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  • 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.