Absolute & relative refractive index

- [Narrator] In this video I want to clarify the difference between absolute refractive index and relative refractive index, okay? So let's start with just refractive index. I like to think of refractive index as a measure of how slow light travels in one medium compared to another medium, and we'll treat that second medium as a reference medium, okay? So we'll take some examples and then this statement will be super clear to us. So let's say we have been given that the refractive index of glass with respect to vacuum. That's how we usually write refractive index, N is the letter we use for refractive index, is given as one point five. Now, what does this mean? Well if you go back to the definition, this number is telling us is a measure of how slow light travels in glass, because glass is our medium, compared to vacuum. This time, in this example, vacuum is our reference medium. So in other words, this, this thing is telling us that the speed of light in glass is one point five times slower compared to speed of light in vacuum. Now I think this will make more sense if I write it down mathematically. This means speed of light in glass equals speed of light in vacuum. See one point five times slower compared to vacuum so it's speed of light in vacuum, which we'll usually write as C, don't worry too much about that, that's speed of light in vacuum. Divided by one point five. Why are we dividing it? Because it's that much slower. You get that? And by the way, we know speed of light in vacuum, that's a very famous number isn't it? So let me just substitute. If we substitute we get three times 10 to the power eight, that's the speed of light in vacuum, meters per second, divided by one point five. Refractive index by the way has no units. And if you divide it, see what you get. You get three divided by one point five so we get two times, three by one point five is two, two times 10 to the power eight meters per second. So you immediately see, what refractive index is used for. It's used to calculate the speed of light in different media, all right? So hopefully this statement is making more sense now. Let's take another example and I want you to try this one. Let's say it's given to us that the refractive index of water, with respect to oil is two. Can you think of what this means? I want you to try and pause the video and see if you can think about what is the meaning of this statement and see whether you can write an equation like this over here. Go ahead, pause the video and try. All right if you've tried, let's see. Well this time, this is saying that the speed of light in water, because our medium now is water, is two times slower compared to speed of light in oil. This time our reference is oil. So again, if you write it down mathematically, this tells us speed of light in water is two times slower compared to oil, that means it's speed of light in oil divided by two. Hopefully you got this. You see we did the same thing that we did over here. We, we took the speed of light in our reference medium and we divided by the refractive index, that's what refractive index is all about. Now since I don't know what the speed of light in oil is, I don't even know which oil you're talking about, since I don't know that, I can't substitute it. If I knew it, I could substitute just like what I did over here, and then we could get the answer, but I don't know it so I'm not going to substitute. And if you, if you ask me, that's pretty much it. That's what refractive index is all about. Now, you can see one thing from this by the way. Notice that when we definite it with respect to vacuum, since we know what the speed of light in vacuum is, it's a pretty famous number, it's very easy to calculate there, velocity. We can immediately calculate the speed of light in glass, or in that medium. But when we are defining the refractive index with some other medium, and if we don't know what the speed of light in that medium is, then that's a pretty useless number. I can't do anything with it, unless I know the speed of light in other media. And it's for that reason, most of the times, and almost all the cases, we're going to define refractive index with respect to vacuum, because we know what the speed of light in vacuum is, so that number becomes super useful to us, okay? And since it is so common to use vacuum, we just start, let's drop that letter, let's not even specify it, right? We're gonna use, we're gonna make vacuum as a standard. Which means just to keep it short, because we're gonna use it over and over again, we're now going to, we're not even going to mention that it's vacuum, but it's there all right? So whenever we don't mention the second medium, it's understood it's vacuum. So in your textbooks you'll just see refractive index of glass is one point five. And you may be wondering, well what are we comparing with? It's vacuum. If it's not mentioned, it's vacuum. And if it's some other medium, it will be mentioned, all right? So just to give you another example so that we are super clear on this, if it's mentioned somewhere, I'm gonna write it down over here, that refractive index of water is one point three three, that's it, just this much. What does this mean? Well, since the second medium is not mentioned, it means this is the refractive index of water with respect to vacuum is one point three three. That means speed of light in water is one point three three smaller, or one point three three times slower compared to the speed of light in vacuum. And using this number, I can now figure out what the speed of light in water is. So that's pretty much what refractive index is all about. You may be wondering, what's this absolute and relative refractive index? Actually it's a very, very small thing, that's why I kept it til the end. So you see, when we are measuring the refractive index with respect to vacuum, and we choose vacuum as the reference medium, we just call it as absolute refractive index. So this is absolute refractive index. Similarly, this is also absolute refractive index. And when we measure the refractive index with respect to some other medium, we call it as relative refractive index. That's it. It's just names that we have coined. Nothing else, okay? And that's important because I used to think that I should genuinely think that these are two different kinds of refractive indices that we have, but no, they're just names that we give depending on what we're using as a reference. If you're using the standard reference as vacuum, and by the way, some people instead of saying vacuum they will say air, that's also fine, because the speed of light in air is pretty close to three times 10 power eight meters per second. So in most of the times, unless and it is specified, most of the times vacuum and air mean the same thing for us. I know in reality it's not, but from the refraction point of view, vacuum and air is pretty much the same. So to quickly summarize what we learned in this video, refractive index is a number that tells us how slow light travels in a, in a medium compared to some other medium, and when we are comparing with vacuum, or air, we usually don't write that, because it's a standard, it's like it's understood, and we call that as absolute refractive index. And when we're comparing with some other medium, then we'll call it as relative refractive index. And to be honest, most of the times you won't even use these words, all right? So over here, we will just say refractiveness of glass is one point five, that's it. And over here we'll say refractiveness of water with respect to oil is two. That's it, all right? We won't explicitly mention absolute or relative, but now you know the meanings of those words.