So how do telescopes work? This will be a very quick rundown of geometrical optics, which I think you're also getting in some of your physics classes. But let's just go through some of the basic concepts. The first one is the refraction. When light rays encounter boundary between two different medium they will, well three things can happen to them. They can get absorbed, they can get reflected, or they can go through but under little different angle. The reason for this is that the speed of light in any finite medium is less than the speed of light, because photons get absorbed or scattered internally. And so the net propagation of light is less than the speed of light and back. Now that is the so-called index of refraction, which is the ratio of the speed of light in vacuum to the one in given medium. And so for the air, it's three parts in 10,000, so air is almost like vacuum. But for water, it's like four thirds. Which is if you try to look underwater, say swimming, you're extremely near-sighted. You can't buy glasses that would be good enough. This is why you have to wear a mask. And, there's of course, Snell's Law that gives the relation between the incoming and outgoing angles. This can be easily derived. I don't have time to go through this, but you can do this. Now it's obvious that if you hit the surface that's sufficiently an oblique angle, than you will not be able to go through surface, but just be internal reflection. And this is how optical fibers work, the light just keeps bouncing along in the fiber it never goes out until the end. This is the actual approximate formula for a index of refraction of the air and you think this will make no difference whatsoever, but now that we observe objects which we see at very large redshifts. The rest frame light. It started from ultraviolet. We observe it on planet Earth in the air, so we have to make this correction that turns out to be important correction. Now, the real problem with the air having index of refraction that's not unity is that blobs of air are slightly denser. Would act like little lenses, irregular lenses. And as the starlight propagates through its atmosphere with all of its turbulence and blobs, it would be like if you're looking through one of those uneven glass sheets like sometimes the put on doors in the sun. This is why we have so called adaptive optics. I'll come to this in a second, just to define few terms here. For a lens or mirror for that matter, there is a focal length, which is the distance from this optical element in which the rays converge. It could be on the front side or back side. Now the set of all those points depending from which angle you're looking at forms the focal point. Which is not really a plane through a curve. But conventionally it's pretty close to a plane. And for single lens the images are inverted. So, way back in the 17th century, people who built glasses, and spyglasses, and telescopes figured out the, so called lensmaker's formula, which relates the focal lengths of the two lenses and the magnification power. This is pretty simple trigonometry, so I will just leave that for section to work this one out. But thing to remember is that the magnification will be essentially the ratio of the two focal lengths of the two lenses. And the scale of what angle corresponds to what linear scale in a focal plane would be given by this small angle formula. It'll be one over the focal length. Now, lenses and some mirrors have so-called aberrations. Not every part of the reflecting or refracting surface will send the rays in the same direction. And so also the speed of light in glass will depend on the wavelength, so that means the focal length will be different for different wavelengths, and that's called Chromatic Aberration. The deviations from perfect symmetry are different kind of aberrations. Distortions they're all really well worked out and a lot of skill and designing modern optical systems, whether it's your camera that you take pictures, or a big telescope, is in how to match minimal number of these optical elements with minimum amount of distortion. A couple things to know about reflecting telescopes. If you just have a spherical mirror, which is the easiest one to abolish. Light rays from different radius relative to the optical axis will intersect in different places. So the focal point will move depending on where the impact of the light ray is. This is not the case for parabola and only for parabola. This is why telescope mirrors abolish this parabola. It's because there is a unique focal point. Now where do you send the light defines the corporational focus. This is a cross-section of 200-inch telescope at Palomar. The simplest thing is called prime focus. Light comes in, bounces off the primary mirror. It's focused in a point up there where that person is sitting, it's called prime-focus cage, and you directly observe it from there. Alternatively you can put another mirror right there, send it back down. There is a hole in the primary mirror, and behind that you can put heavier instruments, and that's called a Cassegrain. Or you can put mirror in between, send it off to the side, and that's called a Nasmyth focus. All of those and various users Depending on what purposes. Well, okay. So, how sharp can you see? Here is an important formula to remember. There aren't very many formulas for you to remember. This one really is important. When you take a picture of a point source, absolutely point source, with the telescope the image you get is not a point. It has a finite size and looks like this Bessel function. And the reason for this is that the image collected by telescope is really a Fourier transform of the aperture. [INAUDIBLE]. The point is that there is a finite width of the light distribution, and that width is proportional to the ratio or the wavelength to the diameter. So for a given wavelength, say visible light, the bigger telescope bigger resolution. Okay? Let's see if we can figure this one out. So this was in radians, of course. 1.22 is approximately equal to 1. And so let's say 5000 angstroms, which is 500 nanometers, wavelength of visible light, and there is a 5 meter diameter of telescope. What would be the angle that corresponds to absolutely best resolution in principle have? Right? 500 nanometers is five times ten to the the minus seven, right? For meters, so divided by five, so it's ten to the minus seven of radian, and a radian is how many arc seconds? How many astronomical units in a unit parsecs? That's the same number. It's about 200,000. So this would be a tiny fraction of an arcsecond, however we never see that because the atmosphere blurs it out to about one or two arcseconds. And the reason for that is that typical sizes of these blobs of air that pass in front of your telescope is of the order of a few centimeters. So it doesn't matter how big your telescope is. It's these distorting little blobs of air, it's their size that matters. Okay. So this is why we see the blur and things don't really fall into focus. The way people fight this is so-called with adaptive optics. And it works like this. Suppose there is a really bright star, you may be looking at that star or something near that star. You know that it's supposed to be a point. You make a little segmented mirror sensor, and you find out what was the distorting surface so to speak of this error lens, to make it blur any given time. Then you compute those backwards, you readjust the surface of this small formable mirror to exactly compensate to whatever atmosphere has done. And then bring that in focus. In that way you would untwinkle the stars. That actually works amazingly well. And here is an example from the Keck Telescope. This was a surface plot indicates intensity of light on focal plane, the texture. And the one on the left is just ordinary image, it's blurred out by the atmosphere. This was magnified heavily. You turn on the adaptive optics systems and kaboom. And guessing to this tiny spike, which is almost but not quite like the diffraction limit. Well what if you don't have a bright point source next to the one you want to observe? Well in that case, you can put one there. You can shine a laser up. These are relatively powerful lasers, and they're tuned to the wavelength of the sodium, like those ugly orange streetlights, the sodium goblet 5980 [INAUDIBLE]. There is sodium in the upper atmosphere. It comes from burning meteors. And there's a thin layer of sodium ions about 100 kilometers up, and serves as a screen. So it's like having a laser pointer from a telescope. You know exactly where you want it. It creates a little spot, which is artificial star, and now you can deploy your adaptive optics into corrective. Amazingly enough, that works too. And now this is becoming almost the standard way of observing astronomy, of removing turbulence of Earth's atmosphere.