Hey y’all. I have a question regarding a post I saw on the internet somewhere, I can’t remember it exactly but I made a quick diagram of what it was about.
Say you’re at the beach on the sand, but a little bit down the shoreline, you see your friend struggling to stay above the water, and you want to get there to help them as quickly as possible.
https://i.imgur.com/4VlG4N2.png
You could just run/swim in a straight line towards them, but obviously you can’t swim as fast as you can run, so a straight line might not be that quick.
https://i.imgur.com/6ExnT9c.png
You could also try to run as close as you can to them on the shore to minimize the time you spend swimming, but this is a longer route.
https://i.imgur.com/hqyKyC1.png
The main point of the video is that as it turned out, the quickest route to save your friend actually follows Snell’s Law of Refraction, depending on how fast you can travel through the mediums of sand and water.
https://i.imgur.com/Swsguj6.png
This connection makes sense in my head, but at the same time I can’t really put into words why. I’m still really fuzzy with how refraction works as a whole, honestly. If someone could shed some light (haha) on how this works and how it connects to the quickest route between mediums, it would be much appreciated. Thank you! 😊
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Refraction of light: “Imagine a car driving on a straight road, and the front right wheel hits a patch of mud. That wheel slows down, causing the car to turn right. Similarly, when light enters glass at an angle, the leading edge of the light ray slows down first, causing the entire light ray to bend”
snells law is just z”you can’t measure the speed of you in water, why not measure the angle?” and all the time some angles are the same.
It’s because both follow the principle of least time, so the mathematics is the same. Light always takes the path of least time from point A to point B, regardless of the speed it might move through for each medium. Likewise, the best route to save your drowning friend is the one that takes the least time
Maybe I’m just restating what you already know, but the quickest route through the different mediums is just the combination of the amount of time it takes to get to the specific spot on the water line plus the time it takes to swim from there to the friend.
I hope for your friends sake this isn’t a time sensitive question.
Can you clarify if this is a physics question and the drowning friend is an analogy, or are you genuinely asking the best way to save a drowning friend?
youre refering to veritasium video “Something Strange Happens When You Trust Quantum Mechanics” start at 0:25
Sometimes you can describe light as a wave and sometimes you can describe light as a particle.
Both are valid.
Sometimes you end up with weird counterintuitive results though.
Like how would a photon know which path is the shortest in order to go through that path?
If you are the photon proxy on the beach you wouldn’t know which angle to run in order to reach your friend the fastest.
However light is not a like a person running on a beach, it does weird stuff like going in all directions at once.
Fermat (the guy of last principle fame) has another principle called “principle of least time” named after him that tried to explain it.
Basically, you have to envision the lifeguard as a wave not a ray to make them reach the drowning guy without having to think about it.
You get this sort of thing in math or physics occasionally where there is more than one valid way to think of something, but one way of looking at it sort of makes it look like inanimate objects or pure math has sort of precognitive ability.
(Aside: The book that the movie Arrival was based on by Ted Chiang sort of takes this weird perspective shift paradox to its ultimate conclusion by envisioning aliens who live with a perspective where they always know the future.)
Math is cool and all that, but having tried to run in sand before I think the correct answer (not the Snell’s law answer) would be to run straight to the edge of the water and follow the shore where the sand is at least damp, not as hard to run through, and then run towards your friend?
For example, this guy thought he was in shape, but he’s no match for sand: https://www.reddit.com/r/funny/s/Rcdouz2cLn
This is not the fastest way to answer your question, but Ted Chiang’s short story “Story of Your Life” (on which Arrival was based) briefly addresses the principle of least time!
Snell’s law attempts to minimize the action of the path. Since this is about speed in both cases it applies for both
With light, you might think of it this way: a sine wave arrives at a boundary and one point of the sine wave hits first and changes speed. A moment later another point hits but, because it’s stuck to the first point, it gets dragged around by it, like if you catch your toe and trip. The whole sine wave sort of spins around that catch point and heads off in a new direction. The amount of drag and curl is determined by how fast the light was going in the first medium and how fast it goes in the second one.
Not the best analogy but, hey, you’re five.
I just want to say that your devotion to explaining this, by making those drawings, is something I applaud.
Ah well I taught my kids that if there friend is drowning to stay clear cause they will take you down with them ….