What does a telescope do that is so special? Intrusively we know or we think we know that we can see much better or much farther with the telescope than just with our eyes. In this video we will explore this question and try to make it more precise. There is an image of the moon taken with an 8 inch diameter telescope and next to it for comparison is a picture of the moon as you might see it with the naked eye. Although we usually think of telescopes as making things look bigger and there is a reason for that that we will talk about later. In fact the size of the image is irrelevant. After all we can blow up or shrink an image to any size we want. In this illustration the two images that we are comparing are exactly the same size. The difference is that the telescope image contains a lot more detail than the naked eye image. If you compare similar regions in both you will see a lot of small features in the telescope image that are nowhere to be found in the naked eye picture. In other words the telescope image contains a lot more information. To understand this let's begin by considering what small and large means. We know that objects that are identical in size appear smaller with distance. If I look at the moon and I imagine two lines of sight from my eye to the upper and lower edge what determines how big the moon appears is the angle between the two lines. I know this because a much smaller but closer object that forms the same angle will appear just as big. The angle formed by either object is known as its angular size. So a penny can block the moon. Why not try it? Before we continue a word about how we measure angles. Say we want to measure this angle theta. So first draw a circle of any radius centered at the vertex of the angle. Now the angle cuts off an arc of the circle of length S and the ratio of S to the radius R is always the same for any given angle, whatever the radius R is. So this is a good measure of the angle theta. We say in this case that the angle is measured in radians although really it's dimensionless because it's just a ratio of two lengths. If the angle is very small and this will always be the case in astronomical applications the arc S can be approximated as a very tiny straight line. So now we're looking at an isosceles triangle measuring the angle as a ratio of the base to the height. To measure the angular size of a distant object then we imagine a triangle formed by lines of side to its extremes and the diameter of the object itself. The ratio of its diameter to the distance is the angular size. Remember that this formula gives theta in radians. If you want it in some other angular measure like arc seconds you have to do the conversion. So what is the angular size of the moon for an observer on the earth? Before you do the calculation take a guess. Also try to estimate a lower bound that you're sure the moon cannot possibly be smaller than this as well as an upper bound that you're sure the moon cannot possibly exceed. Now hit pause, look up the necessary information and see if the value falls within your bounds. The answer is about half a degree. That is perhaps surprisingly small. What is perhaps even more surprising is that by a strange fluke the angular size of the sun from the earth is almost the same as the angular size of the moon so that in a solar eclipse the moon blocks out the sun almost exactly. So to return to our original question what does a telescope do that is so special and how does it do it? We can state this a bit more precisely. The angular size of the smallest features that we can see with the telescope is much smaller than what we can see with the eye alone. But how does a telescope do this? In the next video we will explore how imaging instruments work in general to begin to answer that question.