In this video we're going to try to learn a little bit about reflection. Or I guess you could say we are going to reflect on reflection. I think most of us have a sense of what this is, but we'll try to get a little bit more exact about it. So there are actually two types of reflection, and everything that reflects is doing one or the other, or something in between. So we have two types. Let me draw them. So the first type, and this is kind of what we normally associate with reflection is specular reflection. And in specular reflection, let's say that this is the top of a mirror. This is the surface of a mirror. If I have a light ray coming in-- So let me draw a light ray coming in. And just to get the terminology right, this light ray coming in, this ray, is the incident ray. And it's the incident ray because it's the ray as it approaches the reflective surface. Let me write that down. That right there is the incident ray. It'll approach the surface. And you can almost imagine that it bounces off at essentially the same angle, but in the other direction. So then it'll hit the surface, and then it'll bounce off, and it'll go just like that. And then we would call this the reflected ray, after it is kind of bounced off of the surface. Reflected ray. And you may have already noticed this if you've played around a lot with mirrors you would see-- and we're going to look at some images. So you can think about it a little better. Next time you're in front of the bathroom mirror you can think about this, and think about the angle of incidence and the angle of reflection. But they're actually equal. So let me define them right here. So if I were to just drop a straight line that is at a 90 degree, or that is perpendicular to the surface of the actual mirror right over here, we would define this, right here, as the angle of incidence. I'll just use theta. That's just a fancy letter to show that the angle at which we're coming in, the angle between this ray and the vertical right there, that's the angle of incidence. And then the angle between that vertical and the blue ray right there, we call that the angle of reflection. And it's just a property of especially mirrors when you're having specular reflection. And you can see this for yourself at all the regular mirrors that you might experience is that the angle of incidence is equal to the angle of reflection. And actually we could see that in a couple of images over here. So let me show you some images of specular reflection, just to make it clear here. So you have some light from the sun hitting this mountain. And we're going to talk about diffuse reflection in a little bit, and that's what's happening. It's being reflected diffusely. That's why we don't see the actual image of the sun here. We just see the white. But then those white light rays, and they're actually being scattered in every direction, some of them are hitting the water. I'm going to try to match up parts of the mountain. So you have this part of the mountain. Let me do this in a better color. You have this part of the mountain up here, and the part of the reflection right over there. So what's happening right here is light is coming from that part of the mountain, hitting this part of the surface of the water. Let me see if I can draw this better. It's hitting this part of the surface of the water, and then it's getting reflected, specular reflection, to our eyes. And it's actually coming straight at us, but I'll draw it at a slight angle. And then it's just coming straight to our eyes like this. If our eye was-- Let's say our eye was here. It's actually coming straight out at us so I actually should just draw a vertical line, but hopefully this makes it clear. And what we just said, the angle of incidence is equal to the angle of reflection, so if you were to draw a vertical, and it might not be that obvious here, but this angle right over here-- Let me draw this a little darker color. This angle right over here, that's the angle-- Let me do that in a light color. This right here is the incident angle. We drew a vertical. And the angle at which the light ray is approaching the surface of the water, right before it bounces, that's the incident angle relative to vertical. And then this angle right here-- and I know it's hard-- it doesn't look like they're the same but that's just because of the perspective that we're dealing with. This is the angle of reflection. And they're actually going to be equal. And you could also make a similar case. And sometimes my brain has easier thinking about this. If this angle is equal to that angle-- and this is what's defined to be the angle of incidence and the angle of reflection-- we also know that this angle, right here, is going to be equal to that angle right there. And my brain sometimes thinks that because that's kind of the angle between the ray and the actual surface, but they're really the same notions. And obviously it's a different angle, but if this is equal to that then this is equal to that because these two are going to add to 90, these two are going to add to 90. So another way you could view it is-- So if we look at the surface of the water. Let me draw a line along the surface of the water. Another way to think about it is that this angle, this angle right over here, is going to be the same as this angle right over there. And you can also see it in this reflection right over here. So the light from the sun is going directly to the water here, and then getting reflected at that point on the surface of the water, and then coming over to our eyes. And so we could either say that this angle is equal to this angle, so the angle between the incident ray and the surface of the water is equal to the angle of the reflected ray and the surface of the water, or we could draw a perpendicular right over here-- I'm not doing that too well-- we can draw a perpendicular right over here to the surface of the water, and say that the incident angle, the angle of incidence right there between the ray and that perpendicular, is going to be the same as the reflected angle. And it's hard to see there, once again, because of the perspective, but hopefully that starts to make sense. And I encourage you, go to your bathroom and look in the mirror, and look at objects in the mirror, and think about the angle that the light from the object must be hitting the mirror for it to get to your eye, and where it's actually hitting the mirror. It's actually a pretty interesting thing to do if you're looking for things to do in the bathroom. Now all we've talked about is specular reflection, but the other type of reflection is diffuse reflection. And this is the type of reflection that it may not be as obvious to you that it's occurring everywhere you look. Diffuse reflection. And in diffuse reflection, because the surface isn't smooth, it's not what we kind of associate as a mirrored surface. So I'll draw it, I'll zoom in a bunch. So in diffuse reflection, maybe the surface looks like that, what happens is-- and let me be clear. In specular reflection any light ray that comes in like that, the reflection will come off at the same-- the angle of incidence will always be equal to the angle of reflection. This is for the situation of, say, a mirror. It'll always be the same. If I come in at a steeper angle, then I'll go out in a steeper angle, just like that. That's for specular reflection. For diffuse reflection all sorts of crazy things happen. And that's because we don't have this really smooth surface, or the molecules that make up the surface do crazy things to light. So if I come in in one direction, right over here, over at that point the light might reflect in that direction. Although if I come in at the same angle over here, now all of a sudden the light might go in that direction. And then if I come in at the same angle over here, now all of a sudden the light might go in that direction. And if I come in-- and I think you get the general idea here-- if I come in over here, now the light might scatter in that direction. If I come in over here at the same angle, now the light might scatter in that direction. So the general idea is, with diffuse reaction, the reflected rays are going in all sorts of crazy directions, and they're getting all mixed up. So think about here, if you had an image here of the sun, and I'm not drawing it in particular, but let's say that these rays right here are coming directly from the sun, then when they reflect it'll kind of preserve the image. You'll have the reflected image of the sun. But over here, if all of these light rays are coming from the sun, they're not all going off in the same direction. This will be a part of the sun, part of the sun. And it's happening at a really, really small level. So you're really just capturing the light, but you're losing all of the information from the actual image. And if you're wondering where diffuse reflection occurs just look around your room. Anything that's not a mirror is reflecting diffusely. It's diffusing the light. Do you see that here? The mountain right here is diffuse reflection. You have light coming from the sun, but that's being reflected in all sorts of crazy directions. So you don't see a reflection of the sky over here. The water here, that's specular reflection because it's so super smooth that it preserves-- The angle of incidence is going to be the angle of reflection. It's always going to be the same angle because it's a kind of almost perfectly smooth surface. The trees, that's diffuse reflection. And I also want to be clear on something like the trees. So on something that's white, and white is the entire spectrum of light-- and we'll do more videos on that in the future-- it's reflecting the entire spectrum. It's just mixing it all up so you don't see an actual reflection. But if you look at the trees, you have the entire spectrum from the sun coming down on the trees, but the trees themselves-- and you should watch the videos on photosynthesis-- they're absorbing every other frequency of light except for the greens you see. So they are just reflecting the green back to us. And they're doing it in a way they're diffusely reflecting it. So we actually don't see an actual reflection in those trees. And I'll just finish up with one kind of neat thing because it's kind of like playing billiards here, because you can actually have a double reflection. That's why I even had this image over here. The sun is being reflected on the water here, and then you have a reflection. This is a direct reflection of the sun, but this is a reflection of the sun reflected on the water right over here. So what you have over here is the light from the sun coming to this reflection, reflecting at that point on the water, then going to this point on the paddle, and then coming to our eye. But once again the angle of incidence in every situation here is going to be equal to the angle of reflection. Although the paddle looks like it's a little bit distorted here, so it's not a completely smooth surface, so it makes the math a little harder. But when you start thinking about this it becomes pretty interesting just to look at almost any reflective surfaces and to think about the actual angles.