Video: Reflection of Light

In this lesson, we will learn how to describe the paths of light reflected from specular and diffuse surfaces, applying the law of reflection.

15:17

Video Transcript

In this video, we’re talking about the reflection of light. It’s not something we may think about very often. But actually, the reflection of light is responsible for most of what we see in our day-to-day life. For example, consider this room with light coming in through the window and a lamp over there by the side of the couch. As far as our eyes are concerned, these are the only two light sources involved here. But nonetheless, we’re still able to see everything else in the room, the end table, the couch, the carpet, the picture on the wall. Each one of these objects is not itself a source of light. But we see it because light reflects off it to our eye. As we learn in this lesson how all this reflection works, let’s start out by considering the light itself that is reflected.

Light itself has always been a bit of a mystery to us. In some ways, it seems that light is a wave. One of the reasons for that is that if we send two separate light waves towards one another, they interfere, either constructively or destructively or somewhere in between, just like waves do. But at the same time, light also behaves in some ways like a particle. We see this in particular in an effect called the photoelectric effect. In this effect, we can send a single packet of light, called a photon, into a metal surface. And if that single bit of light, that particle, is energetic enough, when it hits the surface, it will cause the ejection of an electron.

Since light clearly has both of these properties, the ability to interfere with itself and the ability to eject single electrons, maybe for now, instead of saying that light is a wave and a particle, instead of saying that light is a wave as well as a particle, let’s put it this way. In some ways, light acts like a wave. And in some ways, it acts like a particle. When it comes to the subject of the reflection of light, in this case, it’s more helpful to think of light as a particle than it is like a wave. Specifically, we’ll imagine that light is a particle that moves in a straight line. That means whenever we see a bit of light, we’ll draw it like a ray, a line that’s headed in some direction. If this ray of light never runs into anything, say it’s just in our space, it will go on and on in that line forever. But if there is some object for the ray to run into, then all of that changes. Just like we would expect, if we were, for example, throwing a ball at a wall, just like that ball might do, the ray of light reflects. We could almost think of it as bouncing off of this object.

It turns out that when the light does reflect, it does so according to a very specific rule, known as the law of reflection. Here’s what this law of reflection tells us. It says that the angle at which a ray of light is incident on a surface, and we’ll see what that means in a second, is equal to the angle at which it’s reflected from that surface. To better understand this law, let’s consider another light reflection example. Say that we have some surface. It could be a tabletop or a piece of glass. It doesn’t really matter what the material is for the purpose of figuring out the reflection though. And let’s say that, onto this surface, we send a single ray of light. Now, the question is how will this light reflect off of the surface that it’s running into. In other words, how will the light bounce off of this surface on which we say it’s incident?

The law of reflection helps us understand this reflected angle. As we saw, this law refers to two specific angles. The first one is the angle at which this ray of light is incident on the surface. Here’s how we figure out what that angle is. First, what we do is we look at the line of our surface or the plane of the surface. And then, at the location where our ray of light hits or runs into that surface, we sketch in a line which is perpendicular to the surface. This is sometimes called the normal line, where here normal means perpendicular. This normal line is going to be very important because it’s gonna help us understand what is the angle at which this particular ray of light is incident on the surface. Looking at this sketch, two separate angles may stand out to us, either one of which can be considered the angle of incidence.

The first angle is from the surface of a material up to the ray. We’ll call that angle 𝜃 one. And the second angle starts out at the normal line and then goes down to our ray. And we’ll call this 𝜃 two. Now, either one of these angles, what we’ve called 𝜃 one or 𝜃 two, could be the measure of the angle of incidence of this ray of light. And notice, by the way, that if we add together 𝜃 one and 𝜃 two, then we’ll get 90 degrees. But anyway, what’s helpful to know at this point is that the angle that’s been chosen, by convention, to indicate what’s called the angle of incidence is what we’ve labelled as 𝜃 two. In other words, to measure the angle of incidence of a ray of light on a surface, we’ll need to measure the angle between the normal line to that surface and the ray of light incident on it. Oftentimes in symbolic shorthand, these angles refer to a status of 𝑖. And that’s the symbol we’ll use to indicate the angle of incidence.

Okay, we now know the angle of incidence of this ray of light, in terms at least of what it looks like on our diagram. But that still leaves the second angle which our law of reflection talks about, the angle at which the ray is reflected from the surface. And here’s where this law comes in so handy because it tells us that the angle of incidence, what we’ve called 𝜃 sub 𝑖, is equal to the angle of reflection. In other words, if we were to start at our normal line and measure an angle off that line to the right, which was equal to 𝜃 sub 𝑖, the angle of incidence, then that will be the angle of reflection, which we could call 𝜃 sub 𝑟. And it’s this angle that tells us just how this incident ray of light is reflected from our surface.

So as a quick recap of this law of reflection, when a ray of light is incident on a surface, that is, when it runs into a surface, then the angle at which that ray hits the surface, called the angle of incidence, which is measured off of the line at normal to or perpendicular to the surface, is equal, the law of reflection says, to the angle at which that ray is reflected from the surface. What we’ve called 𝜃 sub 𝑟, where that angle, just like the angle of incidence, is again measured with respect to the normal line. Using our symbols for the angle of incidence and the angle of reflection, we can say that the law of reflection is this mathematical statement. 𝜃 sub 𝑖 is equal to 𝜃 sub 𝑟.

One great thing about the law of reflection is that it always applies no matter what kind of surface our light is running into. Let’s consider what some of those surfaces might be. Imagine that you have some very smooth polished surface like a mirror. And you send a ray of light into it. But then imagine that you have a very different type of surface, an uneven one, say it’s rough sandpaper. For each one of these surfaces, the smooth and the rough one, our question is the same. In what direction will the reflected light travel? For both these types of surfaces, the law of reflection applies.

Considering our smooth mirror, we can sketch out a line in the plane of that mirror, where the ray hits the mirror. And then, at 90 degrees or perpendicular to that line, we can sketch in our normal line then measure the angle between that normal line and our incident ray. And we’ll call that 𝜃 sub 𝑖. And then, to figure out the reflected angle, we’ll measure the same angle off of the normal line, but to the right, where this is 𝜃 sub 𝑟, the angle of reflection. And then, we can sketch in our reflected ray according to this reflection angle. That’s the procedure for our smooth mirror surface. And actually, it’s the same procedure we’ll use for a rough sandpaper surface. For a rough surface, we’ll find out very precisely where this ray is gonna hit that surface. Then what we do is we sketch out our dashed line, which again is in line with the plane of the surface at that point, where the ray is going to hit it.

Notice that this dashed line we’ve drawn in at the point where the ray hits the surface is parallel to the surface. That’s important because we want this line to show us just what the angle of the surface is at the point where the ray hits it, not at any other point. With that line drawn in, we can then sketch in our normal line, at 90 degrees to the one we’ve just made. Then, on this sketch, we can identify our angle of incidence of our light ray, 𝜃 sub 𝑖. And then, to show the reflected ray direction, we’ll create an angle of the same measure off to the opposite side of the normal line. That’s 𝜃 sub 𝑟. We can then draw in our reflected ray, which answers our question of which way the reflected light goes.

Now, considering these two surfaces, the smooth and the rough ones, we can see that they’re very clearly different. One way to see that difference is to imagine sending in not one ray to these surfaces, but several parallel rays. That would look something like this. And let’s consider just how these rays would reflect off of these two different surfaces. In the case of our smooth mirror surface, all these reflected rays, which came in parallel to one another, would exit or reflect parallel with one another. They’d all be moving at the same angle off of this smooth surface. There’s a special name for this kind of reflection. It’s called specular reflection. This describes reflection where multiple rays come into a surface parallel to one another. And they leave that surface parallel. So that’s what these reflected rays would look like for our mirror. But now let’s consider our sandpaper.

For this surface, even though the rays did come in parallel, they definitely don’t leave that way. The first ray we had drawn in reflected like this, recall. But then, our second ray bounces off this surface here and then bounces off the surface again and goes off in this direction whereas our third initially parallel ray bounces off the surface and goes in this direction. So basically, they come in parallel. But they leave pointed every which way. This is known as diffuse reflection. The name comes from the fact that even if we shined a very bright highly directional light onto this rough surface, the reflected light will be spread out in every direction from that surface. It would be diffused.

An important thing to realize about both these types of reflection is that the law of reflection applies in both cases. The only difference is that when our surface is very smooth, like our mirror, then we don’t have to be very particular about where we choose to draw our line parallel with the plane of that surface because that plane is always pointed the same way. But on the other hand, with diffuse reflection, that point we choose matters a lot. When we drew our initial line in this case, we had to make sure we drew it at the exact point on that surface, where the ray hit it. That way, we could reflect the slope of the surface at that point. Of course, the slope of the surface was very different for these other two parallel rays. In the case of the second ray, it would look something like this and in the case of the third ray, something like this. The slope changes when the surface is rough.

We mentioned earlier that it’s the reflection of light that lets us see everyday objects, which themselves are not light sources. This means that whenever we’re seeing something which is not a source of light, what we’re really seeing is light that we could trace back to a light source that has bounced off that object. Let’s consider how this works when our surface, like it is in this case, is a flat mirror. Say that we have a big plain mirror on the wall. And we’re standing in front of it, so that our eye is at this position. And say further that there’s a flashlight above us shining a directed beam of light onto this mirror. The law of reflection tells us that the reflected angled of this ray will equal its incident angle.

Now, like we mentioned, in this case what we’re seeing is not actually the mirror. But it’s the light reflected by the mirror. In other words, our eye is looking at the source of this light, the flashlight. Interestingly, thanks to this reflection, our eye doesn’t see the flashlight where it actually is though. It sees it behind the mirror, along the line that reached our eye in the first place. So the image that our eye sees of this flashlight isn’t real. It’s called a virtual image.

This type of image, not a real one but a virtual one, is created whenever we see an object in a mirror. When we look in a mirror, the light that reaches our eyes, just like in the case of this flashlight, seems to our eye to be coming from a point behind the mirror. But we know that’s not where the object actually is. Therefore, we call this image a virtual image. Knowing all this about the reflection of light, let’s get a bit of practice with these ideas through an example.

What is the incident angle of the light ray shown in the diagram?

We have our incident ray of light here that reflects off of our flat surface here. And then, this ray drawn in is the reflected ray. On our diagram, this 35-degree angle represents the angle here between a reflected ray and the surface. We want to know what is the incident angle of this light ray. Now, the first thing we can do is figure out which part of our figure represents that incident angle.

At this point, it’s important to remember that the incident angle as well as the reflected angle of a light ray, by convention, are always measured with respect to the normal line to the surface the ray reflects off of. That means that this dashed line here, the normal line to the surface that’s perpendicular to it, is a reference point for the incident as well as reflected angles of this ray. The ray’s incident angle is measured from this normal line to the ray itself. And we can represent this angle symbolically as 𝜃 sub 𝑖. And then, the reflected angle of the ray, likewise, is measured from this normal line. We start at the normal line and go to the reflected portion of that ray. And this angle we can represent symbolically as 𝜃 sub 𝑟, the angle of reflection.

Now, there’s an important relationship between 𝜃 sub 𝑖 and 𝜃 sub 𝑟 that’s worth recalling. The law of reflection tells us that the angle of incidence of a light ray is equal to its angle of reflection. Written down as an equation, we say that 𝜃 sub 𝑖 is equal to 𝜃 sub 𝑟. Looking back at our diagram then, we can see that if we can solve for 𝜃 sub 𝑟, then we’ll also have solved, by the law of reflection, for 𝜃 sub 𝑖. They’re equal. So what is 𝜃 sub 𝑟, the reflected angle of this ray?

If we look at the plane of the surface that the ray reflects off of, we know that this plane is at 90 degrees to the line we’ve drawn, called the normal line. That means that this angle here that we’ve drawn in must itself be equal to 90 degrees. And with that being the case, we can now write an equation for 𝜃 sub 𝑟 in terms of these two angles, 90 degrees and 35 degrees. Looking at the diagram, we can see that 𝜃 sub 𝑟, whatever that is, plus 35 degrees is equal to 90 degrees. We can see that this reflected angle, 𝜃 sub 𝑟, plus this 35-degree angle must sum up to 90.

So to solve for 𝜃 sub 𝑟, let’s subtract 35 degrees from both sides of this equation. When we do, that term cancels out with the positive 35 on the left-hand side. And we see that 𝜃 sub 𝑟 is equal to 90 degrees minus 35 degrees and that that is equal to 55 degrees. Now, remember that we wanted to solve for the incident angle but that by the law of reflection, that incident angle is equal to 𝜃 sub 𝑟. Therefore, we can write that 𝜃 sub 𝑖, the angle of incidence, is equal to 55 degrees. And that’s our final answer.

Let’s summarize now what we’ve learned about the reflection of light. When it comes to the reflection of light, the most important principle to recall is the law of reflection. This tells us that the angle of incidence of a ray of light onto a surface equals its angle of reflection from that surface. We saw that the way to figure out these two angles, angle of incidence and angle of reflection, have to do with drawing a normal line to the surface that the ray of light bounces off of. Both angles are drawn starting from that normal line and then going until they reach the ray. Using these symbols, the law of reflection can be summed up mathematically by this equation. The angle of incidence is equal to the angle of reflection.

Furthermore, we saw that light can experience specular as well as diffuse reflection from a surface. Specular reflection occurs when the surface is smooth and diffuse when the surface is rough. And lastly, we learned that images formed by flat mirrors are called virtual images. This is because the image that our eye sees exists behind the mirror in virtual space.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.