To put some more precision on our language, we need to define what we need by red, blue and green. The way we traditionally do this is to use a set of specific colors for blue, yellow or green, and red here. Those are actually the spectroscopic lines discovered by Fraunhofer when he first put a prism in sunlight and saw that there were distinct lines of emission and absorption in what appeared to be white light. He numbered these alphabetically and the particular colors we want to use are his F, D and C lines that correspond to blue, yellow and red at around 486, 589 and 656 nanometers. Typically for example, when someone says, "The index of a material is some number." They will mean the middle here, the sodium turns out absorption D line. So, if you don't get a wavelength with the refractive index it probably means that. But of course it does change with wavelength and that's important. So here is a plot of the index refraction versus wavelength over a bit more than the visible spectrum, and I've labeled these F, D and C lines on here for two typical glasses. It turns out historically glasses are called flint and crown and you could go look up why that is. It's not too terribly relevant today except that we still use the same language. The important point is that in general, flint glasses are higher refractive index than crowns, and they're going to have about proportionally higher dispersion, higher ability to spread the light out in angle for example coming out the back of a prism. So, I have used here the optic studio dispersion diagram which shows you how refractive index changes with wavelength. I've pulled off the relevant refractive indices for this particular glass crown and this particular flint glass. We'd now like to take this data and come up with a single number which characterizes how much the wavelength changes with refractive index, and the rather obvious thing to do there would be some sort of a linear approximation to these curves that expressed delta N, the change in wavelength say the change in refractive index over maybe between F and C. As a matter of fact that is what we do and we see that right here, this is the index F in the blue, that's of course a higher number, minus the index at the red, the C line, that's a lower number, so this is delta N, the change in refractive index across the visible spectrum. It turns out it's convenient to normalize that by the index in the yellow, the middle of the spectrum minus one, we will see why that is soon. It's also convenient to turn it upside down. So you might take delta N over the mean refractive index but it turns out it's convenient to turn it upside down and the reason is is that the amount of index change from the blue to the red is kind of small and so this number, NF minus NC, might be as we see here in the second or third decimal point. It's more convenient to have integer numbers so we turn it upside down. By we, I mean a guy named Abbe who first defined this V number. So I've calculated V number, this equation right here, for this crown and flint Glass. You see that for the crown glass which is generally a lower dispersion there's less absolute change of the refractive index here. We get a high V number because this is an inverse. For the flint glass with a larger change of refractive index from F to C, we get a low number. So it's mildly inconvenient that a high V number means low dispersion and a low V number means high dispersion but we pay that pain because then we get integer numbers to deal with.