 Let's summarize the ideas of refraction, Snell's law and refractive index. When light goes from one medium to another like say from water to glass, it bends and this bending follows a rule and for that rule we drop in normal and then if we define this angle as the angle of incidence and this is the angle of refraction and the rule of refraction which is called Snell's law is the sign of the angle of incidence by sign of the angle of refraction is a constant. This constant depends upon the two media for example for water and glass it happens to be 1.13 as an example but for different different media this will be a different numbers but what's important is that even if I had incident and another ray of light at a different angle I'll have different angle of incidence different angle of refraction but sin i by sin r will stay the same and this term this constant is called the refractive index. Let's talk more about refractive index. The symbol that we use for refractive index is N. Now since refraction is happening in glass we will use the subscript G NG but since the light came from water we will say this is refractive index of glass with respect to water. That's how you read this. Refractive index of glass with respect to water that is 1.13 But what decides this number? Why is this number equal to 1.13? Well turns out refraction happens due to the change in the speed of light. Speed of light is different in water than in glass and that change is the reason for why light bends and turns out that this refractive index is the ratio of the speed of light in the two media. So in this case the refractive index of glass with respect to water happens to be this number is actually the speed of light in water divided by speed of light in glass. Now something to be very careful about over here not to get confused between which number comes on top. See the speed of light of the reference medium see here we are calculating refractive index of glass with respect to water so water is our reference medium. The speed of light of the reference medium comes on the top and the speed of light of our refraction medium comes on the bottom. For example if I asked you what is the refractive index of diamond with respect to say oil what would that be? Well that would be the speed of light in oil the reference medium comes on the top divided by the speed of light in diamond. Did that make sense? Okay one more question what if I asked you what is the refractive index of glass with respect to vacuum? What if the first medium was vacuum? Then we don't really write vacuum. Vacuum is special for some reason we will just write refractive index of glass. If we don't mention the reference medium it automatically means that it's vacuum that is the convention that we follow. So what is refractive index of glass equal to? Well just like over here it'll be the speed of light of the reference medium that comes on the top. Since the reference medium is vacuum speed of light of vacuum comes on the top and that is C which you probably know as 3 times 10 to the power 8 meters per second. So the same formula it will be now speed of light in vacuum divided by speed of light in glass. Okay now let's quickly check our understanding. Suppose I'm given that a ray of light is incident at an angle of 30 degrees undergoes refraction at an angle of 60 degrees into another medium. We're asked to calculate what is the refractive index of medium B with respect to medium A. Can you try and figure this out using Snell's law? All right so Snell's law says the sign of the angle of incidence which is 30 degrees divided by the sign of the angle of a refraction here the angle of a fraction is 60 degrees that equals the refractive index. Refractive index of which medium? Where is the refraction happening here? So refractive index of medium B because this is where the refractive ray is, this is where refraction is happening but with respect to which medium? With respect to A. And I can just substitute and solve this. So that equals sine 30 which is half divided by sine 60 which is root 3 over 2 that gives us 1 over root 3 and there we have it. That is the refractive index of B with respect to A. Now quick question what if I asked you what is refractive index of A with respect to B? What would that number be? Can you pause and think about how would you calculate that? Well now I want refractive index of A with respect to B which means I want to consider refraction happening in this medium. Well for that to happen just reverse this. You can just imagine reversing this and now refraction happens in this medium. So this now becomes the angle of incidence, this now becomes the angle of refraction. So the Snells law will say sine 60 divided by sine 30 that equals the refractive index of A with respect to B. And if you do if you see that's basically reciprocal of this. So it'll be reciprocal and it's going to be just root 3. So you can see one amazing property that we have found out is that refractive index of B with respect to A is just the reciprocal of refractive index of A with respect to B and that happens because you can just reverse the ray of light. Pretty cool right? Okay now we are given the speed of light in this medium is 2 times 10 to the power 8 meters per second. What is the speed of light in medium A? How would we find that? Well now we can use our connection of refractive index with the speed of light. Remember what we saw? We saw that the refractive index of medium B with respect to A that is the speed of light in A. Remember the reference medium speed comes on top divided by the speed of light in medium B. Now I have found out what this is so I'm just going to substitute. This happens to be 1 over root 3. That equals vA which I don't know divided by vB which is given to me as 2 times 10 to the power 8 meters per second and so from this vA equals 2 times 10 to the power 8 meters per second divided by root 3 and there you go.