ï»¿ When you think about light bouncing off of mirrors it of course bounces at the angle that it came in at. Law of reflection says incident angle equals reflected angle. But what if we have two mirrors at right angles? Okay, so let's take a mirror. And let's take a second mirror and put it right next to the first. And we'll put them at right angles to each other. Okay? So we've made this nice sort of assortment of mirrors here. What happens when a ray comes in? A ray comes in and it bounces off the first surface. And we know that it bounces at the same as its incident angle. And so it's going to look something like that. When it bounces off the second mirror it's going to bounce at an angle like so. And to make this really convenient let's do the following. Let's say that this angle is 45 degrees. And if that angle is 45 degrees then this angle is 45 degrees. Okay, and if those two angles are 45 degrees then those two angles are also 45 degrees. Okay everything adds up. The outgoing ray is in fact parallel to the incoming ray. You might have seen these before, okay. They have these in dressing rooms. And the reason that they put these in dressing room sometimes it's so that you can see your reflection the way other people see it. The bounce off the first mirror flips you from left to right. The bounce off the second mirror flips you back, right to left. So if you stand in front of one of these mirrors and you raise your right hand your image raises its right hand. It's a very nice way to see what you look like but there's a much more important feature here, which is the following. Let's say we didn't just do this in two dimensions. Let's say we did it in three dimensions. If you do it in three dimensions it's called a corner cube and let's see if we can draw it out. Okay, these are the mirror surfaces. And now any incoming ray will bounce three times and come out parallel. And this thing is called a corner cube. This last ray took a little funny jog there. Straighten that out a bit. Okay, it's called a corner cube. And it's used in physics quite a lot. But, you are in fact familiar with this device. Okay, I can guarantee you that at some point today, you have come across a corner cube in your regular daily life. Where have you seen one of these things? Where have you seen a corner cube at some point today? All right? The answer is anywhere you see a reflector like on a bike. Okay, a bike reflector has a whole bunch of little tiny corner cubes in it. All right? Why is that? Well, let's think about what happens. When you're driving in your car Here you are, sitting in your car. Okay, and you're looking out the front of your car. And my car is looking a little backwards, but that's okay. Here you are. These are the headlights on your car. Right here. When you're driving at night, and somebody comes by on their bicycle you would like to be able to see them. Okay, so here is the bike. Person riding along. Happy as can be. On the wheels of their bike, they have these little reflectors. And in that reflector are a whole bunch of these little tiny corner cubes. So, what's the point? The point is this. Light from your headlights will hit that reflector and it will come back on itself. Almost exactly. A little bit off. When it comes back, it just skims over the hood of your car past your headlights and comes to your eyeball. Okay? So that's the whole point of those bike reflectors. Take those headlights send it back to the person driving the car they can then see that it belongs to a bicycle. So it's kind of weird when you think about you're in your car. If somebody is in the car next to you and they have their headlights off they can't see the bike reflector. Okay? Only you can see the bike reflector because those headlights are coming straight back to you. They're not going to other people, they're coming straight back to you. So there's one more place where corner cubes are located. And this is very exciting, okay. They are located on the moon. Way back in the early 70s the Apollo astronauts went up to the moon right, when we "went to the moon" and they brought a whole bunch of mirrors with them. They brought a whole bunch of corner cube reflectors and they put them on the surface of the moon. And the idea was we're going to use these someday, for something important. And guess what? We are using them today for something important. We are taking these big lasers, just like these headlights, shining it at the mirrors on the moon and collecting the light that comes back down to us. And when we do that we can determine very precisely the distance from the earth to the moon. We know how fast light goes. We now know how long it takes in time to go there and back. And so you can measure the distance very precisely to the moon. And there was a talk recently about this and the precision of that measurement currently is 0.8 millimeters. We know the distance from the earth to the moon to within 0.8 millimeters. Which is sort of remarkable, when you think about it.