Another potential title for this course would be Geometrical optics, and we'll see very quickly why that is. We're going to use relatively simple geometry, straight lines and their intersections with the optics that we want to use as the way we calculate optical properties of a system. Geometrical optics is actually a very old field, and we'll discuss the history here in a minute. One of my absolute favorite quotes about geometrical optics is due to Richard Feynman, who stated it as either very simple or very complicated. And you can state things like that if you're Richard Feynman, apparently. The point is it actually is fairly simple. We're going to find the rules are simple, the concepts are very simple. The actual deep understanding that comes from years of practice as a lens designer is very complicated. The goal of this course is to get us through that simple stuff and into a place where we can do good basic designs with geometrical optics. The kinds of things we're going to want to know, the geometrical optics is going to allow us to learn, are if we have an imaging system, there's an object, there's a lens. Where is the image? Is it on the film, so that you're in focus or not? How large is that image? Does it fit on the film or the image sensor or not? How bright is that image? Have I over or underexposed my photograph if I was using a camera? And later on in this specialization, what is the quality of that image? is it blurry, is it distorted? These are the kinds of things that geometrical optics is good at telling us. It turns out that people have been looking at these kinds of questions and using geometrical optics to answer them for a very long time. And I won't read through all of this, you might take a look at it. But clear back in 280 BC, Euclid figured out that light had this apparent property of going in straight lines. Oddly, he got the direction backwards. He thought that the light came from your eye and went to the object. And that persisted for quite a long time. It wasn't until about 1,000 AD that Arab philosophers got the direction right, that light comes from an object to your eye, which tells you the influence of expertise in maintaining, in this case, an error. It was somewhat before that, that they realized that light travels the shortest path between two points. And we're going to use that fact here in just a moment. Somewhere in the 1600s, a Dutch mathematician, who's now referred to as Snell, figured out the law of science, and how light bent and interfaced, and that came to be called Snell's Law, somewhat later. And in that same time period, just a little bit later, Fermat demonstrated mathematically this idea of the shortest path that had been known at least 1,000 years before. And the thing that I find fascinating is all of that was figured out before Maxwell wrote down the fundamental equations, which actually govern how electromagnetic waves, and therefore light, propagate. We're going to find that rays, these things that go in straight lines, that Euclid observed, are actually formal solutions to the partial differential equations that Maxwell wrote down. And yet, these people were all so smart that they were able to get to the rays and to use them and derive properties of them, long before they actually had the fundamental theory that went with them.