 So, we know that light travels slower when it moves through materials. The reason it does that is that it's interacting with those materials. And just to spoil things a little bit, light's actually an electromagnetic wave, and the reason it does that is that molecules are made of little charges that can oscillate, and so that when the wave comes through, it interacts with those oscillators. And it made me no surprise that the frequency that the light's oscillating at, and the oscillation of the molecules, matter. So when the light has a particular frequency, it's going to interact with certain molecules more than others. And the practical upshot of that is that light actually travels at different speeds for different colors. So different frequencies, different colors of the light, when they go through a material, often travel at slightly different speeds. So all these lenses are actually only going to have a particular focus for a particular color. Let's zoom in on a certain part of a lens. So if we just have a wedge of glass, say like this, that's called a prism. And if we shine light on a prism, we can see how the different colors of light split up. So if I have green light coming in at an angle, we know that at this interface, it's going to bend in because light's traveling slower in the glass. And then when it gets to this angle, it's going to bend out. And so my light is traveling through like that. However, supposing I have blue light, it's going to come in. And supposing it doesn't bend quite as much. So the change in speed isn't quite as dramatic. And it's going to diverge a little bit, spread out. And the angle's not going to change quite as much here either. And so it's going to spread like that. And so on for red, supposing red bends a little bit extra. Then what we get is we have things that are initially going in all parallel. But then the different colors spread out. And the different frequencies fan out. And what we've got here is a rainbow. And this is exactly how Newton found that white light was made up of different colors. He had a prism. He had sunlight coming through. And you can see the beautiful rainbow made. And this is exactly how actual rainbows are made. Except instead of glass, the prism is made of water. So it's water droplets. Actually, the production of rainbows in water droplets is a little bit more complicated because you often have multiple times when the light actually bounces around inside the water droplet. And the reason it does that is something called total internal reflection. Supposing you have a surface of a water droplet like this. And if we look at the normal vector, then if a light ray comes in really close to that normal vector, then it's not going to bend very much. This is going to bend a little bit. And if we have this is the water on the inside. And this is the air on the outside, out here. And we know that the light ray is going to speed up. And so if it speeds up, it's going to bend away a little bit. And we know how to work out the change in those angles. So the sign of the incident angle divided by the sign of the refracted angle is just the ratio of the speeds. So if the speed of light is V1 inside the water and a larger V2 outside in the air, then the ratio of the signs of the two angles is just the ratio of the two speeds. This is Snell's law. And you'll note that if we come in a little bit blunter like that, then we'll refract out that way and so on. And if we look at this, there comes a special angle at which if we were to come in at that angle, then we'd actually try and refract right along the boundary. So that's where we try and make the sign of the refracted angle equal to 1. And we know that sign can't get bigger than 1. So if our incident angle is any larger than that, something strange has got to happen. What happens is if you come into an angle that can't refract, then it just reflects. And indeed, you always get a little bit of reflection and a little bit of refraction, except when the angle is so big that you can't get any refraction. In that case, you get all reflection. And so what happens in water droplets is you often have a lot of these events where you get complete reflection, and this is called total internal reflection. And this is actually a way of making a very high-efficiency mirror. So some kinds of mirrors are actually based on using total internal reflection.