes its path of travel in water. Turns out a laser, cup of water, and calculus is all you need to understand this phenomenon and better your fishing game and lifeguard skills!
Math The World is dedicated to bringing real world math problems into the classroom and answering the age old question “when will I ever use this?”
We use unique topics for algebra, trigonometry, calculus, and much more and go beyond context problems and use a technique called mathematical modeling to find solutions to real world questions and real world problems. These videos are great for students who plan to enter technical fields that require real world problem solving, and can be a great resource for teachers looking for ways to bring real world contexts into their classroom.
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Created by Doug Corey
Script: Doug Corey and Jade Gregg
Audio: Doug Corey
Animation: Jade Gregg
Editing: Jennifer Canizales
Music: Coma Media
© 2023 BYU

[@northernlight1000]

I love how "homemade" these videos feel! They encourage me to do the math and stuff along at home myself, best way of learning

[@HadesKerbecs1]

This is the same thought process we used to derive snell's law. The refractive index exactly describes the ratio between the two speeds (but as the inverse). Amazing that you got so close to the actualy value with a simple experiment.

[@MathTheWorld]

Yes, I thought of having a follow up video to show how to get to Snell's law from what we did. Maybe I still will. It would have worked well to put it in this video, but we try not to cram too much in or make the vids too long.

[@jcorey333]

This is such a cool video! I love the fact that light "knows" the ideal path to follow. Physics is interesting.

[@jacobmohler3677]

These videos are so well done, and this channel is criminally underrated.

[@blitzvii322]

Wait, can this experiment also check for the speed of light through other mediums? Like maybe oil or some other transparent liquids? I doubt the speed will be the same

[@jadegregg8773]

Great question! I would think so! While doing research for this video I stumbled across a lot of information about the speed of light through glass as well which I thought was interesting. I wished I had a glass block to test it out on.

[@duckymomo7935]

isn't this calculus of variations and path of least resistance/path of least time?

[@finminder2928]

How fast would a lifeguard need to do calculus to save any time? 😂

[@kenrickman6697]

That is an integral part of being a lifeguard.