Okay, let's talk about this idea of going from higher index to lower index. And let's talk about something called total internal reflection. So in our pool, when we had an interface. And we took, let's say we take a flashlight. Okay and we take it underwater with us. Here's our flashlight We're going to shine it towards the surface. We know that that light ray is going to bend. And it will bend away from the normal. So there is the surface normal. If this is water and this is air out here, then this thing will bend away from the normal. So it bends like that. But what happens when I start to increase this angle? In other words, let's move my flashlight up to this position. Now let's shine that ray at the surface. And I'll try to do it in a different color. Where is the light going to go? Well, it again bends away from the normal and eventually it's going to go right along the surface. And if I keep going. If I keep moving my flashlight up, eventually I'm going to get to a position where the light never leaves the water. I can't bend any further away from the normal and so all the light does that. That is what's called total internal reflection. Now total internal reflection only happens when you go from high index to low index. It happens when that transmitted ray equals 90 degrees. So let's see if we can write this out mathematically. We know that Snell's law holds. n i sine theta i equals n t sine of theta t. n i, in this case, was water. Theta i is the incident angle but at a very special angle called the critical angle. The transmitted ray is at 90 degrees. What is the sine of 90 degrees? Is it zero or is it 1? It's 1. So we get n i sine theta c equals n t. Since we're just multiplying by 1. Now you can identify what this critical angle is. Theta c is equal to n t over n i. And then, I better move that over because we got to write the arc sine in there. Arc sine of n t over n i. If this is water and air, let's calculate what theta c is. And you guys punch it into your calculator. So we're going water to air. Theta c is equal to arc sine of n t. Remember this is what it's transmitted into. Which is air. So that is 1. n i is what it came from, which is water. 1.33. So what is the arc sine of 1 over 1.33? Sean, do you have a number for us? >>48. >>48.75 degrees. So this orange one, which is that? The critical angle. Is 48.75 degrees. Anything higher than that, namely the pink one, you don't have the light exiting the water. It all stays inside the water. And this is a really fun experiment to try. But next time you're at, you know, a swimming pool, and you can get the water pretty flat and calm. Go underneath the water and look across the pool. And what you'll see is if you look straight up you, can see the sky. As you start to look at an angle further away at that water interface, you got to do this underwater of course. As you start to look away you can still see the sky, still see the sky. And then when you get to this magic angle, 49 degrees, you can't see the sky anymore. Okay? The water surface becomes a perfect reflector. All you see then is the other side of the pool. It becomes a perfect mirror and it's sort of interesting when you do that. In fact, if you lay on your back underneath the water. And you hold your breath so there's no bubbles disturbing the surface. And you look straight up, you'll see a cone of sky above you. Then outside of that cone, it will be a mirror. You will see the bottom of the pool. It's really kind of a fun experiment to try. Where else do we see total internal reflection? One place you see it is in fiber optics. Fiber optics are pieces of glass, not water of course, but pieces of glass. And you want to keep light in the glass. How do you do it? Well, you come in at a very shallow angle. Such that when it hits the edge of the glass, it all stays inside the glass. It just bounces back and forth all the way down the fiber-optic length. This is, of course, the backbone of the internet. This is how you're seeing me right now. A lot of the signals that you're seeing me are coming through fiber-optic cables right now. But there's another example of total internal reflection and it's sitting right in front of us. This piece of glass, right here, has total internal reflection going on right now. Around the edge of the glass, there are strips of high-power white LEDs. That LED light is staying inside the glass. It's bouncing back and forth on the edges of this glass. And it's just going back and forth all the time. It doesn't come out of the glass, because total internal reflection keeps it inside the glass. Unless you do something to the glass. Unless you put something on the glass, then it will pull the light out. So for instance, if I take my hand and I put it right here. All of a sudden, you can see that light get pulled out. Okay? In fact, if you look closely, you can probably still see some of my fingerprints on the glass. Or you take a pen and you write on the glass and that ink will pull it out. And this is called frustrated total internal reflection. You've added something to the surface, which pulls that light out of the glass. And now you can see it.