 Let's explore the ideas of absolute and refractive indices by solving a few numerical. So here we are given light travels traveling at 3 times 10 to the power 8 through vacuum of outer space falls on a thick glass window of a space shuttle. The glass has an absolute refractive index of 1.6. What is the speed of light inside the glass window? Let's start by defining what refractive index is. The refractive index of one medium, say glass, with respect to some other medium, say water, is defined as the velocity of light in water divided by the velocity of light in glass. Important to note that whichever medium you're comparing with with respect to that medium's speed of light comes in the numerator. That's the important one. This is called relative refractive index mainly because we are measuring the refractive index of one medium relative to another medium, relative to water. Then what is absolute refractive index? Well, you can also measure refractive index of glass with respect to vacuum. That would be, just like over here, speed of light in vacuum divided by the speed of light in glass. And notice, whichever medium you're comparing with relative to that medium's speed is coming on the top. Now when you're comparing with vacuum, we just call it absolute. That's it. So remember, absolute means you're comparing with vacuum and we often don't write it. It's understood. So we write it this way. And so in the problem, refractive index of glass with respect to vacuum is given to us as 1.6. Now can you pause and see if you can try to solve this problem yourself? All right. So we are given refractive index of glass is 1.6. The speed of light in vacuum is three times 10 to the eight meters per second. And we are asked to figure out what is the speed of light in glass. Well, I can use the absolute refractive index formula. So I get 1.6 equals 3.0 times 10 to the power eight divided by Vg. And from this, I get Vg as 3.0 times 10 to the power eight divided by 1.6. And that happens to be, if you calculate it, 1.88 times 10 to the power eight meters per second. And that's our answer. And now you can also note one more cool thing. See this number tells you how much the light slows down in glass. And the number is 1.6. It means that in that medium, light slows down 1.6 times compared to the first medium. That is the vacuum. And that's the meaning of the word refractive index. It's a measure of how much light slows down in one medium compared to the other medium. Okay, time for a second problem. Why don't you pause the video again, give this a read and see if you can solve this yourself. All right. This time, we are given the speed of lights in two media, water and sugar solution. And we're asked to find the refractive index of sugar solution with respect to pure water. So refractive index of sugar solution with respect to water, that just like over here is the speed of light in water, remember, which your medium is over here, which you're comparing with that comes on numerator divided by the speed of light in sugar solution. And both the numbers are given to me. So velocity of light in water is given to me as 2.26 times 10 to the power 8 divided by velocity of light in sugar solution is given to me as 2.08 times 10 to the power 8. Both are meters per second. And so what do we get this cancels this cancels and we end up with 1.09. So that is the refractive index of the sugar solution with respect to water. And again, what does it mean? It means that velocity of light in sugar is 1.09 times slower compared to that of water. Let's do a third one. We are given relative refractive index of water with respect to diamond. They're also given of water with respect to amber that is given. And we are asked the relative refractive index of diamond with respect to amber. This is different. This looks a little tricky, but let's get back to our basics. So we are asked, what is the refractive index of diamond with respect to amber? Well, from our definition, we know that it is the speed of light in amber because remember, whichever you're measuring with respect to that speed comes on top speed of light with respect in amber divided by speed of light in diamond. I know that, but speed of lights are not given to me. Instead, what's given to me are two more refractive indices. Let's just write them down. So we are given the refractive index of water with respect to diamond. And we know that by definition, that will be the speed of light in diamond divided by speed of light in water. And we are given, and this is given to be 0.55. And we're also given the refractive index of water with respect to amber. And we know from our definition that is the speed of light in amber divided by speed of light in water. And that's given to us as 0.86. So we're given these two numbers. The question is, can I figure this out? Just look at this. This is now a math problem. Can you pause the video and see what could be the next solution for this? All right, if I divide this by this, let's do that. So let's do NWA. I'm now treating this as a math problem. The physics is done. Divide by NWD. What we get is this, VA by VW divided by VD by VW. And then notice, VW cancels out. And what remains is VA divided by VD. And VA divided by VD is what we want. And the refractive index of diamond with respect to amber. Which means all I have to do is divide these two numbers to get what I want. And that is basically 0.86 divided by 0.55. And that turns out to be 1.56. And there's our answer. So do I have to now remember these formulas to solve these kinds of problems? No, you just have to remember the basics and we're done. And what does the basics say? Well, refractive index of glass with respect to water is the speed of light in water. Whichever you're measuring with that comes on top, divided by the speed of light in glass. That's called relative refractive index. And when you're measuring the refractive index relative to vacuum, we just call it absolute refractive index. And therefore the speed of vacuum comes on the top. And the number is a measure of how much light slows down in that medium compared to the other medium.