If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains ***.kastatic.org** and ***.kasandbox.org** are unblocked.

Main content

Current time:0:00Total duration:9:19

in this video we'll find the expression for relative refractive index and we'll do that with the help of a numerical so let's say we've been given this refractive index of glass or for active index of water and we are asked to find what's the refractive index of glass with respect to water now before we begin let's just quickly recall what refractive index was remember that refractive index is a number that tells you how slow light is traveling in one medium compared to some reference medium so this number helps us find out what's the speed of light in a particular medium so I like to think of it mathematically if you write it if refractive index of some medium is given as n then it tells us that the speed of light in that medium is the speed of light in the reference divided by n it's n times slower compared to the speed of light in that reference and if that reference medium is not mentioned like over here then we'll always treat it to be vacuum okay so forth over here it would be this tells us that for example speed of light in glass is speed of light in vacuum divided by 1.5 same is the case over here and if the reference medium is mentioned for example over here water is mentioned then over here with the here on the numerator there will be speed of light in water okay and if this is not clear to you then we've discussed a lot about this in a previous video so be great idea to go back watch that video first and then come back over here alright so with this let's start let's start finding this so we have to find what this number is so let me just write that down and G of W is what we want to find and since I don't want to keep writing n.g.w all the time let me just call this as something I'll call this as X okay and we'll start with the definition if this number is X what does that mean this this means speed of light in glass speed of light in glass is speed of light in water speed of light in water divided by X makes sense I'm using the same definition divided by X and since I want to find what X is I'm going to rearrange this so all right we can this as x equals we of W divided by V of G and so to figure out what X is I need to know what the speed of light in water is and I need to know what the speed of light in glass is and can we figure that out is the question and the answer is yes we can because I know wants to refractive index of glass so I can use the same definition and figure out this speed and similarly I can find using this number what this speed is okay so great idea to pause the video now and see if you can solve this further yourself all right let's do this let me continue that over here so X will be equal to speed of light in water well speed of light in water is speed of light in vacuum because the reference here is vacuum and that we usually refer to as C divided by 1.33 this will be the speed of light in water divided by speed of wineglass again using the same definition is the speed of light in vacuum speed of light in vacuum divided by 1.5 and we are pretty much done with the physics over here all we have to do now is solve this fraction since there is a fraction over a fraction I like to do it this way I'm going to write the numerator as it is C divided by one point three three multiplied by the reciprocal of the denominator okay see it's one point five reciprocal of the denominator this always avoids well it helps me avoid confusion see what I'm doing basically is if I have like three divided by five we can always write that as 3 into the reciprocal of the denominator isn't it that's the same thing I'm doing over here so now that we have this notice that the C cancels out C divided by C is just 1 and therefore our answer is 1 point 5 divided by 1 point 3 3 so that's it we just have to divide this and since I don't want to divide I'm just gonna go down and get my calculator there it is so one point five divided by one point three three and voila there it is one point one two seven approximated as 1 point 1 3 oh yeah there this so this is gonna be equal to one point 1 3 and there is our answer that's the refractive index of glass X is that refractive index of glass with respect to water so this number tells us that speed of light in glass is speed of light in water divided by this number it's that much slower in glass all right let's see if you can generalize this can you write a general expression for ngw in terms of ng and NW well let's see well let's look at what we calculated X is just is that refractive index let's get the color right refractive index of glass with respect to water and notice that that is equal to C divided by 1 point 3 3 well what's one point three three a that's the refractive index of water with respect to vacuum and what's is one point five that's the refractive index of glass with respect to a cube so you see what we got eventually we eventually got as one point 5 which is ng so let me just write that down I'm just writing this down in terms of these variables so we got this as n G divided by and W and W and notice that is our general expression we can treat this as a general expression now okay so what we see is that the refractive index of glass with respect to water is equal to refractive index of glass divided by refractive index of water so if we just remember this expression then we can solve problems like this in one step and you know I actually like to remember this because I like to think of it this way see whenever we have glass with respect to water the refractive index of glass comes on the top and the refractive index of water comes in the bottom so if I were to write this in more general terms I generalize it even more so if it was given in general what is refractive index of medium one some medium one with respect to some other medium too you can write this as refractive index of medium 1 with respect to vacuum divided by refractive index of medium 2 I'm dividing by medium 2 because it's with respect to medium 2 so we can think of this as the general formula that connects the relative refractive index this is the relative refractive index right whenever second medium is not vacuum its relative with absolute refractive index notice when the second medium is wax well vacuum we usually call it as absolute value so that's the connection and before we wind up I just want to go a little bit deeper to show you even more generalized result all right so just just stay with me and you'll get this imagine we were not given the refractive indices with respect to vacuum imagine we were given with respect to some other medium these two values were with respect to some other medium I'll show you that this formula still works ok this expression still works so let's say this was given with respect to oil both of these were given with respect to oil and not a naught vacuum and yes of course these numbers will change but let's not worry about the numbers then when we solve this till here everything would still be the same and while substituting the speed of light in water instead of C in the numerator we would have speed of light in oil in the numerator isn't it because our reference medium is oil and the same thing would have happened over here it there will be speed of light in oil in the numerator and notice when we would have calculated those two anyways cancel out so do you see that regardless of which reference medium we use over here they will get cancelled out when you're calculating their relative refractive indices which means even if this was even if this was with respect to oil this would number would still work ok so long story short long story short what I'm trying to tell you is if you know refractive indices of 2 media with respect to some other common medium say let's call it as exome or some common medium X then if you divide them you will calculate what the refractive index of one medium is with respect to another medium this is a generalized result and so you see if you remember this then problems like this can be solved with ease in just one or two steps and of course if you ever forget this no problem you just go back to your definition and from there we can always derive this