Hey Crazies. If you haven’t heard, light bends when it passes from something like air into water or glass. The result is weird optical illusions like this. In true Science Asylum style, we’re going to question everything. Let me show you how deep this rabbit hole goes. This episode was made possible by generous supporters on Patreon. Alright, let’s start with a basic line of reasoning. ATV clone is driving along the concrete when he suddenly encounters some mud. As you can imagine, this noticeably slows the ATV, but not all at once. The front right tire slows down before the other three tires. That means there’s a speed imbalance on either side of the ATV, which causes the ATV to turn. Its path becomes bent. What’s this have to do with light? I’m getting there. Chill out! Light seems to do the same thing. Let’s say a drone is hovering in the air near my Scuba Clone. The light that gets to his eyes isn’t going to be the light that went in a straight line. See, light travels at a different speed in the air than it does in water. Well, not really, but it’s useful to pretend that it does. Light certainly seems like it slows down, at least on our level of existence, so it’s path is going to bend just like the ATV’s path did. Just go with it. The light that was originally headed for Scuba Clone’s eyes doesn’t make it there. It gets bent away. We call this refraction, which comes from the Latin word “refractio” meaning “broken up." The light that enters his eyes actually came from over here, which means he doesn’t see the drone where it actually is. Wait, what?! Chill out and let me explain! Aye yai yai. We judge where things are by subconsciously assuming light travels along a straight line. It’s called line of sight. However, that’s not always the case. So, when we see light coming at us from a certain angle, our brains assume it never bent. The light is interpreted as if it was always traveling in a straight line. Scuba Clone sees the drone over here. This even explains the straw illusion at the beginning of the video. If we look at this from above, the straw scatters light in all directions, but the light headed directly toward our eyes doesn’t ever make it there. The light that actually gets to our eyes came from this direction. But our brain thinks it came from a different direction. We see the straw in a different place. Optical illusion explained! How are you calculating all those angles though? Snell’s law! We’ve got the incoming angle on one side and the transmitted angle on the other. This “n” is called the refractive index. That’s just a number you look up in a table somewhere, like this one on Engineering Toolbox. Each material has its own refractive index and how they compare controls the bending of light. A change in the incoming angle, means a change in the transmitted angle. That refractive index is also related to the apparent speed of a light beam in that material. Speaking of speed, there might be a better way to look at this. Let’s say our drone from earlier is being flown by Drone Clone when it runs out of energy and begins falling into the lake. Wanting to get there as fast as possible, his immediate thought is to run in a straight line. Unfortunately, when he reaches the water, it slows him down and he can’t get there in time. Goodbye drone! A straight line might be the fastest path if you’re running through the air the whole time or even the water the whole time. But, if you have to travel through one and then the other, a straight line is not the fastest. This straight line is the shortest distance, but that doesn’t mean it’s the shortest time. Drone Clone can actually get a faster time by staying out of the water a bit longer, since he runs faster through the air. But, that might give you the impression that he needs to stay in the air as long as possible, which isn’t true either. That path is too big of a distance. The fastest path is somewhere in between. That’s the one that balances distance with speed, something like this. A similar thing happens with light. The path light takes is described by something called Fermat’s Principle, which states that light will always take the path that requires the least amount of time. Not the shortest distance. The least time. Light does what Drone Clone did without making any conscious decisions of any kind. But why though?! Why do those two laws work that way? Quantum mechanics. Here we go again. Let’s ask ourselves a question: What if light takes all possible paths, not just the least-time path? I mean, we know a beam doesn’t do this, but maybe individual photons can? Somehow? Alright, let’s take another look at Scuba Clone. We know light travels from the drone to his eyes, but we don’t actually know the path. All we really know is that it started at the drone and ended at his eyes. Each photon could have taken any path between those two points. We might secretly hope it’s the least-time path, but we don’t know that for sure. See, a photon's behavior is described by a wave, a wave of probability. And, according to quantum mechanics, all of these paths contribute to that probability. Yes, all of them! We used this same technique in our video about mirrors. If you’re getting uncomfortable, you should go watch that. I'll wait. Ok, welcome back. Rather than deal with wave mechanics, we’re going to imagine the photon’s wave is a little arrow called a phase vector or phasor for short. Over time, that arrow spins around at a pace given by the frequency of the photon. Visible light frequencies are pretty high though, so this arrow is spinning around, like, crazy fast. Fast fast! Ultimately, each available path for the photon takes a different amount of time, so those spinning arrows end up in different orientations when they’re done. To find the total probability that a photon will reach Scuba Clone’s eyes, we need to add all these arrows together. We do that by placing them all tail-to-head just like we’d add regular vectors. But, the arrows caught up in the spirals tend to cancel themselves out, leaving only a few paths to contribute in any noticeable way. Those are the ones near the least-time path. Fermat’s principle just comes from the probabilities of photons. It’s just probabilities. But that’s just a math trick, right? The photon is really only taking the least-time path, right?! Nope! All the paths matter and I can prove it. Let’s keep things simple and say there’s a laser and a detector on opposite sides of the screen. Quantum tells us we must consider all paths between the laser and detector. It’s just that the probabilities of most paths cancel themselves out, leaving only the least-time path and the paths nearby. But, what if we could slow some of those photons down by just the right amount. The amount of time each path takes looks something like this. The center path is the shortest time and they get progressively longer the farther they are from the center. We know from earlier that a material like glass will slow the light down, so we can adjust the timing if we just put some glass in the way. Adding glass along the short path means the time it takes a photon to travel that path is longer. You can see the graph has changed. Now, what we want is for more of the paths to contribute to the probability. We want the timing for a bunch of the paths to be the same. That way, they’ll add together instead of canceling each other out. Each path needs a different time adjustment, which calls for a different amount of glass. We get a device that looks like this. It’s just a lens. We just used quantum mechanics to explain how lenses work. Photons have many paths available. A lens just changes the travel time for each of those paths. That makes their probabilities add together differently and more paths contribute in a noticeable way. That’s why this shape focuses light. Kind of cool, huh? We’ve seen that refraction, or the bending of light, can cause all sorts of optical illusions. Like this famous one with the straw. We could explain it with Snell’s law or even Fermat’s principle of least-time. But why those laws work comes down to quantum mechanics. Light is made of photons and photons are a quantum mechanical object. Ultimately, they’re probabilistic. Those probabilities help us explain refraction at multiple levels of complexity. They can even explain how lenses work. It’s all really the same behavior. It’s all about probabilities. So, got any questions about refraction or just light in general? Please ask in the comments. Thanks for liking and sharing this video. Don’t forget to subscribe if you’d like to keep up with us. And until next time, remember, it’s ok to be a little crazy. The featured comment comes from Tom Kerruish. Ka-rew-ish? Ka-rewsh? Why look up the refractive index when you can just calculate it? Laziness? Ok, Tom’s got a point though. You can calculate it from the material’s EM field constants. The equation looks like this. Anyway, thanks for watching!
