Okay, so you're all familiar with this idea of a microscope, you've I'm sure look through a microscope at some point in your life. Right, you put the bug on the table and you take your microscope and you zoom in and you can see the bug in great detail. So, a microscope in fact has two lenses in it. Okay, it is a two lens system and there is an objective and there is an eyepiece. Okay, and we're drawing it vertically because these things are usually mounted vertically on the table, and you put your sample right here. And then you of course look down through this eyepiece. Now there is some sort of housing between this stuff and that housing has a particular length associated with it, and that length is given by L. And then there is a focal length for the objective and a focal length for the eyepiece, and we would like to know what is the magnification of the whole system. Okay, and this is a little bit tough, the derivation, so we're gonna jump to the answer and if you really want to see the full derivation you can come visit me in my office, but the magnification M of a microscope is the following: negative L minus fe times N divided by fo fe. What are these different things? L is that length that we just talked about, it's the length of this tube. Okay, and that's usually about 16 centimeters for a microscope, it's purely governed by how high is the table when you're sitting and looking down, what's a comfortable point for you to view it. That determines the length L of that tube. Fe is the eyepiece focal length. Okay, so that eyepiece up there, you can actually pull it out on the microscope and look through it, it's a very short focal length eyepiece. Fo is the focal length of the objective. Okay, so that's the thing on the bottom and usually you can rotate different ones and they'll say like 16x, 20x, 100x, right? Those are also very short focal length lenses and they sit very close to the sample. N is the near point of your eye and that is usually written as 25 centimeters. Okay, like the tube is usually about 16 centimeters. So, you want good magnification in your microscope and if you look at this equation right here, that means you want this number down here to be small, and so a microscope, in fact, has a short focal length fo and it has a short focal length fe. Both of those lenses have very short focal lengths, and like I said you can take them out and you can look at them individually. Okay. When you go to a jeweler and they pull out their loupe to check out your ring and see if it's real or not, okay? They are using one of these things. Either one, it's just a short focal length lens and that allows them to look at it very closely, just like we did with the magnifying glass, okay. But put them together in the right orientation and now you get dramatic increase in the magnification because those are multiplying each other down here. So if both those things are small, M can be very big, and you've looked through microscopes that are 100x, 200x, 500x, okay, you can get incredible amounts of magnification.