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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.

  • 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,