Welcome to another episode of Michael draws on pieces of white cardstock Meets… Michael’s toys That’s right, today we have a combo episode for you, and we’re gonna be talking about… vision. We’re going to be talking about how images are made. Let’s say you want to see something. Alright, let’s say you want to see, um…a black line, uuuuh wonderful. Now, to see, you’re going to need something that can receive photons, So how ’bout we put a retina right…here oooh, that’s a beautiful retina. Now, we see because light either reflects off of an object, or is emitted by the object. And that light contains information about the object. But here’s the problem: Let’s take a look at a point on the object like this one, I’ll call it point “A” for “bottom” Now, light is leaving point A in all directions; you can see it from, you know, anywhere. But here’s the problem: some of that light might land on the retina right here, but light from another point, like, uh…this one I’ll call this point “B” for “top”, might also fall in the exact same spot on the retina. So you wind up with this big, blurry mess of light information that makes no sense. It’s kind of like what you would see if you took the lens off of a camera. In order to see, in order to form an image, we need to build a one to one correspondence between points on the object and…where light from them lands on the retina. The way our eye does it (in an extremely simplified way) Is by using a pin-hole. So I’m now gonna block the light coming off of this object reaching our retina with a… *draws* opaque plane, right here, peeerfect. But this plane is gonna have a tiny hole in it, a pin hole. Now watch what happens. When this light flies off, some… in fact just one ray of light that is leaving “A”, intersects with the pinhole. Only one line connects two points on this Euclidean plane. And it will intersect that point, our pinhole, at a particular angle, and it will come through on the other end… like this! So here on the retina, we have information about point A, the bottom of our black line. Pretty cool, pretty cool. And notice that because we’re using a pin-hole, any light rays that are leaving B with a trajectory towards… … this part of the retina, are getting blocked by this plane right here. Only light rays from B that intersect… with that pinhole get through. But the angle they intersect at will be unique, So! The place they land on the retina will also be unique. If we choose a point that’s just a little bit above A, I’ll call this one A prime (A’), this ray that goes through the pinhole will have a slightly different angle and will thus come out… slightly…differently… *mumbling* nnnsortoflikethiss andthenitsgonnacomeout there it is, and so A’ will be about here. As you can see, by using a pinhole, we have created a one to one correspondence between points on the object we’re looking at, and points on the retina. We are constructing an image, of this black line, AB, on the retina that happens to be upside down. This is really how your eye works; the light information that lands on your retina is an upside down version of whatever you’re looking at. luckily we have brains, and our brains know to turn things right-side-up again. This pinhole way of seeing explains why things appear smaller when they’re further away. Watch this. Let me draw the same object, this black line, AB, but I’m gonna draw it further away. I’m gonna draw it… I wanna make sure that it’s about the same height. It doesn’t have to be perfect because this is just a little illustration, but let’s say that we have our object over here, there’s its bottom, there’s its top, now take a look at the paths of the light rays that pass through that pinhole. I’m gonna use a straight edge here just so I can get this right. and…let’s see what color should I use? Uh, I like this orange. Alright, so light rays, that are reflecting off of point A, pass through the pinhole, and they come through onto the retina like this. Ah, wow, So now, when the object is further away, point A corresponds to a point on the retina that’s below where it corresponded when the object was closer. Let’s take a look at point B. mmmkay Light from B that has the correct trajectory to pass through the pin-hole will come out the other side and land on the retina right there. Well, my gosh! If A is one edge of the object and B is the other, look how much smaller…the black line’s image on the retina is going to be than when it’s close, and it is this big. From that A… down to that B. This is geometrically what’s going on when an object is seen from further away. The image they put on our retina is literally smaller. But this isn’t the only way you can create an image! Another way to do that is to grab another sheet of paper… yeaah, beautiful! *cough* and watch Michael draw on more pieces of white cardstock. Now let’s say that we are going to look at a line, alright, here it is, and I’ll even give it the same endpoints, A and B. But this time, what we’re going to project onto the retina will not… be a one to one correspondence due to a
pin-hole but will instead will be a one to one correspondence created by some sort of magical filter that only allows light rays to go through that strike the surface of this filter at a right angle. What I mean by that is that light flying off of point A, on a trajectory like this, OOoooh… That is not a right angle, nope! This light gets absorbed or reflected away, something like that. However, light leaving point A like this, awwww, yeaah 90 degrees! This light is able to pass through the object, come out the other side, and land on the retina. Each point on the object will correspond to just one point on the retina that is… at exactly 90 degrees. So if this is point A’, only light like this will be able to pass through the filter and reach this side and give us A’. Same with B, there we go, and there’s B. Notice that in this case, the image that we are forming is right side up. It’s not flipped like it is when it went through the
pin-hole. Uh, just to be very clear, if there’s a ray leaving from A, that happens to have a trajectory like this, that would bring it exactly to B, in which case we don’t have a one to one correspondence, we’ve got a mess, it doesn’t matter because of cource this light ray won’t go through, it’s not hitting at a 90 degree angle, so we have no problem. But here’s what’s interesting! As you can see, the dimension of the black line AB, the actual object in the world and the image formed on the retina are the same size! How cool would the universe look if things did not shrink in apparent size as they moved away from us. It might be kind of scary, exactly but who knows what it would actually look like OH WAIT! There’s a way to know. Thank you… *paper flops onto floor* thanks to minerals. I have here some fantastic samples of various minerals. This is a piece of ulexite. Ulexite is a borate mineral, that as you can see is made of fibers that all go in one direction, they’re all parallel to one another. Now ulexite will often have kind of dark colored sort of brown…issues in it. The rest of these rocks are selenite, which is a variety of gypsum, And it also is made out of, as you can see, parallel fibers. Because this mineral only allows parallel light rays to travel through, there is a one to one correspondence between light information coming from a point on whatever the mineral is on top of and on the surface, the other side of the mineral. For this reason, looking through the mineral isn’t like looking through something that’s transparent, Instead, an actual image of what is below is created on top. Ooh yeah, look at that! Here’s the selenite, and… there’s the image. Anyway, why am I bringing these up? Well, if our eyes were not eye balls, but were instead loooong pieces of minerals, like ulexite or selenite, and we literally had to touch our eye organs to whatever we wanted to see, it wouldn’t matter how far away the thing was, it would always be the same size. Take a look at this. This is an enormous piece of selenite, which is perfect because, when you look from this camera right here I’m pointing at this camera right above me when you look from there down at say this number 30, the light from that 30 is converging towards the lens on that camera or towards your eye. And so it’s smaller if it’s further away. But! oh wow this is like falling apart into sharp fragments… Be careful… I don’t know actually how sharp they are. … Hannah could you come lick this? It looks like…it looks like if you inhaled this stuff you’d be in a lot of trouble. I will… keep going though. Because your knowledge is more important than my health. without the selenite, the distance between the edges of the number 30, converge right away. But! With the mineral, they spend a whole lotta time travelling parallel to one another, and only after that do they begin converging. So it’s as if the ruler is closer to you. That’s why the number 30 looks bigger when the crystal is on top of it. Why is this coming apart so much? I wonder if I could eat it… *licks* Eeeah! You know what? The table ith thalty from like… having sweaty hands and sweaty Michael around it. *exhales* This episode is supposed to be about optics properties, not taste, but *sniffs* *licks* It’s funny it really tastes, uh, cold, but of course it’s just room temperature, it just has a much better… uh…uh, capacity to conduct heat, than air does. Cause I’m not tasting cold, I’m just losing heat from my tongue more quickly to this than I do to the air. Eauh now there’s a bunch on my tongue. what ha— *spits* What happened to that? Why is it…shedding? Anyway, that…um, should have answered all questions you could have ever possibly asked about optics. You are now… a professor of optics. Just kidding there’s a lot more to learn, but I love these things and I love imagining the way some sort of extraterrestrial might see the world if they saw the world by literally reaching out some kind of organ, attaching it to a surface, and then seeing that surface through a fiber optic kind of eyeball Man! They would have no idea about perspective the way we do. The way railroad tracks converge together, the way when you look at a cube the back face seems to be smaller than the front face. Their lives would be completely different, but they wouldn’t be wrong. They would just be different. So. There’s an analogy or some kind of metaphor or parable in there somewhere I’m sure. And as always, thanks for watching.