Dispersion of light in prism
Prism & dispersion of light
- [Instructor] Let's do a classic experiment. We will stare at this tube light through this plastic transparent ruler first from the middle section and then from the top part of it. Now since my camera has a big lens, we can see both at the same time. So this is the image of the tube light from the middle section and this is the image of the tube light from this top edge section. And if we decrease the exposure, we can see that the tube light from the top looks colored. But when seen from the middle, it doesn't look colored. So the question is why is this happening? Here is a better image. Why is that when you look through the ruler from the top the same tube light looks colored but from the middle it doesn't look colored. So to figure this out, let's look at this whole situation from the side view. Look at it from the side. So I'm going over here. So here is that side view. This is the ruler. This is where our camera was placed or where our eyes are. And here's the source of light. So if you draw a couple of rays of light, one towards the middle section of the ruler, and one towards the top section of the ruler, why is that we are seeing no colorations here but we are seeing some colorations over there. So what's the difference between those two? So let's zoom in and figure this out. If we zoom in enough we can see the difference. The major difference is that over here notice the two sides are parallel to each other All right? But over here the two sides are not parallel to each other. So for some reason there are no colorations happening when white light passes through a parallel sided medium. But there are colorations when white light passes through a non parallel side. And that what's we need to figure out as to why that is happening. So first we will look at what happens to light as it passes through the top part of this ruler which has non parallel sides which we have drawn over here. And then we'll see what happens to that as it passes through the parallel side of the medium. All right now whenever we have non parallel sided media, in general such media are called as prisms. But most of the time when we use the word prism what we mean is a triangular prism. So if you are looking at a triangular prism from three dimensions, it will look somewhat like this. You see two triangular faces that's why it's called a triangular prism. One of the faces seen over here we're looking at the same prism from the front. And the two triangular faces are connected by notice three rectangular faces. You can see one rectangular face here, one rectangular face over here, and one rectangular face at the bottom over here. All right so this prism is in general called a triangular prism. Tri-angular prism. And the angle made by these two rectangular faces this particular angle is usually called the angle of the prism. So this over here is the angle of the prism. And over here, this is also a triangular prism. If we look at it carefully this is a triangle. It's a right angle triangle. So this is a triangular prism. And this now becomes the angle of this prism. All right? So let's see what happens when a ray of light passes through a triangular prism like this. So imagine that there is a ray of light coming in from the left. So let's zoom in over here and draw that way. So let's imagine we have a ray of light that's coming in this way from the left. Now to understand what happens to this it's going to bend because it's changing medium. So to understand how it bends, we usually drop in normal in there. So we will draw a line perpendicular to this so that's going to be our normal let's say it looks like this. And now, this ray of light is moving from vacuum into some other medium like glass or maybe plastic. Whatever. And as a result, the light is going to slow down because light has the fastest speed in vacuum. And as light slows down, it will always bend towards the normal. And this is something that we have seen in videos on refraction. So if you need more clarity on why that happens, it would be a great idea to pause this video and go back and watch that video and then come back over here. So, it's going to bend so it was going this way but now as it slows down, it will bend towards the normal like this. Oops, wrong color. So it's going to bend towards the normal. And now again it hits the interface and so it's again going to bend. So let's again draw another normal. So if we draw another normal. Now it's moving from this medium into vacuum. That means it's going to speed up. And when light speeds up, it's going to bend away from the normal. So this ray will now bend. It was going this way, it's now going to bend away from the normal. So this way. And there we have it. That's what light does as it moves through this prism. And what we can see, is that this light has bent twice in the same direction. Both cases it bent downwards. And as a result the emergent beam is deviated from its initial path. Can you see that? Initially the ray of light was moving in this direction but that ray is no longer moving in that direction. It has now deviated by some angle like this and it's now moving this way. And that's what prisms do. Prisms deviate the path of light when you enter in light on it. And so you might be wondering what's this got to do with what we saw. Well, remember that this is one single color of light. But if we enter in white light, like what we are having over here, then white light is made up of different colors of the rainbow. Seven colors of the rainbow. And we've see in previous videos that when white light passes from one medium to another then different colors bend differently. The red color will bend the least and the violet will bend the most. And as a result, as they bend differently eventually when the colors come out they will all be separated. So let's look at that. So here's what it would look like. This figure is a little bit exaggerated. But you can see this is the white light both rays have bent downwards as we saw over here. But because red bends the least it has bent a little bit and violet or blue, I've shown blue over here, bends the most. And so as a result, notice the colors have been separated out. And that's why we see coloration from the top. Well why wouldn't the same thing happen over here? Well let's now talk about what happens when you incident light over here. Let's first ignore this portion. Let's only consider a single color. And we have seen what happens before. We have seen that when you enter in light on a parallel sided medium, the emergent ray is parallel to the incident ray. In other words, the emergent ray is in the same direction as the incident ray. And this happens because over here light bends towards the normal, then it bends away from the normal. And since the two sides are parallel the two bendings cancel out. And as a result, this emergent ray becomes parallel to the incident ray. That's the big difference between this and this. Over here because they are angled the two sides are angled, the emergent ray doesn't is not parallel to the incident ray. All right? And so now if we were to replace this with a white light, what we would see is dispersion. So let's replace that with a white light and see what happens. So if you replace it with a white light, again just like what we saw over here we see that the red bends the least and blue bends the most but because the emergent rays have to be parallel to the incident ray, notice the red and the blue will emerge out parallel to each other. Right. So that's the big difference over here red and blue are not parallel to each other. But over here, they are parallel to each other. And because the colors are parallel to each other over here, when we look at it we don't see any colorations. We just see white. But why is that exactly? This will make a lot of sense if we remember one important detail. That in reality, we don't just get a single ray of light. We will always get multiple rays of light. So let's draw one more ray of light and see what happens. If we were to draw one more ray of light at the bottom there are a couple of ways in which we can convince ourselves that we won't see any colorations. One way to convince is we can see that because we have two parallel rays of light, if these rays of light were close to each other, then can you see that the blue and the red would overlap with each other? Similarly if we are to draw another parallel ray, another white light maybe its yellow will overlap with the blue over here and if we draw another one, its green might overlap over here. So, in short, what's happening is if we were to consider all lots and lots of rays in between and if we were to consider all the colors, then because these rays are all parallel to each other, they would always keep overlapping. All the colors would overlap. And that's why we would just see white light. But over here, that won't happen. So let's consider another ray over here as well. The major difference is the colors are not parallel to each other. So they won't stay overlapped. You see, even though it's overlapping over here, eventually it separates out. And that's why blue and the red would separate out when seen from here. Another way to convince ourselves that this is really happening is just to go one step further. And personally I like this, okay. So let's figure out what happens to these rays as they enter into our eyes. Because that's really what matters. Right? Well that's what we'll do over here. Let's go down to where I have drawn eyes over here. Notice that when these rays hit our eyes our eyes basically have a converging lens and a retina. All the colors, all the rays are parallel to each other. And as a result of all parallel rays are incident on our eyes, you may recall they will all get focused at one single point. Remember, all parallel rays will get focused at a single point. Now where they get focused, that depends upon the angle that these rays make with the principle axis. But what's important is that they are getting focused at a single point. And as a result, we just see a white dot. And that's why we won't see any colorations. Because the emergent rays are parallel to each other. On the other hand, over here if we were to consider the rays of light, red color comes in at one particular angle and so these rays will get converged at one single a spot. But blue rays are not parallel to these. So they come at a different angle. And so they will get focused at a different point. So hopefully this convinces us that when we have parallel rays colorations, colors are coming out parallel. We don't see the colors. But when they do make angles with each other, we do see them. So long story short, when light passes through a prism, the emergent ray is not parallel to the incident ray. And that's why when we have white light, the colors separate out. But when white light is incident on a parallel sided medium, the emergent ray is parallel to the incident ray, that's why all the colors come out parallel to each other and hence, we don't see the colorations. That's the reason why we don't see any colorations when look from the middle part of this ruler, but we do see the colorations when we look from the top side of the ruler.