In the last lecture, we learned how light causes a change in the electrical activity of neurons, but I haven't yet told you how that neural response says anything at all about where in space that light came from. That's what we're going to begin to talk about today, how the eye forms an image of where light is coming from. We're going to talk about how it works and how scientists and scholars from fields like astronomy and philosophy deduced what happens. Now let's start with a very simple observation, and that is that not all light sensing actually involves image formation. The key difference is where sensors are located. Plants and simple animals such as flatworms known as planaria have light receptors on the surface of their bodies. They're able to generally tell day from night and they have a rough sense of the direction that light is coming from. That is how trees grow upwards towards the sun, for example. But they certainly don't have the ability to recognize differences between different patterns of light the way we do when we recognize someone's face. So light sensing in these organisms involves cells that are located on the surface of their bodies. But light sensing that does involve image formation occurs in organisms that have receptors inside the eye. And all organisms that have any spatial visual abilities all involve eyes in which the receptors, these light sensors, are located inside the structure of the eye. So, why does this happen? Well, the critical question is how the eye actually forms an image. And to understand how the eye forms an image, you need to know something about how light actually travels. There's a few key insights to keep in mind. Light spreads outward from every point in the visual scene. Light at every other point in the visual scene arrives there from every other point. And light travels between these points in straight lines. Let's follow through on this idea, and let me show you an example of what I'm talking about. So let's slow down and think a little bit about what actually is happening in the visual scene. So let's take this pretty scene. This is a painting by Auguste Renoir entitled a Luncheon of the Boating Party. And I like it for this purpose because there are many people in it and they are all looking at different things. So it makes a nice example of what our eyes and brain have to do. They have to be able to tell what things are out there and where they are. Now let's think about a single point in this scene, say one of these wine bottles. And from any given point in the scene the light is going to spread in all directions, reaching the eyes of all the observers that are looking at that scene. So that's the answer to one of the things that puzzled the early Greek and Islamic scholars, why the same object can be seen by multiple observers. You can't do that with touch or not quite so easily. So the light reflected from the wine bottle is reflected in all directions and thus is able to reach the eyes of all the observers that are looking at this bottle. Now, I could just as well have said the same thing about any other point in the scene, for example, this wine glass. Light is getting to all the eyes that are observing the scene from all the different objects in the scene. So how does the eye keep it all straight? How does it preserve information about where the light is coming from, from these multiple different sources? Why doesn't it just get mixed together? So to form an image we need a couple of things. We need to be able to sort light and keep it organized. We need to be able to keep light from different objects and locations separate, and we need to be able to create a one-to-one correspondence between the location of origin of the light, and the location on the set of light sensors. So how do you actually form such an image? Well in part, you can do it by filtering through pinholes. The image-forming properties of pinholes were first discovered in ancient Greece and in ancient China around the fourth or fifth century BCE. A device known as the camera obscura was invented independently in both places and described both by philosophers such as Aristotle in Greece, and the philosopher Mozi in China. A camera obscura is something like this. It is a room with a wall blocking light from the outer world. It has a very small opening, an aperture, in the wall, a pinhole. And then there's another wall behind that first wall. Light from out in the world comes through that pinhole and forms an image on the back surface. The reason it forms an image is because light from a particular location in the visual scene travels through the pinhole and reaches a particular location on that rear surface. Light coming from that same location in the visual scene but traveling along different paths is blocked by the wall. From another location in the visual scene, the light travels through the aperture and reaches the back surface of the camera obscura, but it reaches a different location on that rear wall. Again, light traveling along different trajectories is blocked by the first wall and prevented from reaching the rear surface, and from blurring, the image that is formed by those unique paths of light. So that's how a camera obscura forms an image of the visual scene. Well, the eye has a pinhole too, and the pinhole of the eye is known as the pupil. It is this dark spot in the center of the eye that is actually an opening that lets light through to the back of the eye. And here's what it looks like in profile. There's a small opening at the front of the eye and you can imagine that, that aperture works just like a camera obscura to allow the creation of an image of the visual scene on the rear surface of the retina. The creation of this image really requires that the sensors be on the back surface of the eye and not somewhere else, and that is why spatial vision only occurs in creatures that have receptors lining the rear surface of their eyes. But pinholes are not the whole story. And this was first appreciated by astronomers around the turn of the seventeenth century. In particular, Johannes Kepler made the critical discovery that elucidated how pinholes work and why they're not the whole story with regard to our visual spatial abilities. So astronomers of this era used the camera obscura to make measurements of the size of celestial bodies. And when you make a measurement like this the size of the aperture produces a certain amount of blur in the image. If you have a smaller aperture, you get less blur. Astronomers of this time period understood that they needed to correct for the aperture size, but they didn't fully understand why they needed to make those corrections. And that's where Kepler came in. He showed that how light passes through apertures in straight lines forms the image. In the process of figuring this out he realized that the pupil of the eye is not enough to support our visual spatial abilities. To understand this, I need to introduce you to the unit of measure used by vision scientists for describing the visual scene. And that unit is the visual angle. Units of visual angle are expressed as degrees on the retina. So, if light is, coming from the top of that tree and reaching the retina, and light comes from the bottom of that tree and reaches the retina, we can describe the angle between those two rays and call that the, the size of the tree in terms of visual angle. So, Kepler realized that if the pinhole aperture created by the pupil at the front of the eye was the only source of image formation that vision should be blurrier. So the pupil is about 2.5 millimeters in diameter, the distance from the pupil to the back surface of the retina is about 25 millimeters and you can calculate that that should produce about six degrees of blur. Well, putting those size units back in terms of more familiar units of size, six degrees corresponds approximately to the width of my hand when my arm is held at arm's length. And I can certainly tell the difference between whether or not I'm holding up my thumb or my pinky finger. So I can see much more clearly than you would predict based on the size of the pupil. We see roughly 300 times better than would be predicted by the pupil alone. So in the next lecture, I'm going to tell you what it is that Kepler discovered that resolved this mystery. In particular, what he figured out was that the pupil acts in concert with the lens to focus the image on the rear surface of the eye.