Refraction and Snell's law

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In the last couple of videos we talked about reflection.

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And that's just the idea of the light rays bouncing off of a surface.

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And if the surface is smooth, the incident angle is going to be the same thing as the reflected angle.

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We saw that before, and those angles are measured relative to a perpendicular.

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So that angle right there is going to be the same as that angle right there.

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That's essentially what we learned the last couple of videos.

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What we want to cover in this video is

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when the light actually doesn't just bounce off of a surface

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but starts going through a different medium.

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So in this situation, we will be dealing with refraction.

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Refraction. Refraction, you still have the light coming in to the interface between the two surfaces.

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So let's say--so that's the perpendicular right there,

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actually let me continue the perpendicular all the way down like that.

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And let's say we have the incident light ray coming in at some, at some angle theta 1,

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just like that...what will happen--and so let's say that this up here, this is a vacuum.

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Light travels the fastest in a vacuum.

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In a vacuum. There's nothing there, no air, no water, no nothing, that's where the light travels the fastest.

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And let's say that this medium down here, I don't know, let's say it's water.

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Let's say that this is water.

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All of this. This was all water over here.

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This was all vacuum right up here.

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So what will happen, and actually, that's kind of an unrealistic--

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well, just for the sake of argument, let's say we have water going right up against a vacuum.

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This isn't something you would normally just see in nature

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but let's just think about it a little bit.

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Normally, the water, since there's no pressure, it would evaporate and all the rest.

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But for the sake of argument, let's just say that this is a medium where light will travel slower.

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What you're going to have is

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is this ray is actually going to switch direction, it's actually going to bend.

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Instead of continuing to go in that same direction, it's going to bend a little bit.

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It's going to go down, in that direction

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just like that. And this angle right here, theta 2,

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is the refraction. That's the refraction angle. Refraction angle.

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Or angle of refraction. This is the incident angle, or angle of incidence,

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and this is the refraction angle. Once again, against that perpendicular.

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And before I give you the actual equation of how these two things relate

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and how they're related to the speed of light in these two media--

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and just remember, once again, you're never going to have vacuum against water,

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the water would evaporate because there's no pressure on it and all of that type of thing.

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But just to--before I go into the math of actually how to figure out these angles

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relative to the velocities of light in the different media

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I want to give you an intuitive understanding of

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not why it bends, 'cause I'm not telling you actually how light works

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this is really more of an observed property

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and light, as we'll learn, as we do more and more videos about it,

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can get pretty confusing.

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Sometimes you want to treat it as a ray, sometimes you want to treat it as a wave,

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sometimes you want to treat it as a photon.

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But when you think about refraction

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I actually like to think of it as kind of a, as a bit of a vehicle,

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and to imagine that, let's imagine that I had a car.

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So let me draw a car. So we're looking at the top of a car.

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So this is the passenger compartment, and it has four wheels on the car.

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We're looking at it from above.

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And let's say it's traveling on a road.

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It's traveling on a road. On a road, the tires can get good traction.

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The car can move pretty efficiently, and it's about to reach an interface

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it's about to reach an interface where the road ends and it will have to travel

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on mud. It will have to travel on mud. Now on mud, obviously, the tires' traction

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will not be as good. The car will not be able to travel as fast. So what's going to happen?

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Assuming that the car, the steering wheel isn't telling it to turn or anything,

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the car would just go straight in this direction.

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But what happens right when--which wheels are going to reach

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the mud first? Well, this wheel. This wheel is going to reach the mud first.

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So what's going to happen? There's going to be some point in time

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where the car is right over here. Where it's right over here.

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Where these wheels are still on the road, this wheel is in the mud,

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and that wheel is about to reach the mud.

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Now in this situation, what would the car do?

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What would the car do? And assuming the engine is revving and the wheels are turning,

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at the exact same speed the entire time of the simulation.

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Well all of a sudden, as soon as this wheel hits the medium, it's going to slow down.

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This is going to slow down. But these guys are still on the road.

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So they're still going to be faster.

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So the right side of the car is going to move faster than the left side of the car.

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So what's going to happen?

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You see this all the time. If the right side of you is moving faster than the left side of you,

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you're going to turn, and that's exactly what's going to happen to the car.

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The car is going to turn. It's going to turn in that direction.

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And so once it gets to the medium, it will now travel, it will now turn--

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from the point of the view from the car it's turning to the right.

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But it will now travel in this direction. It will be turned when it gets to that interface.

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Now obviously light doesn't have wheels, and it doesn't deal with mud.

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But it's the same general idea. When I'm traveling from a faster medium

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to a slower medium, you can kind of imagine the wheels on that light

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on this side of it, closer to the vertical, hit the medium first, slow down,

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so light turns to the right.

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If you were going the other way, if I had light coming out of the slow medium,

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so let's imagine it this way. Let's have light coming out of the slow medium.

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And if we use the car analogy, in this situation, the left side of the car is going to--

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so if the car is right over here, the left side of the car is going to come out first

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so it's going to move faster now. So the car is going to turn to the right, just like that.

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So hopefully, hopefully this gives you a gut sense of just how to figure out which direction

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the light's going to bend if you just wanted an intuitive sense.

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And to get to the next level, there's actually something called Snell's Law.

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Snell's Law.

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Snell's Law. And all this is saying is that this angle--

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so let me write it down here--so let's say that this velocity right here is velocity 2

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this velocity up here was velocity 1, going back to the original.

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Actually, let me draw another diagram, just to clean it up.

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And also that vacuum-water interface example, I'm not enjoying it,

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just because it's a very unnatural interface to actually have in nature.

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So maybe it's vacuum and glass. That's something that actually would exist.

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So let's say we're doing that. So this isn't water, this is glass. Let me redraw it.

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And I'll draw the angles bigger.

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So let me draw a perpendicular.

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And so I have our incident ray,

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so in the vacuum

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it's traveling at v1--and in the case of a vacuum,

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it's actually going at the speed of light, or the speed of light in a vacuum,

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which is c, or 300,000 kilometers per second,

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or 300 million meters per second--let me write that--

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so c is the speed of light in a vacuum,

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and that is equal to 300--

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it's not exactly 300, I'm not going into significant digits--

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this is true to three significant digits--300 million meters per second.

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This is light in a vacuum.

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Light in vacuum. And I don't mean the thing that you use to clean your carpet with,

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I mean an area of space that has nothing in it.

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No air, no gas, no molecules, nothing in it. That is a pure vacuum

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and that's how fast light will travel.

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Now it's travelling really fast there, and let's say that--and this applies to any two mediums--

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but let's say it gets to glass here, and in glass it travels slower,

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and we know for our example, this side of the car

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is going to get to the slower medium first

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so it's going to turn in this direction.

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So it's going to go like this.

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We call this v2.

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Maybe I'll draw it--if you wanted to view these as

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vectors, maybe I should draw it as a smaller vector

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v2, just like that.

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And the angle of incidence is theta 1.

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And the angle of refraction is theta 2.

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And Snell's Law just tells us

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the ratio between v2 and the sin--

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remember Soh Cah Toa, basic trig function--

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and the sin of the angle of refraction

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is going to be equal to the ratio of v1 and

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the angle--the sin of the angle of incidence.

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Sin of theta 1.

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Now if this looks confusing at all, we're going to

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apply it a bunch in the next couple of videos.

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But I want to show you also that

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there's many many ways to view Snell's Law.

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You may or may not be familiar with the idea of

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an index of refraction.

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So let me write that down.

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Index of refraction.

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Index, or refraction index.

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And it's defined for any medium, for any material.

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There's an index of refraction for vacuum, for air,

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for water.

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For any material that people have measured it for.

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And they usually specify it as n.

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And it is defined as the speed of light in a vacuum

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That's c. Divided by the velocity of light in that medium.

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So in our example right here, we could rewrite this.

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We could rewrite this in terms of index of refraction.

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Let me do that actually. Just cause that's sometimes

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the more typical way of viewing Snell's Law.

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So I could solve for v here if I--one thing I could do

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is just--if n is equal to c divided by v

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then v is going to be equal to c divided by n.

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And I can multiply both sides by v

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if you don't see how I got there.

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The intermediary step is, multiply both sides times v,

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you get v times n is equal to c, and then

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you divide both sides by n, you get

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v is equal to c over n.

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So I can rewrite Snell's Law over here as

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instead of having v2 there, I could write

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instead of writing v2 there I could write

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the speed of light divided by the refraction index

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for this material right here.

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So I'll call that n2.

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Right, this is material 2, material 2 right over there.

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Right, that's the same thing as

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v2 over the sin of theta 2

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is equal to v1 is the same thing as c divided by n1

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over sin of theta 1. And then we could do a little bit

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of simplification here, we can multiple both sides of

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this equation--well, let's do a couple of things. Let's--

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Actually, the simplest thing to do is actually

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take the reciprocal of both sides.

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So let me just do that.

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So let me take the reciprocal of both sides,

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and you get sin of theta 2 over cn2 is equal to

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sin of theta 1 over c over n1.

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And now let's multiply the numerator and

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denominator of this left side by n2.

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So if we multiply n2 over n2.

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We're not changing it,

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this is really just going to be 1,

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but this guy and this guy are going to cancel out.

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And let's do the same thing over here,

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multiply the numerator and the denominator

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by n1, so n1 over n1.

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That guy, that guy, and that guy

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are going to cancel out.

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And so we get n2 sin of theta 2 over c is equal to

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n1 sin of theta 1 over c.

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And now we can just multiply both sides

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of this equation by c and we get the form of

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Snell's Law that some books will show you,

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which is the refraction index for the slower medium,

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or for the second medium, the one that we're entering,

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times the index of the sin of the index of refraction

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is equal to

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the refraction index for the first medium

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times the sin of the angle of incidence.

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The incident angle.

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So this is another version right here

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This is another version right there of Snell's Law.

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Let me copy and paste that.

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And if this is confusing to you,

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and I'm guessing that it might be,

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especially if this is the first time you're seeing it,

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we're going to apply this in a bunch of videos,

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in the next few videos, but I really just want to make sure,

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I really just want to make sure you're comfortable with it.

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So these are both equivalent forms of Snell's Law.

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One deals with the velocities, directly deals with

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the velocities, right over here,

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the ratio of the velocity to the sin of the incident

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or refraction angle

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and here it uses the index of refraction.

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And the index of refraction really just tells you

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it's just the ratio of the speed of light to the actual velocity.

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So something where light travels really slowly

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where light travels really slowly,

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this will be a smaller number.

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And if this is a smaller number,

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this is a larger number.

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And we actually see it here.

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And you're going to see a little tidbit of the next video

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right over here.

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But here's a bunch of refraction indices

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for different materials.

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It's obviously 1 for a vacuum, because for a vacuum

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you have the refraction index is going to be c

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divided by the speed of light in that material.

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Well, in a vacuum it's traveling at c.

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So it's going to be 1.

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So that's where that came from. And you can see in air,

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the speed is only slightly smaller,

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this number's only going to be slightly smaller

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than the speed of light in a vacuum.

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So in air, it's still pretty close to a vacuum.

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But then for a diamond, it's traveling a lot slower.

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Light is travelling a lot slower in a diamond

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than it is in a vacuum.

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Anyway, I'll leave you there,

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we're going to do a couple more videos,

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we're going to do more examples using Snell's Law.

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Hopefully you got the basic idea of refraction.

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And in the next video, I'll actually use this graphic right here to help us visualize

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why it looks like the straw got bent.


Specular and diffuse reflection 2

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Language: en

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I wanna talk a little bit more about reflection and specular and diffuse reflection in particular

00:00:06.133 --> 00:00:11.067
and to start of, I wanna make a minor correction to the last video, and it's actually a pretty interesting

00:00:11.067 --> 00:00:13.000
correction because in this image right here

00:00:13.000 --> 00:00:14.800
I talked about a double reflection

00:00:14.800 --> 00:00:18.733
I talked about the light from the sun hitting this pond

00:00:18.733 --> 00:00:22.733
or specularly reflecting off of the surface of this pond

00:00:22.733 --> 00:00:26.889
and than reflecting off of this paddle to get to our eye

00:00:26.889 --> 00:00:29.304
and when I said where the light ray was passing

00:00:29.304 --> 00:00:36.000
in the last video, I said "it goes from the sun to this point-to this point on the surface

00:00:36.000 --> 00:00:37.733
cause that's where we saw the reflection

00:00:37.733 --> 00:00:40.472
and I said, "than from that point to this point of the paddle

00:00:40.472 --> 00:00:42.733
than to our eye that the correction here

00:00:42.733 --> 00:00:45.558
--and someone pointed this out on the message board and it's a very good catch--

00:00:45.558 --> 00:00:50.225
is that this point is where the light if reflecting to our eye

00:00:50.225 --> 00:00:52.709
so that because we see it, we see the sun there

00:00:52.709 --> 00:00:57.267
so this light ray right here is coming directly to, directly to

00:00:57.267 --> 00:00:59.629
someone's eye-let me draw someone's eye right there

00:00:59.629 --> 00:01:02.467
or our eye, our eye coming straight out of the page

00:01:02.467 --> 00:01:06.400
the light that got reflected here is going to be reflected

00:01:06.400 --> 00:01:07.867
a little bit more shallowly

00:01:07.867 --> 00:01:10.960
so it came from the sun, it came from the sun

00:01:10.960 --> 00:01:14.722
now obviously this won't be exact, but it came from the sun

00:01:14.722 --> 00:01:19.134
it probably had a slightly more shallow (uh uh) angle of incidence

00:01:19.134 --> 00:01:22.222
or angle between the ray and the surface

00:01:22.222 --> 00:01:24.200
and than it would have gotten to

00:01:24.200 --> 00:01:27.214
than it would have gotten to the paddle

00:01:27.214 --> 00:01:31.067
than it would have gotten to the paddle, than it would get to our eye

00:01:31.067 --> 00:01:31.742
and I wanna make clear

00:01:31.742 --> 00:01:34.227
we don't see the sun at the point that it is reflected

00:01:34.227 --> 00:01:38.133
because that light that image of the sun is going to the paddle

00:01:38.133 --> 00:01:39.933
which than goes to our eye

00:01:39.933 --> 00:01:42.800
the point where we see the sun-the reflection of the sun

00:01:42.800 --> 00:01:45.467
that light's going straight into our eye

00:01:45.467 --> 00:01:47.467
it wouldn't have to be reflected by the paddle

00:01:47.467 --> 00:01:51.293
so that was an interesting and good catch when you think about the double reflection

00:01:51.293 --> 00:01:53.638
the other thing I wanna talk about

00:01:53.638 --> 00:01:58.724
is when you have both specular and diffuse reflection happening at the same time

00:01:58.724 --> 00:02:00.200
now, we see this all over the place

00:02:00.200 --> 00:02:02.400
any time you see kind of a shiny object

00:02:02.400 --> 00:02:04.600
something that's not a mirror, but it's a shiny object

00:02:04.600 --> 00:02:08.000
and we see that right here in the apple, just to make this clear

00:02:08.000 --> 00:02:13.067
so you can see, this-this- white part right here, which we've all seen on a nicely waxed apple

00:02:13.067 --> 00:02:16.208
this is, it's like a reflection of the actually light source

00:02:16.208 --> 00:02:19.867
while everywhere else, it's just kind of the color of the apple

00:02:19.867 --> 00:02:21.270
let's think about what's happening here

00:02:21.270 --> 00:02:26.133
so if I were to draw the surface, if I were to draw the surface of the apple

00:02:26.133 --> 00:02:29.333
let me draw it, let me draw it in a neutral color

00:02:29.333 --> 00:02:32.555
so let's say we have the surface of the apple right over here

00:02:32.555 --> 00:02:36.000
we have the surface of the apple right over there

00:02:36.000 --> 00:02:40.800
and than maybe I'll draw it as a slight circle, just so you can appreciate that it's a circular apple

00:02:40.800 --> 00:02:42.533
so the surface of the apple right over here

00:02:42.533 --> 00:02:46.557
you have some light source, so you have some light source

00:02:46.557 --> 00:02:50.551
,so if you have some light source over here

00:02:50.551 --> 00:02:53.639
and it's, and it's emitting light

00:02:53.639 --> 00:02:59.067
so it is emitting light in some direction, onto the surface of the apple

00:02:59.067 --> 00:03:00.800
and what's happening on the surface of the apple, there's

00:03:00.800 --> 00:03:02.067
there's a couple of things that's happening

00:03:02.067 --> 00:03:07.667
you're having some of this light is reflecting specularly

00:03:07.667 --> 00:03:12.215
or, another way of thinking about it is it's maintaining the image, a little of it, but not all of it

00:03:12.215 --> 00:03:14.800
so let me just draw it, so if you're coming in at that incident angle

00:03:14.800 --> 00:03:18.972
you're going to leave at that reflected angle

00:03:18.972 --> 00:03:23.476
and if you came in at this incident angle, you're going to leave at that reflected angle

00:03:23.476 --> 00:03:27.000
and if you came in at this incident angle, going to leave at that reflected angle

00:03:27.000 --> 00:03:31.200
and I'm doing dotted lines to show that it's not all of the light that's getting reflected that way

00:03:31.200 --> 00:03:34.267
only some of the light is getting that specular reflection

00:03:34.267 --> 00:03:37.000
,but if someone, if this light were to be reaching your eye

00:03:37.000 --> 00:03:48.467
if, let me draw a proper face, so let's say this is someone's face right here that someone's, that's there ear, or there hair

00:03:48.467 --> 00:03:50.133
that's there eyebrows, that's there moustacche

00:03:50.133 --> 00:03:52.803
and, I think you get the general idea

00:03:52.803 --> 00:03:57.215
so this person will see a reasonably good version of the light source

00:03:57.215 --> 00:04:00.071
which we see right over here, but what's going on the rest of the apple

00:04:00.071 --> 00:04:03.670
or even over here, so some of the light is reflecting specularly

00:04:03.670 --> 00:04:05.400
it's kind of maintaining the image of the light source

00:04:05.400 --> 00:04:07.269
although that's getting distorted a little bit

00:04:07.269 --> 00:04:10.636
but the rest of the light, the rest of the light

00:04:10.636 --> 00:04:14.800
and let me be clear here- the rest of-some of it is being absorbed

00:04:14.800 --> 00:04:18.067
some of it is being absorbed by the actual surface of the apple

00:04:18.067 --> 00:04:23.000
but the rest of it reflecting red light, what we see is actually what the light, apple does not absorb

00:04:23.000 --> 00:04:27.215
what the apple is reflecting, but that red light that mainly red

00:04:27.215 --> 00:04:28.887
I mean it's a bunch of different shades over here

00:04:28.887 --> 00:04:35.933
is reflecting diffusely, so that pure light comes in here, some of the pure light get reflected specularly

00:04:35.933 --> 00:04:41.635
or kind of purely maintaining the image, but some of it, because the surface of the apple isn't smooth

00:04:41.635 --> 00:04:47.138
is going in all sorts of directions, so of it's going like that, some of it's going like that

00:04:47.138 --> 00:04:50.600
some of it's going like that, and that's happening at every

00:04:50.600 --> 00:04:53.267
at every point on the apple, so that light source

00:04:53.267 --> 00:04:57.889
let me draw more of the light source, so rays coming in, and rays coming in from our light source

00:04:57.889 --> 00:05:01.976
but every point of the apple is also having this diffuse reflection

00:05:01.976 --> 00:05:08.400
which is reflecting only the red part of the spectrum, it's absorbing all of the other parts of the spectrum

00:05:08.400 --> 00:05:13.307
and, so what you see is, that point where you're getting the pure specular

00:05:13.307 --> 00:05:16.627
the pure specular reflections, that's the point that looks shiny

00:05:16.627 --> 00:05:18.601
where you can kind of see the light source

00:05:18.601 --> 00:05:26.733
and from every other point on the apple, where only this guy right here's only getting the diffuse red light

00:05:26.733 --> 00:05:33.090
and that's why, if you move the apple, or actually even better, if you move where you're looking at the apple

00:05:33.090 --> 00:05:36.667
that, point of reflection's gonna look, like if I start looking at it from this direction

00:05:36.667 --> 00:05:39.754
I'm gonna get a different point of reflection, cause I'm gonna start seeing the light

00:05:39.754 --> 00:05:44.166
though let's see, let's say that someone's eyeball is right, actually right over here

00:05:44.166 --> 00:05:50.273
so that's their eyebrows, that's their eyeball, that's their nose, you get the general idea

00:05:50.273 --> 00:05:54.429
so let's say that this person, let's say that this person, that's their ear

00:05:54.429 --> 00:05:56.400
there, I don't wanna get too involved in the drawing

00:05:56.400 --> 00:06:01.667
so let's say that this person is looking at this supper ginormous apple now relatively to him

00:06:01.667 --> 00:06:03.667
he is not gonna see this white spot there

00:06:03.667 --> 00:06:07.270
he is gonna see the white spot on the point where it looks like

00:06:07.270 --> 00:06:10.800
where he's getting the right angle, where, where the rays are coming in

00:06:10.800 --> 00:06:11.733
let me do it in a different color

00:06:11.733 --> 00:06:14.747
so let's say, let's say the light source is above us

00:06:14.747 --> 00:06:16.867
so the light source is coming straight down

00:06:16.867 --> 00:06:20.333
is coming straight down to the apple and than if it's the right angle

00:06:20.333 --> 00:06:24.933
if the angle of incidence and the angle of reflection relative to the surface of the apple

00:06:24.933 --> 00:06:29.200
and we can draw that out, we can draw it perpendicular to the surface of the apple

00:06:29.200 --> 00:06:34.089
this is the angle of incidence, this is the angle of reflection

00:06:34.089 --> 00:06:36.867
so those points, at that point right there he's getting a little bit

00:06:36.867 --> 00:06:37.804
and I should draw a dotted line

00:06:37.804 --> 00:06:43.200
he's getting a little bit of the, of the specular reflection, but from every other point

00:06:43.200 --> 00:06:48.933
so for every other point on the apple, so over here, the specular reflection would go that way

00:06:48.933 --> 00:06:52.133
not to his eyes, or it would go that way, not to his eyes

00:06:52.133 --> 00:06:55.133
but from those points you also have some of the diffuse reflections

00:06:55.133 --> 00:06:59.467
and some of that is going to his eye in terms of red

00:06:59.467 --> 00:07:03.439
the red part of the frequency is getting to his eye from all of these other random directions

00:07:03.439 --> 00:07:07.533
and that's why this guy over here, he would see this, this reflection

00:07:07.533 --> 00:07:12.800
he would see this reflection rougly over here, and all of this other part of the apple would look red

00:07:12.800 --> 00:07:15.133
and we, since we're on this side of the apple, we see the reflection point

00:07:15.133 --> 00:07:19.600
the light is coming straight down from our light source bouncing right here

00:07:19.600 --> 00:07:21.435
than coming straight out towards our eye

00:07:21.435 --> 00:07:25.067
coming down, and than reflecting, coming straight out towards our eye

00:07:25.067 --> 00:07:28.800
it's also coming down on these other points, but those other points are going straight out

00:07:28.800 --> 00:07:33.439
to some place where our eye isn't, instead we're just seeing, we're just seeing the diffuse part

00:07:33.439 --> 00:07:35.533
that is actually coming to our eye

00:07:35.533 --> 00:07:39.933
anyway, hopefully you found that a little bit more, um, filled in a couple of the gaps of the last video


Specular and diffuse reflection

WEBVTT
Kind: captions
Language: en

00:00:00.232 --> 00:00:01.940
In this video we're
going to try to learn

00:00:01.940 --> 00:00:04.660
a little bit about reflection.

00:00:04.660 --> 00:00:08.940
Or I guess you could say we are
going to reflect on reflection.

00:00:08.940 --> 00:00:11.000
I think most of us have
a sense of what this is,

00:00:11.000 --> 00:00:14.080
but we'll try to get a little
bit more exact about it.

00:00:14.080 --> 00:00:16.520
So there are actually
two types of reflection,

00:00:16.520 --> 00:00:20.400
and everything that reflects
is doing one or the other,

00:00:20.400 --> 00:00:21.840
or something in between.

00:00:21.840 --> 00:00:22.790
So we have two types.

00:00:22.790 --> 00:00:23.889
Let me draw them.

00:00:23.889 --> 00:00:26.180
So the first type, and this
is kind of what we normally

00:00:26.180 --> 00:00:30.525
associate with reflection
is specular reflection.

00:00:35.760 --> 00:00:37.500
And in specular
reflection, let's say

00:00:37.500 --> 00:00:39.727
that this is the
top of a mirror.

00:00:39.727 --> 00:00:41.060
This is the surface of a mirror.

00:00:41.060 --> 00:00:42.840
If I have a light
ray coming in-- So

00:00:42.840 --> 00:00:45.050
let me draw a light
ray coming in.

00:00:45.050 --> 00:00:46.860
And just to get the
terminology right,

00:00:46.860 --> 00:00:51.077
this light ray coming in,
this ray, is the incident ray.

00:00:51.077 --> 00:00:52.660
And it's the incident
ray because it's

00:00:52.660 --> 00:00:55.650
the ray as it approaches
the reflective surface.

00:00:55.650 --> 00:00:57.240
Let me write that down.

00:00:57.240 --> 00:00:59.430
That right there is
the incident ray.

00:01:05.550 --> 00:01:07.130
It'll approach the surface.

00:01:07.130 --> 00:01:09.910
And you can almost imagine
that it bounces off

00:01:09.910 --> 00:01:13.740
at essentially the same angle,
but in the other direction.

00:01:13.740 --> 00:01:16.610
So then it'll hit the surface,
and then it'll bounce off,

00:01:16.610 --> 00:01:18.830
and it'll go just like that.

00:01:18.830 --> 00:01:20.800
And then we would call
this the reflected ray,

00:01:20.800 --> 00:01:24.250
after it is kind of
bounced off of the surface.

00:01:24.250 --> 00:01:28.080
Reflected ray.

00:01:28.080 --> 00:01:29.640
And you may have
already noticed this

00:01:29.640 --> 00:01:33.796
if you've played around a lot
with mirrors you would see--

00:01:33.796 --> 00:01:35.420
and we're going to
look at some images.

00:01:35.420 --> 00:01:36.670
So you can think about
it a little better.

00:01:36.670 --> 00:01:37.890
Next time you're in
front of the bathroom

00:01:37.890 --> 00:01:39.760
mirror you can think
about this, and think

00:01:39.760 --> 00:01:42.630
about the angle of incidence
and the angle of reflection.

00:01:42.630 --> 00:01:43.840
But they're actually equal.

00:01:43.840 --> 00:01:45.550
So let me define
them right here.

00:01:45.550 --> 00:01:47.890
So if I were to just
drop a straight line

00:01:47.890 --> 00:01:50.560
that is at a 90
degree, or that is

00:01:50.560 --> 00:01:54.080
perpendicular to the
surface of the actual mirror

00:01:54.080 --> 00:01:57.780
right over here, we would
define this, right here,

00:01:57.780 --> 00:01:59.690
as the angle of incidence.

00:01:59.690 --> 00:02:00.590
I'll just use theta.

00:02:00.590 --> 00:02:03.250
That's just a fancy letter to
show that the angle at which

00:02:03.250 --> 00:02:05.340
we're coming in, the
angle between this ray

00:02:05.340 --> 00:02:09.009
and the vertical right there,
that's the angle of incidence.

00:02:09.009 --> 00:02:11.790
And then the angle
between that vertical

00:02:11.790 --> 00:02:17.440
and the blue ray
right there, we call

00:02:17.440 --> 00:02:19.480
that the angle of reflection.

00:02:19.480 --> 00:02:22.279
And it's just a property
of especially mirrors when

00:02:22.279 --> 00:02:23.695
you're having
specular reflection.

00:02:23.695 --> 00:02:25.710
And you can see
this for yourself

00:02:25.710 --> 00:02:30.950
at all the regular mirrors
that you might experience

00:02:30.950 --> 00:02:34.230
is that the angle
of incidence is

00:02:34.230 --> 00:02:38.390
equal to the angle
of reflection.

00:02:38.390 --> 00:02:40.140
And actually we could
see that in a couple

00:02:40.140 --> 00:02:41.280
of images over here.

00:02:41.280 --> 00:02:44.280
So let me show you some
images of specular reflection,

00:02:44.280 --> 00:02:46.030
just to make it clear here.

00:02:46.030 --> 00:02:49.686
So you have some light from
the sun hitting this mountain.

00:02:49.686 --> 00:02:51.685
And we're going to talk
about diffuse reflection

00:02:51.685 --> 00:02:53.559
in a little bit, and
that's what's happening.

00:02:53.559 --> 00:02:54.860
It's being reflected diffusely.

00:02:54.860 --> 00:02:57.640
That's why we don't see the
actual image of the sun here.

00:02:57.640 --> 00:02:59.522
We just see the white.

00:02:59.522 --> 00:03:01.730
But then those white light
rays, and they're actually

00:03:01.730 --> 00:03:04.370
being scattered in every
direction, some of them

00:03:04.370 --> 00:03:06.700
are hitting the water.

00:03:06.700 --> 00:03:08.840
I'm going to try to match
up parts of the mountain.

00:03:08.840 --> 00:03:10.423
So you have this
part of the mountain.

00:03:10.423 --> 00:03:11.930
Let me do this in
a better color.

00:03:11.930 --> 00:03:14.030
You have this part of
the mountain up here,

00:03:14.030 --> 00:03:16.950
and the part of the
reflection right over there.

00:03:16.950 --> 00:03:18.790
So what's happening
right here is

00:03:18.790 --> 00:03:21.710
light is coming from that
part of the mountain,

00:03:21.710 --> 00:03:25.040
hitting this part of the
surface of the water.

00:03:25.040 --> 00:03:26.960
Let me see if I can
draw this better.

00:03:26.960 --> 00:03:29.380
It's hitting this part of
the surface of the water,

00:03:29.380 --> 00:03:32.870
and then it's getting
reflected, specular reflection,

00:03:32.870 --> 00:03:33.384
to our eyes.

00:03:33.384 --> 00:03:35.050
And it's actually
coming straight at us,

00:03:35.050 --> 00:03:36.620
but I'll draw it
at a slight angle.

00:03:36.620 --> 00:03:42.187
And then it's just coming
straight to our eyes like this.

00:03:42.187 --> 00:03:44.020
If our eye was-- Let's
say our eye was here.

00:03:44.020 --> 00:03:46.860
It's actually coming straight
out at us so I actually

00:03:46.860 --> 00:03:49.120
should just draw
a vertical line,

00:03:49.120 --> 00:03:50.676
but hopefully this
makes it clear.

00:03:50.676 --> 00:03:52.550
And what we just said,
the angle of incidence

00:03:52.550 --> 00:03:54.050
is equal to the
angle of reflection,

00:03:54.050 --> 00:03:56.880
so if you were to
draw a vertical,

00:03:56.880 --> 00:03:59.540
and it might not be that obvious
here, but this angle right

00:03:59.540 --> 00:04:02.010
over here-- Let me draw
this a little darker color.

00:04:02.010 --> 00:04:05.000
This angle right over
here, that's the angle--

00:04:05.000 --> 00:04:07.490
Let me do that in a light color.

00:04:07.490 --> 00:04:09.680
This right here is
the incident angle.

00:04:09.680 --> 00:04:11.090
We drew a vertical.

00:04:11.090 --> 00:04:12.840
And the angle at
which the light ray

00:04:12.840 --> 00:04:14.910
is approaching the
surface of the water,

00:04:14.910 --> 00:04:17.160
right before it bounces,
that's the incident angle

00:04:17.160 --> 00:04:19.060
relative to vertical.

00:04:19.060 --> 00:04:21.029
And then this angle
right here-- and I

00:04:21.029 --> 00:04:22.890
know it's hard-- it doesn't
look like they're the same

00:04:22.890 --> 00:04:24.410
but that's just because
of the perspective

00:04:24.410 --> 00:04:25.500
that we're dealing with.

00:04:25.500 --> 00:04:28.400
This is the angle of reflection.

00:04:28.400 --> 00:04:30.360
And they're actually
going to be equal.

00:04:30.360 --> 00:04:31.984
And you could also
make a similar case.

00:04:31.984 --> 00:04:35.370
And sometimes my brain has
easier thinking about this.

00:04:35.370 --> 00:04:37.000
If this angle is
equal to that angle--

00:04:37.000 --> 00:04:39.370
and this is what's defined
to be the angle of incidence

00:04:39.370 --> 00:04:41.630
and the angle of
reflection-- we also

00:04:41.630 --> 00:04:44.230
know that this
angle, right here,

00:04:44.230 --> 00:04:46.319
is going to be equal to
that angle right there.

00:04:46.319 --> 00:04:48.360
And my brain sometimes
thinks that because that's

00:04:48.360 --> 00:04:50.760
kind of the angle between the
ray and the actual surface,

00:04:50.760 --> 00:04:52.709
but they're really
the same notions.

00:04:52.709 --> 00:04:54.250
And obviously it's
a different angle,

00:04:54.250 --> 00:04:56.541
but if this is equal to that
then this is equal to that

00:04:56.541 --> 00:04:58.330
because these two are
going to add to 90,

00:04:58.330 --> 00:04:59.880
these two are
going to add to 90.

00:04:59.880 --> 00:05:01.740
So another way you
could view it is-- So

00:05:01.740 --> 00:05:04.830
if we look at the
surface of the water.

00:05:04.830 --> 00:05:07.360
Let me draw a line along
the surface of the water.

00:05:07.360 --> 00:05:12.270
Another way to think about it
is that this angle, this angle

00:05:12.270 --> 00:05:16.240
right over here, is going
to be the same as this angle

00:05:16.240 --> 00:05:17.330
right over there.

00:05:17.330 --> 00:05:21.390
And you can also see it in this
reflection right over here.

00:05:21.390 --> 00:05:24.450
So the light from the sun is
going directly to the water

00:05:24.450 --> 00:05:27.880
here, and then getting reflected
at that point on the surface

00:05:27.880 --> 00:05:30.770
of the water, and then
coming over to our eyes.

00:05:30.770 --> 00:05:32.710
And so we could either
say that this angle is

00:05:32.710 --> 00:05:35.480
equal to this angle, so the
angle between the incident ray

00:05:35.480 --> 00:05:38.280
and the surface of the
water is equal to the angle

00:05:38.280 --> 00:05:40.730
of the reflected ray and
the surface of the water,

00:05:40.730 --> 00:05:45.350
or we could draw a
perpendicular right over here--

00:05:45.350 --> 00:05:48.867
I'm not doing that too well-- we
can draw a perpendicular right

00:05:48.867 --> 00:05:50.450
over here to the
surface of the water,

00:05:50.450 --> 00:05:53.180
and say that the incident
angle, the angle of incidence

00:05:53.180 --> 00:05:55.440
right there between the
ray and that perpendicular,

00:05:55.440 --> 00:05:58.355
is going to be the same
as the reflected angle.

00:05:58.355 --> 00:05:59.980
And it's hard to see
there, once again,

00:05:59.980 --> 00:06:01.550
because of the
perspective, but hopefully

00:06:01.550 --> 00:06:02.633
that starts to make sense.

00:06:02.633 --> 00:06:04.660
And I encourage you,
go to your bathroom

00:06:04.660 --> 00:06:07.076
and look in the mirror, and
look at objects in the mirror,

00:06:07.076 --> 00:06:09.810
and think about the angle
that the light from the object

00:06:09.810 --> 00:06:12.030
must be hitting the mirror
for it to get to your eye,

00:06:12.030 --> 00:06:13.821
and where it's actually
hitting the mirror.

00:06:13.821 --> 00:06:16.040
It's actually a pretty
interesting thing

00:06:16.040 --> 00:06:19.400
to do if you're looking for
things to do in the bathroom.

00:06:19.400 --> 00:06:22.020
Now all we've talked about
is specular reflection,

00:06:22.020 --> 00:06:24.764
but the other type of reflection
is diffuse reflection.

00:06:24.764 --> 00:06:26.180
And this is the
type of reflection

00:06:26.180 --> 00:06:28.010
that it may not be
as obvious to you

00:06:28.010 --> 00:06:30.940
that it's occurring
everywhere you look.

00:06:30.940 --> 00:06:35.156
Diffuse reflection.

00:06:35.156 --> 00:06:37.970
And in diffuse reflection,
because the surface

00:06:37.970 --> 00:06:41.690
isn't smooth, it's not
what we kind of associate

00:06:41.690 --> 00:06:44.060
as a mirrored surface.

00:06:44.060 --> 00:06:46.060
So I'll draw it,
I'll zoom in a bunch.

00:06:46.060 --> 00:06:49.040
So in diffuse reflection,
maybe the surface looks

00:06:49.040 --> 00:06:52.230
like that, what happens
is-- and let me be clear.

00:06:52.230 --> 00:06:53.900
In specular reflection
any light ray

00:06:53.900 --> 00:06:57.030
that comes in like that,
the reflection will come off

00:06:57.030 --> 00:06:58.680
at the same-- the
angle of incidence

00:06:58.680 --> 00:07:00.680
will always be equal to
the angle of reflection.

00:07:00.680 --> 00:07:03.820
This is for the situation
of, say, a mirror.

00:07:03.820 --> 00:07:05.010
It'll always be the same.

00:07:05.010 --> 00:07:09.010
If I come in at a
steeper angle, then I'll

00:07:09.010 --> 00:07:10.980
go out in a steeper
angle, just like that.

00:07:10.980 --> 00:07:12.620
That's for specular reflection.

00:07:12.620 --> 00:07:15.030
For diffuse reflection all
sorts of crazy things happen.

00:07:15.030 --> 00:07:17.840
And that's because we don't
have this really smooth surface,

00:07:17.840 --> 00:07:20.430
or the molecules that
make up the surface

00:07:20.430 --> 00:07:22.210
do crazy things to light.

00:07:22.210 --> 00:07:25.580
So if I come in in one
direction, right over here,

00:07:25.580 --> 00:07:28.010
over at that point
the light might

00:07:28.010 --> 00:07:29.690
reflect in that direction.

00:07:29.690 --> 00:07:33.130
Although if I come in at
the same angle over here,

00:07:33.130 --> 00:07:35.660
now all of a sudden the light
might go in that direction.

00:07:35.660 --> 00:07:38.970
And then if I come in at
the same angle over here,

00:07:38.970 --> 00:07:41.346
now all of a sudden the light
might go in that direction.

00:07:41.346 --> 00:07:43.928
And if I come in-- and I think
you get the general idea here--

00:07:43.928 --> 00:07:45.730
if I come in over
here, now the light

00:07:45.730 --> 00:07:47.190
might scatter in that direction.

00:07:47.190 --> 00:07:51.264
If I come in over here
at the same angle,

00:07:51.264 --> 00:07:53.180
now the light might
scatter in that direction.

00:07:53.180 --> 00:07:56.060
So the general idea is,
with diffuse reaction,

00:07:56.060 --> 00:08:01.700
the reflected rays are going in
all sorts of crazy directions,

00:08:01.700 --> 00:08:05.720
and they're getting
all mixed up.

00:08:05.720 --> 00:08:08.879
So think about here, if you
had an image here of the sun,

00:08:08.879 --> 00:08:10.420
and I'm not drawing
it in particular,

00:08:10.420 --> 00:08:16.210
but let's say that these rays
right here are coming directly

00:08:16.210 --> 00:08:19.590
from the sun, then
when they reflect

00:08:19.590 --> 00:08:21.180
it'll kind of
preserve the image.

00:08:21.180 --> 00:08:23.830
You'll have the reflected
image of the sun.

00:08:23.830 --> 00:08:25.880
But over here, if all
of these light rays

00:08:25.880 --> 00:08:28.270
are coming from the
sun, they're not all

00:08:28.270 --> 00:08:29.770
going off in the same direction.

00:08:29.770 --> 00:08:31.794
This will be a part of
the sun, part of the sun.

00:08:31.794 --> 00:08:33.919
And it's happening at a
really, really small level.

00:08:33.919 --> 00:08:36.110
So you're really just
capturing the light,

00:08:36.110 --> 00:08:38.980
but you're losing all
of the information

00:08:38.980 --> 00:08:40.039
from the actual image.

00:08:40.039 --> 00:08:42.539
And if you're wondering where
diffuse reflection occurs just

00:08:42.539 --> 00:08:43.470
look around your room.

00:08:43.470 --> 00:08:46.300
Anything that's not a mirror
is reflecting diffusely.

00:08:46.300 --> 00:08:48.160
It's diffusing the light.

00:08:48.160 --> 00:08:49.050
Do you see that here?

00:08:49.050 --> 00:08:51.340
The mountain right here
is diffuse reflection.

00:08:51.340 --> 00:08:55.920
You have light
coming from the sun,

00:08:55.920 --> 00:09:00.670
but that's being reflected in
all sorts of crazy directions.

00:09:00.670 --> 00:09:04.200
So you don't see a reflection
of the sky over here.

00:09:04.200 --> 00:09:06.290
The water here, that's
specular reflection

00:09:06.290 --> 00:09:09.417
because it's so super
smooth that it preserves--

00:09:09.417 --> 00:09:12.000
The angle of incidence is going
to be the angle of reflection.

00:09:12.000 --> 00:09:14.125
It's always going to be
the same angle because it's

00:09:14.125 --> 00:09:17.090
a kind of almost
perfectly smooth surface.

00:09:17.090 --> 00:09:18.897
The trees, that's
diffuse reflection.

00:09:18.897 --> 00:09:21.230
And I also want to be clear
on something like the trees.

00:09:21.230 --> 00:09:23.856
So on something that's
white, and white

00:09:23.856 --> 00:09:25.230
is the entire
spectrum of light--

00:09:25.230 --> 00:09:27.590
and we'll do more videos
on that in the future--

00:09:27.590 --> 00:09:29.090
it's reflecting the
entire spectrum.

00:09:29.090 --> 00:09:30.850
It's just mixing
it all up so you

00:09:30.850 --> 00:09:32.290
don't see an actual reflection.

00:09:32.290 --> 00:09:35.660
But if you look
at the trees, you

00:09:35.660 --> 00:09:39.790
have the entire spectrum
from the sun coming down

00:09:39.790 --> 00:09:42.660
on the trees, but the trees
themselves-- and you should

00:09:42.660 --> 00:09:45.710
watch the videos on
photosynthesis-- they're

00:09:45.710 --> 00:09:50.280
absorbing every other frequency
of light except for the greens

00:09:50.280 --> 00:09:51.590
you see.

00:09:51.590 --> 00:09:58.320
So they are just reflecting
the green back to us.

00:09:58.320 --> 00:10:00.770
And they're doing it in
a way they're diffusely

00:10:00.770 --> 00:10:01.360
reflecting it.

00:10:01.360 --> 00:10:05.350
So we actually don't
see an actual reflection

00:10:05.350 --> 00:10:07.125
in those trees.

00:10:07.125 --> 00:10:09.250
And I'll just finish up
with one kind of neat thing

00:10:09.250 --> 00:10:11.230
because it's kind of
like playing billiards

00:10:11.230 --> 00:10:13.563
here, because you can actually
have a double reflection.

00:10:13.563 --> 00:10:16.125
That's why I even had
this image over here.

00:10:16.125 --> 00:10:18.310
The sun is being reflected
on the water here,

00:10:18.310 --> 00:10:19.830
and then you have a reflection.

00:10:19.830 --> 00:10:21.455
This is a direct
reflection of the sun,

00:10:21.455 --> 00:10:23.720
but this is a reflection
of the sun reflected

00:10:23.720 --> 00:10:25.290
on the water right over here.

00:10:25.290 --> 00:10:27.190
So what you have over
here is the light

00:10:27.190 --> 00:10:29.520
from the sun coming
to this reflection,

00:10:29.520 --> 00:10:31.290
reflecting at that
point on the water,

00:10:31.290 --> 00:10:35.640
then going to this
point on the paddle,

00:10:35.640 --> 00:10:38.930
and then coming to our eye.

00:10:38.930 --> 00:10:42.060
But once again the angle of
incidence in every situation

00:10:42.060 --> 00:10:45.030
here is going to be equal
to the angle of reflection.

00:10:45.030 --> 00:10:47.450
Although the paddle looks like
it's a little bit distorted

00:10:47.450 --> 00:10:49.380
here, so it's not a
completely smooth surface,

00:10:49.380 --> 00:10:51.240
so it makes the math
a little harder.

00:10:51.240 --> 00:10:52.904
But when you start
thinking about this

00:10:52.904 --> 00:10:54.320
it becomes pretty
interesting just

00:10:54.320 --> 00:10:56.660
to look at almost any
reflective surfaces

00:10:56.660 --> 00:10:59.510
and to think about
the actual angles.


Carbon 14 dating 2

WEBVTT
Kind: captions
Language: en

00:00:00.670 --> 00:00:02.800
In the last video, we
talked about the idea

00:00:02.800 --> 00:00:07.310
that if I dug up a bone
someplace, if I dug up a bone,

00:00:07.310 --> 00:00:09.300
and if I were to
measure its carbon-14,

00:00:09.300 --> 00:00:13.140
and I found that it had half
of the carbon-14 that I would

00:00:13.140 --> 00:00:17.440
expect to find in a living
animal or plant, that I said,

00:00:17.440 --> 00:00:20.710
hey, maybe one half life
has gone by, or roughly

00:00:20.710 --> 00:00:25.700
for carbon-14, one half
life is 5,730 years.

00:00:25.700 --> 00:00:29.290
So I said maybe it's 5,730
years since this bone was

00:00:29.290 --> 00:00:32.880
part of a living animal,
or it's roughly that old.

00:00:32.880 --> 00:00:35.800
Now, when I did that, I made
a pretty big assumption,

00:00:35.800 --> 00:00:39.450
and some you all have touched on
this in the comments on YouTube

00:00:39.450 --> 00:00:41.930
on the last video,
is how do I know

00:00:41.930 --> 00:00:46.140
that this estimate I made
is based on the assumption

00:00:46.140 --> 00:00:48.430
that the amount of
carbon-14 in the atmosphere

00:00:48.430 --> 00:00:52.840
would have been roughly constant
from when this bone was living

00:00:52.840 --> 00:00:53.940
to now?

00:00:53.940 --> 00:00:57.270
And so the question is,
is the amount of carbon-14

00:00:57.270 --> 00:00:59.490
in the atmosphere
and in the water,

00:00:59.490 --> 00:01:02.450
and in living plants and
animals, is it constant?

00:01:02.450 --> 00:01:05.700
And if it isn't constant, how do
you calibrate your measurement

00:01:05.700 --> 00:01:08.910
so you can actually figure
out how much carbon-14 there

00:01:08.910 --> 00:01:13.692
is relative to living plants
and animals at that time?

00:01:13.692 --> 00:01:15.650
And the way that you can
make that calibration,

00:01:15.650 --> 00:01:18.310
because it turns out it
isn't perfectly constant,

00:01:18.310 --> 00:01:20.950
the way that you can make that
calibration, there's two ways,

00:01:20.950 --> 00:01:22.760
and I have pictures
here of both of them,

00:01:22.760 --> 00:01:24.930
one is to look at tree things.

00:01:24.930 --> 00:01:25.640
Tree rings.

00:01:25.640 --> 00:01:30.150
And I'm told this will work
up to about 10,000 years.

00:01:30.150 --> 00:01:32.840
Up to 10,000 years old.

00:01:32.840 --> 00:01:34.685
I don't know of any
10,000 year old trees,

00:01:34.685 --> 00:01:36.520
I don't think anyone
does, but maybe there's

00:01:36.520 --> 00:01:38.901
some remains of old trees.

00:01:38.901 --> 00:01:41.400
And you can look at their tree
rings, and I think most of us

00:01:41.400 --> 00:01:45.140
are familiar with this idea that
every year that a tree grows,

00:01:45.140 --> 00:01:47.440
it forms another layer of bark.

00:01:47.440 --> 00:01:49.880
And so you can look back
to that layer of bark

00:01:49.880 --> 00:01:53.800
just for the half
life of carbon-14,

00:01:53.800 --> 00:01:56.580
and then figure out how
much carbon-14 was there

00:01:56.580 --> 00:01:58.760
in the atmosphere at
that period in time.

00:01:58.760 --> 00:02:01.970
And so it's kind of a
record of the atmosphere up

00:02:01.970 --> 00:02:03.310
to 10,000 years.

00:02:03.310 --> 00:02:04.920
If you want to go
even further back,

00:02:04.920 --> 00:02:07.200
you can look at cave
deposits, and the fancy word

00:02:07.200 --> 00:02:11.780
for these cave deposits
are speleothems.

00:02:11.780 --> 00:02:14.020
Speleothems.

00:02:14.020 --> 00:02:14.940
Speleothems.

00:02:14.940 --> 00:02:16.840
You might be familiar
with stalagmites.

00:02:16.840 --> 00:02:19.180
Those are those speleothems
that are kind of coming out

00:02:19.180 --> 00:02:22.054
of the bottom of the
cave, or stalactites.

00:02:22.054 --> 00:02:23.470
Those are the
speleothems that are

00:02:23.470 --> 00:02:25.562
coming from the top of the cave.

00:02:25.562 --> 00:02:27.020
But the reason why
these are useful

00:02:27.020 --> 00:02:29.650
is these are formed
by calcium carbonate,

00:02:29.650 --> 00:02:33.580
so they have carbon in them,
and slowly over, really,

00:02:33.580 --> 00:02:37.010
tens of thousands of years,
the water in the cave deposits

00:02:37.010 --> 00:02:38.140
that calcium carbonate.

00:02:38.140 --> 00:02:41.980
So it's a record of the fraction
of carbon-14 in some of those

00:02:41.980 --> 00:02:42.480
years.

00:02:42.480 --> 00:02:45.830
And you can go down to
resolutions of as small as 10

00:02:45.830 --> 00:02:46.740
years.

00:02:46.740 --> 00:02:48.940
And so this will give
us pretty good estimates

00:02:48.940 --> 00:02:52.220
over tens of thousands of
years, up to 50,000 years.

00:02:52.220 --> 00:02:55.020
And frankly, carbon-14
isn't even useful

00:02:55.020 --> 00:03:00.205
beyond, really, 50,000
or 60,000 years.

00:03:00.205 --> 00:03:04.350
So this gives us a good
record of carbon-14

00:03:04.350 --> 00:03:05.930
in the atmosphere,
assuming that it's

00:03:05.930 --> 00:03:07.830
fairly uniform throughout
the atmosphere,

00:03:07.830 --> 00:03:11.380
and all evidence suggests
that, and that that uniformity

00:03:11.380 --> 00:03:14.740
through the atmosphere also
goes into the water supply,

00:03:14.740 --> 00:03:17.450
and into living
plants and animals.

00:03:17.450 --> 00:03:20.160
Now, the other thing, and I
looked into this a little bit,

00:03:20.160 --> 00:03:24.360
it actually turns out because we
are spewing so much fossil fuel

00:03:24.360 --> 00:03:27.660
right now, we are
changing the amount,

00:03:27.660 --> 00:03:32.510
or the proportion of carbon-14
much, much faster than has

00:03:32.510 --> 00:03:34.880
happened in other time periods.

00:03:34.880 --> 00:03:36.770
So just to answer
the question, it's

00:03:36.770 --> 00:03:39.310
actually probably in
really, the last 50 years

00:03:39.310 --> 00:03:41.060
where the fossil
fuel use has really

00:03:41.060 --> 00:03:43.050
exploded that we've
really been changing

00:03:43.050 --> 00:03:45.080
the proportion of
carbon-14 relative

00:03:45.080 --> 00:03:47.300
to the other isotopes of carbon.

00:03:47.300 --> 00:03:51.190
But anyway, hopefully
that rests some

00:03:51.190 --> 00:03:53.810
of your worries
about the assumption

00:03:53.810 --> 00:03:56.270
that I made in the last
video about carbon-14

00:03:56.270 --> 00:03:57.590
being relatively constant.

00:03:57.590 --> 00:04:00.820
There are ways to look
back at specific years

00:04:00.820 --> 00:04:03.910
and figure out the relative
amounts of carbon-14,

00:04:03.910 --> 00:04:07.810
so it is a pretty
good way of estimating

00:04:07.810 --> 00:04:10.560
how old living things
are, especially

00:04:10.560 --> 00:04:14.460
things that are less
than 50,000 years old.


Carbon 14 dating 1

WEBVTT
Kind: captions
Language: en

00:00:00.624 --> 00:00:02.040
What I want to do
in this video is

00:00:02.040 --> 00:00:04.330
kind of introduce
you to the idea of,

00:00:04.330 --> 00:00:07.650
one, how carbon-14
comes about, and how

00:00:07.650 --> 00:00:10.470
it gets into all living things.

00:00:10.470 --> 00:00:12.884
And then either later in this
video or in future videos

00:00:12.884 --> 00:00:14.300
we'll talk about
how it's actually

00:00:14.300 --> 00:00:17.750
used to date things, how we
use it actually figure out

00:00:17.750 --> 00:00:20.660
that that bone is
12,000 years old,

00:00:20.660 --> 00:00:24.800
or that person died 18,000
years ago, whatever it might be.

00:00:24.800 --> 00:00:27.040
So let me draw the Earth.

00:00:27.040 --> 00:00:29.459
So let me just draw the
surface of the Earth like that.

00:00:29.459 --> 00:00:31.750
It's just a little section
of the surface of the Earth.

00:00:31.750 --> 00:00:34.200
And then we have the
atmosphere of the Earth.

00:00:34.200 --> 00:00:35.490
I'll draw that in yellow.

00:00:35.490 --> 00:00:39.630
So then you have the Earth's
atmosphere right over here.

00:00:39.630 --> 00:00:43.710
Let me write that
down, atmosphere.

00:00:43.710 --> 00:00:48.740
And 78%, the most abundant
element in our atmosphere

00:00:48.740 --> 00:00:49.630
is nitrogen.

00:00:49.630 --> 00:00:52.670
It is 78% nitrogen.

00:00:52.670 --> 00:00:54.270
And I'll write nitrogen.

00:00:54.270 --> 00:00:59.430
Its symbol is just N.
And it has seven protons,

00:00:59.430 --> 00:01:01.670
and it also has seven neutrons.

00:01:01.670 --> 00:01:05.050
So it has an atomic
mass of roughly 14.

00:01:05.050 --> 00:01:07.650
Then this is the most
typical isotope of nitrogen.

00:01:07.650 --> 00:01:09.180
And we talk about
the word isotope

00:01:09.180 --> 00:01:10.470
in the chemistry playlist.

00:01:10.470 --> 00:01:14.420
An isotope, the protons
define what element it is.

00:01:14.420 --> 00:01:16.860
But this number up here
can change depending

00:01:16.860 --> 00:01:18.890
on the number of
neutrons you have.

00:01:18.890 --> 00:01:21.220
So the different versions
of a given element,

00:01:21.220 --> 00:01:22.760
those are each called isotopes.

00:01:22.760 --> 00:01:25.630
I just view in my head as
versions of an element.

00:01:25.630 --> 00:01:27.130
So anyway, we have
our atmosphere,

00:01:27.130 --> 00:01:29.580
and then coming from
our sun, we have

00:01:29.580 --> 00:01:31.451
what's commonly
called cosmic rays,

00:01:31.451 --> 00:01:32.700
but they're actually not rays.

00:01:32.700 --> 00:01:34.820
They're cosmic particles.

00:01:34.820 --> 00:01:36.930
You can view them as just
single protons, which

00:01:36.930 --> 00:01:39.400
is the same thing as
a hydrogen nucleus.

00:01:39.400 --> 00:01:40.897
They can also be
alpha particles,

00:01:40.897 --> 00:01:42.730
which is the same thing
as a helium nucleus.

00:01:42.730 --> 00:01:44.742
And there's even
a few electrons.

00:01:44.742 --> 00:01:46.450
And they're going to
come in, and they're

00:01:46.450 --> 00:01:48.283
going to bump into
things in our atmosphere,

00:01:48.283 --> 00:01:50.650
and they're actually
going to form neutrons.

00:01:50.650 --> 00:01:54.230
So they're actually
going to form neutrons.

00:01:54.230 --> 00:01:58.170
And we'll show a neutron
with a lowercase n, and a 1

00:01:58.170 --> 00:02:00.350
for its mass number.

00:02:00.350 --> 00:02:02.450
And we don't write
anything, because it

00:02:02.450 --> 00:02:04.100
has no protons down here.

00:02:04.100 --> 00:02:06.130
Like we had for nitrogen,
we had seven protons.

00:02:06.130 --> 00:02:07.379
So it's not really an element.

00:02:07.379 --> 00:02:09.229
It is a subatomic particle.

00:02:09.229 --> 00:02:11.050
But you have these
neutrons form.

00:02:11.050 --> 00:02:13.220
And every now and
then-- and let's

00:02:13.220 --> 00:02:15.720
just be clear-- this isn't
like a typical reaction.

00:02:15.720 --> 00:02:18.680
But every now and then
one of those neutrons

00:02:18.680 --> 00:02:21.510
will bump into one
of the nitrogen-14's

00:02:21.510 --> 00:02:30.020
in just the right way
so that it bumps off

00:02:30.020 --> 00:02:36.710
one of the protons
in the nitrogen

00:02:36.710 --> 00:02:39.200
and essentially replaces
that proton with itself.

00:02:39.200 --> 00:02:40.200
So let me make it clear.

00:02:40.200 --> 00:02:42.510
So it bumps off
one of the protons.

00:02:42.510 --> 00:02:45.970
So instead of seven protons
we now have six protons.

00:02:45.970 --> 00:02:49.030
But this number 14
doesn't go down to 13

00:02:49.030 --> 00:02:50.650
because it replaces
it with itself.

00:02:50.650 --> 00:02:52.970
So this still stays at 14.

00:02:52.970 --> 00:02:56.860
And now since it
only has six protons,

00:02:56.860 --> 00:02:58.940
this is no longer
nitrogen, by definition.

00:02:58.940 --> 00:03:00.680
This is now carbon.

00:03:00.680 --> 00:03:04.446
And that proton that was bumped
off just kind of gets emitted.

00:03:04.446 --> 00:03:06.320
So then let me just do
that in another color.

00:03:06.320 --> 00:03:07.250
So plus.

00:03:07.250 --> 00:03:09.450
And a proton that's
just flying around,

00:03:09.450 --> 00:03:12.790
you could call that hydrogen 1.

00:03:12.790 --> 00:03:14.501
And it can gain an
electron some ways.

00:03:14.501 --> 00:03:16.000
If it doesn't gain
an electron, it's

00:03:16.000 --> 00:03:19.290
just a hydrogen ion, a
positive ion, either way,

00:03:19.290 --> 00:03:21.020
or a hydrogen nucleus.

00:03:21.020 --> 00:03:22.660
But this process--
and once again, it's

00:03:22.660 --> 00:03:24.980
not a typical process,
but it happens every now

00:03:24.980 --> 00:03:28.760
and then-- this is
how carbon-14 forms.

00:03:28.760 --> 00:03:30.820
So this right here is carbon-14.

00:03:30.820 --> 00:03:33.590
You can essentially
view it as a nitrogen-14

00:03:33.590 --> 00:03:37.580
where one of the protons
is replaced with a neutron.

00:03:37.580 --> 00:03:39.306
And what's interesting
about this is this

00:03:39.306 --> 00:03:41.180
is constantly being
formed in our atmosphere,

00:03:41.180 --> 00:03:43.397
not in huge quantities, but
in reasonable quantities.

00:03:43.397 --> 00:03:44.480
So let me write this down.

00:03:49.140 --> 00:03:50.070
Constant formation.

00:03:52.620 --> 00:03:54.050
And let me be very clear.

00:03:54.050 --> 00:03:57.330
Let's look at the
periodic table over here.

00:03:57.330 --> 00:04:03.280
So carbon by definition
has six protons,

00:04:03.280 --> 00:04:06.830
but the typical isotope, the
most common isotope of carbon

00:04:06.830 --> 00:04:08.830
is carbon-12.

00:04:08.830 --> 00:04:13.000
So carbon-12 is the most common.

00:04:15.680 --> 00:04:19.050
So most of the carbon in
your body is carbon-12.

00:04:19.050 --> 00:04:22.570
But what's interesting
is that a small fraction

00:04:22.570 --> 00:04:26.030
of carbon-14 forms,
and then this carbon-14

00:04:26.030 --> 00:04:30.430
can then also combine with
oxygen to form carbon dioxide.

00:04:30.430 --> 00:04:32.490
And then that
carbon dioxide gets

00:04:32.490 --> 00:04:35.620
absorbed into the rest of the
atmosphere, into our oceans.

00:04:35.620 --> 00:04:37.716
It can be fixed by plants.

00:04:37.716 --> 00:04:39.340
When people talk
about carbon fixation,

00:04:39.340 --> 00:04:41.970
they're really talking about
using mainly light energy

00:04:41.970 --> 00:04:44.020
from the sun to
take gaseous carbon

00:04:44.020 --> 00:04:46.810
and turn it into actual
kind of organic tissue.

00:04:46.810 --> 00:04:54.150
And so this carbon-14, it's
constantly being formed.

00:04:54.150 --> 00:04:59.580
It makes its way into oceans--
it's already in the air,

00:04:59.580 --> 00:05:03.160
but it completely mixes
through the whole atmosphere--

00:05:03.160 --> 00:05:04.400
and the air.

00:05:04.400 --> 00:05:08.660
And then it makes
its way into plants.

00:05:08.660 --> 00:05:11.170
And plants are
really just made out

00:05:11.170 --> 00:05:12.910
of that fixed carbon,
that carbon that

00:05:12.910 --> 00:05:17.070
was taken in gaseous
form and put into,

00:05:17.070 --> 00:05:19.860
I guess you could say,
into kind of a solid form,

00:05:19.860 --> 00:05:21.010
put it into a living form.

00:05:21.010 --> 00:05:22.830
That's what wood pretty much is.

00:05:22.830 --> 00:05:24.770
It gets put into
plants, and then it

00:05:24.770 --> 00:05:28.850
gets put into the things
that eat the plants.

00:05:28.850 --> 00:05:30.620
So that could be us.

00:05:30.620 --> 00:05:33.230
Now why is this
even interesting?

00:05:33.230 --> 00:05:35.600
I've just explained a mechanism
where some of our body,

00:05:35.600 --> 00:05:38.690
even though carbon-12 is the
most common isotope, some

00:05:38.690 --> 00:05:41.600
of our body, while we're
living, gets made up

00:05:41.600 --> 00:05:43.780
of this carbon-14 thing.

00:05:43.780 --> 00:05:45.950
Well, the interesting
thing is the only time

00:05:45.950 --> 00:05:48.650
you can take in this carbon-14
is while you're alive,

00:05:48.650 --> 00:05:50.470
while you're eating new things.

00:05:50.470 --> 00:05:52.000
Because as soon
as you die and you

00:05:52.000 --> 00:05:53.700
get buried under
the ground, there's

00:05:53.700 --> 00:05:56.520
no way for the carbon-14 to
become part of your tissue

00:05:56.520 --> 00:05:59.690
anymore because you're
not eating anything

00:05:59.690 --> 00:06:01.860
with new carbon-14.

00:06:01.860 --> 00:06:04.560
And what's interesting
here is once you die,

00:06:04.560 --> 00:06:06.790
you're not going to
get any new carbon-14.

00:06:06.790 --> 00:06:09.940
And that carbon-14 that you
did have at you're death

00:06:09.940 --> 00:06:18.970
is going to decay
via beta decay--

00:06:18.970 --> 00:06:24.460
and we learned about this--
back into nitrogen-14.

00:06:24.460 --> 00:06:27.080
So kind of this
process reverses.

00:06:27.080 --> 00:06:30.920
So it'll decay back into
nitrogen-14, and in beta decay

00:06:30.920 --> 00:06:36.220
you emit an electron and
an electron anti-neutrino.

00:06:36.220 --> 00:06:38.030
I won't go into the
details of that.

00:06:38.030 --> 00:06:40.310
But essentially what
you have happening here

00:06:40.310 --> 00:06:44.250
is you have one of the neutrons
is turning into a proton

00:06:44.250 --> 00:06:47.630
and emitting this
stuff in the process.

00:06:47.630 --> 00:06:48.944
Now why is this interesting?

00:06:48.944 --> 00:06:50.360
So I just said
while you're living

00:06:50.360 --> 00:06:53.940
you have kind of
straight-up carbon-14.

00:06:53.940 --> 00:06:57.445
And carbon-14 is constantly
doing this decay thing.

00:06:57.445 --> 00:06:58.820
But what's
interesting is as soon

00:06:58.820 --> 00:07:01.800
as you die and you're
not ingesting anymore

00:07:01.800 --> 00:07:04.640
plants, or breathing from the
atmosphere if you are a plant,

00:07:04.640 --> 00:07:05.890
or fixing from the atmosphere.

00:07:05.890 --> 00:07:07.223
And this even applies to plants.

00:07:07.223 --> 00:07:10.260
Once a plant dies, it's no
longer taking in carbon dioxide

00:07:10.260 --> 00:07:14.010
from the atmosphere and
turning it into new tissue.

00:07:14.010 --> 00:07:16.480
The carbon-14 in that
tissue gets frozen.

00:07:16.480 --> 00:07:23.700
And this carbon-14 does this
decay at a specific rate.

00:07:23.700 --> 00:07:26.430
And then you can use that
rate to actually determine how

00:07:26.430 --> 00:07:28.740
long ago that
thing must've died.

00:07:28.740 --> 00:07:32.200
So the rate at
which this happens,

00:07:32.200 --> 00:07:38.910
so the rate of carbon-14 decay,
is essentially half disappears,

00:07:38.910 --> 00:07:49.110
half gone, in
roughly 5,730 years.

00:07:49.110 --> 00:07:51.130
And this is actually
called a half life.

00:07:51.130 --> 00:07:52.580
And we talk about
in other videos.

00:07:52.580 --> 00:07:54.684
This is called a half life.

00:07:54.684 --> 00:07:55.850
And I want to be clear here.

00:07:55.850 --> 00:07:57.474
You don't know which
half of it's gone.

00:07:57.474 --> 00:07:58.670
It's a probabilistic thing.

00:07:58.670 --> 00:08:01.046
You can't just say all the
carbon-14's on the left are

00:08:01.046 --> 00:08:03.170
going to decay and all the
carbon-14's on the right

00:08:03.170 --> 00:08:05.630
aren't going to decay
in that 5,730 years.

00:08:05.630 --> 00:08:09.480
What it's essentially saying
is any given carbon-14 atom

00:08:09.480 --> 00:08:15.020
has a 50% chance of
decaying into nitrogen-14

00:08:15.020 --> 00:08:17.270
in 5,730 years.

00:08:17.270 --> 00:08:20.650
So over the course of 5,730
years, roughly half of them

00:08:20.650 --> 00:08:21.700
will have decayed.

00:08:21.700 --> 00:08:24.740
Now why is that interesting?

00:08:24.740 --> 00:08:27.350
Well, if you know that
all living things have

00:08:27.350 --> 00:08:33.650
a certain proportion of
carbon-14 in their tissue,

00:08:33.650 --> 00:08:35.770
as kind of part of
what makes them up,

00:08:35.770 --> 00:08:38.100
and then if you were to
find some bone-- let's

00:08:38.100 --> 00:08:43.640
just say find some
bone right here

00:08:43.640 --> 00:08:46.580
that you dig it up on some
type of archaeology dig.

00:08:46.580 --> 00:08:54.680
And you say, hey, that bone has
one half the carbon-14 of all

00:08:54.680 --> 00:08:57.010
the living things that
you see right now.

00:08:57.010 --> 00:09:00.280
It would be a pretty
reasonable estimate

00:09:00.280 --> 00:09:04.310
to say, well, that thing
must be 5,730 years old.

00:09:04.310 --> 00:09:06.970
Even better, maybe you
dig a little deeper,

00:09:06.970 --> 00:09:10.650
and you find another bone.

00:09:10.650 --> 00:09:13.252
Maybe a couple of
feet even deeper.

00:09:13.252 --> 00:09:15.460
And you say, wow, you know
this thing right over here

00:09:15.460 --> 00:09:20.850
has 1/4 the carbon-14
that I would

00:09:20.850 --> 00:09:23.230
expect to find in
something living.

00:09:23.230 --> 00:09:24.540
So how old is this?

00:09:24.540 --> 00:09:26.532
Well, if it only has
1/4 the carbon-14

00:09:26.532 --> 00:09:28.240
it must have gone
through two half lives.

00:09:28.240 --> 00:09:33.100
After one half life, it would
have had 1/2 the carbon.

00:09:33.100 --> 00:09:35.230
And then after another
half life, half of that

00:09:35.230 --> 00:09:38.890
also turns into a nitrogen-14.

00:09:38.890 --> 00:09:43.950
And so this would
involve two half lives,

00:09:43.950 --> 00:09:49.430
which is the same thing
as 2 times 5,730 years.

00:09:49.430 --> 00:09:54.810
Or you would say that
this thing is what?

00:09:54.810 --> 00:10:02.340
You'd say this thing is 11,460
years old, give or take.


Galactic collisions

WEBVTT
Kind: captions
Language: en

00:00:00.590 --> 00:00:02.370
In the last video
on quasars, I think

00:00:02.370 --> 00:00:06.800
I sparked some interest when I
threw out the idea of the Milky

00:00:06.800 --> 00:00:09.440
Way galaxy actually
colliding with the Andromeda

00:00:09.440 --> 00:00:14.010
galaxy, which people think will
happen in 3 to 5 billion years.

00:00:14.010 --> 00:00:16.260
And I threw out in
the context of maybe,

00:00:16.260 --> 00:00:19.020
maybe the super
massive black holes

00:00:19.020 --> 00:00:21.777
at the core, the galactic
cores of each of those galaxies

00:00:21.777 --> 00:00:23.860
will start getting a little
bit more material when

00:00:23.860 --> 00:00:26.530
that collision happens, and
maybe quasars will happen.

00:00:26.530 --> 00:00:27.072
I don't know.

00:00:27.072 --> 00:00:29.405
But given the interest in
that, what I wanted to do here

00:00:29.405 --> 00:00:31.860
is kind of an unconventional
thing for the Khan Academy,

00:00:31.860 --> 00:00:32.944
and actually show a video.

00:00:32.944 --> 00:00:34.401
And before I play
the video, I have

00:00:34.401 --> 00:00:36.065
to give credit
where credit is due.

00:00:36.065 --> 00:00:39.320
This is a supercomputer
simulation made at the National

00:00:39.320 --> 00:00:42.210
Center for Supercomputing
Applications in NASA,

00:00:42.210 --> 00:00:44.460
and it's by B.
Robertson of Caltech

00:00:44.460 --> 00:00:47.100
and L. Hernquist of
Harvard University.

00:00:47.100 --> 00:00:50.934
And what I want you to remember,
this is super sped up in time.

00:00:50.934 --> 00:00:52.600
Just to give an idea,
the amount of time

00:00:52.600 --> 00:00:55.470
it takes for a star about
as far away as the sun

00:00:55.470 --> 00:00:58.610
to make one orbit
around the galactic core

00:00:58.610 --> 00:01:01.730
is 250 million years.

00:01:01.730 --> 00:01:04.060
And you're going to see
that this is happening

00:01:04.060 --> 00:01:05.970
multiple times over the
course of this video.

00:01:05.970 --> 00:01:08.754
So this video is actually
spanning billions of years.

00:01:08.754 --> 00:01:10.670
But when you actually
speed up time like that,

00:01:10.670 --> 00:01:12.130
you'll see that it
really gives you

00:01:12.130 --> 00:01:14.570
a sense of the actual dynamics
of these interactions.

00:01:14.570 --> 00:01:16.820
The other thing I want to
talk about before I actually

00:01:16.820 --> 00:01:18.640
start the video is
to make you realize

00:01:18.640 --> 00:01:20.510
that when we talk about
galaxies colliding,

00:01:20.510 --> 00:01:22.830
it doesn't mean that
the stars are colliding.

00:01:22.830 --> 00:01:25.000
In fact, there are going
to be very few stars that

00:01:25.000 --> 00:01:25.708
actually collide.

00:01:25.708 --> 00:01:28.372
The probability of a star
star collision is very low.

00:01:28.372 --> 00:01:29.830
And that's because
we learned, when

00:01:29.830 --> 00:01:31.780
we learned about
interstellar scale,

00:01:31.780 --> 00:01:34.080
that there's mostly free
space in between stars.

00:01:34.080 --> 00:01:37.740
The closest star to us
is 4.2 light years away.

00:01:37.740 --> 00:01:42.430
And that's roughly 30 million
times the diameter of the sun.

00:01:42.430 --> 00:01:46.490
So you have a lot more free
space than star space, or even

00:01:46.490 --> 00:01:48.290
solar system space.

00:01:48.290 --> 00:01:50.220
So let's start up
this animation.

00:01:50.220 --> 00:01:51.214
It's pretty amazing.

00:01:51.214 --> 00:01:52.880
And what you're gonna
see here, so these

00:01:52.880 --> 00:01:55.130
are just the-- obviously--
so one rotation is actually

00:01:55.130 --> 00:01:57.980
250 million years, give or take.

00:01:57.980 --> 00:02:00.060
But now you see these
stars right here

00:02:00.060 --> 00:02:02.210
are starting to get
attracted to this core,

00:02:02.210 --> 00:02:05.004
and then they're actually
attracted to that core.

00:02:05.004 --> 00:02:06.420
and then some of
the stuff in that

00:02:06.420 --> 00:02:08.650
core was attracted to
those stars, and they get

00:02:08.650 --> 00:02:09.199
pulled away.

00:02:09.199 --> 00:02:11.920
That was the first pass
of these two galaxies.

00:02:11.920 --> 00:02:15.300
Some stuff is just being thrown
off into intergalactic space.

00:02:15.300 --> 00:02:17.990
And you might worry maybe
that'll happen to the Earth,

00:02:17.990 --> 00:02:18.950
and there's some
probability that it

00:02:18.950 --> 00:02:20.616
would happen to the
Earth, but it really

00:02:20.616 --> 00:02:22.950
wouldn't affect what
happens within those stars'

00:02:22.950 --> 00:02:23.805
solar systems.

00:02:23.805 --> 00:02:25.930
This is happening so slow,
you wouldn't feel, like,

00:02:25.930 --> 00:02:28.160
some type of acceleration,
or something.

00:02:28.160 --> 00:02:29.680
And then this is
the second pass.

00:02:29.680 --> 00:02:31.094
So they passed one pass.

00:02:31.094 --> 00:02:32.510
And once again,
we're doing this--

00:02:32.510 --> 00:02:34.430
this is occurring over
hundreds of millions,

00:02:34.430 --> 00:02:35.490
or billions of years.

00:02:35.490 --> 00:02:39.337
And on the second pass, they
finally are able to merge.

00:02:39.337 --> 00:02:40.920
And all of these
interactions are just

00:02:40.920 --> 00:02:43.420
through the gravity over
interstellar-- almost

00:02:43.420 --> 00:02:45.220
you could call it
intergalactic distances.

00:02:45.220 --> 00:02:47.110
You can see they
merge into what could

00:02:47.110 --> 00:02:51.229
be called as a Milkomeda,
or maybe the Andromedy Way.

00:02:51.229 --> 00:02:51.770
I don't know.

00:02:51.770 --> 00:02:53.227
Whatever you want to call it.

00:02:53.227 --> 00:02:55.310
But even though they've
merged, a lot of the stuff

00:02:55.310 --> 00:02:58.180
has still been thrown off
into intergalactic space.

00:02:58.180 --> 00:03:01.670
But this is a pretty
amazing animation to me.

00:03:01.670 --> 00:03:05.370
One, it's amazing to think
about how this could happen over

00:03:05.370 --> 00:03:09.680
galactic space scales
and time scales,

00:03:09.680 --> 00:03:11.894
but it's also pretty neat
how a supercomputer can

00:03:11.894 --> 00:03:13.560
do all of the
computations to figure out

00:03:13.560 --> 00:03:16.560
what every particle, which
is really a star, cluster

00:03:16.560 --> 00:03:20.350
of stars, or group of stars
is actually doing to actually

00:03:20.350 --> 00:03:22.570
give us a sense of the
actual dynamics here.

00:03:22.570 --> 00:03:24.637
But this is pretty neat.

00:03:24.637 --> 00:03:25.470
This is pretty neat.

00:03:25.470 --> 00:03:26.610
Look at that.

00:03:26.610 --> 00:03:28.250
I mean, these are--
every little dot

00:03:28.250 --> 00:03:30.800
is whole groups of stars,
thousands of stars,

00:03:30.800 --> 00:03:32.350
potentially.


Quasar correction

WEBVTT
Kind: captions
Language: en

00:00:00.610 --> 00:00:02.020
I want to make a
quick correction

00:00:02.020 --> 00:00:03.720
to the video on quasars.

00:00:03.720 --> 00:00:06.230
In that video I said,
and I mistakenly

00:00:06.230 --> 00:00:10.720
said that the creation
disk that's really

00:00:10.720 --> 00:00:12.840
releasing the energy
of the quasar,

00:00:12.840 --> 00:00:14.760
that it's releasing
energy predominately

00:00:14.760 --> 00:00:18.380
in the x-ray part of the
electromagnetic spectrum.

00:00:18.380 --> 00:00:19.690
And that was incorrect.

00:00:19.690 --> 00:00:22.200
Most quasars are
actually emitting

00:00:22.200 --> 00:00:25.410
electromagnetic radiation
across the spectrum, all the way

00:00:25.410 --> 00:00:31.430
from x-rays, as high frequency
as x-rays, all the way down

00:00:31.430 --> 00:00:34.290
to infrared.

00:00:34.290 --> 00:00:38.740
And some quasars even release
super high frequency gamma

00:00:38.740 --> 00:00:42.370
rays, and they'll release low
frequency electromagnetic waves

00:00:42.370 --> 00:00:44.172
all the way down to radio waves.

00:00:44.172 --> 00:00:45.880
So I just wanted to
make that correction.

00:00:45.880 --> 00:00:48.640
It's not predominately in the
x-ray part of the spectrum.

00:00:48.640 --> 00:00:50.840
It's across the spectrum
right over here.

00:00:50.840 --> 00:00:52.830
It's this entire
range of the spectrum,

00:00:52.830 --> 00:00:54.647
and sometimes even
a wider range.

00:00:54.647 --> 00:00:56.230
Now, the other thing
I want to clarify

00:00:56.230 --> 00:00:58.850
is this is the range of the
spectrum that's being emitted.

00:00:58.850 --> 00:01:00.670
But we have to
remember that most,

00:01:00.670 --> 00:01:03.030
or actually all of these
quasars are quite far away.

00:01:03.030 --> 00:01:05.970
The closest is 780
million light years away.

00:01:05.970 --> 00:01:09.410
Many of them are many, many
billions of light years away.

00:01:09.410 --> 00:01:12.370
And so they're moving away
from us at a very fast speed,

00:01:12.370 --> 00:01:14.870
or they're getting redshifted
because the universe is

00:01:14.870 --> 00:01:18.360
expanding so fast relative
to us at that point,

00:01:18.360 --> 00:01:21.650
or that coordinate is moving so
fast away from our coordinate.

00:01:21.650 --> 00:01:24.300
And so even though this is the
spectrum that's being emitted,

00:01:24.300 --> 00:01:26.370
it's all going to be redshifted.

00:01:26.370 --> 00:01:28.650
It's all going to
be redshifted down,

00:01:28.650 --> 00:01:30.600
and so we are going
to observe things

00:01:30.600 --> 00:01:35.710
at a much lower frequency,
maybe around the radio

00:01:35.710 --> 00:01:37.017
part of the frequency.

00:01:37.017 --> 00:01:38.600
So everything will
be redshifted down.

00:01:38.600 --> 00:01:40.100
And that's why these
were originally

00:01:40.100 --> 00:01:42.650
called quasi stellar
radio sources.

00:01:42.650 --> 00:01:45.780
Anyway, hopefully that clears
things up a little bit.


Quasars

WEBVTT
Kind: captions
Language: en

00:00:00.354 --> 00:00:02.520
What I want to do in this
video is talk a little bit

00:00:02.520 --> 00:00:03.180
about quasars.

00:00:06.050 --> 00:00:14.180
And that's a short form for
quasi-stellar radio sources.

00:00:16.740 --> 00:00:18.490
And this name is
just a byproduct

00:00:18.490 --> 00:00:20.646
of the first
observations of quasars.

00:00:20.646 --> 00:00:22.020
Because all they
looked like were

00:00:22.020 --> 00:00:26.450
these kind of point-like sources
of electromagnetic radiation,

00:00:26.450 --> 00:00:29.200
mainly in the radio
part of the spectrum.

00:00:29.200 --> 00:00:32.600
So that's why we called them
quasi-stellar radio sources.

00:00:32.600 --> 00:00:36.100
Now, it turns out that they
are neither stars, or even

00:00:36.100 --> 00:00:37.000
quasi-stellar.

00:00:37.000 --> 00:00:39.880
And actually, their
main energy isn't even

00:00:39.880 --> 00:00:43.760
being released in
the radio band of

00:00:43.760 --> 00:00:44.990
the electromagnetic spectrum.

00:00:44.990 --> 00:00:47.180
They're far more
energetic than that.

00:00:47.180 --> 00:00:52.760
What they really are are the
active nucleuses of galaxies.

00:00:52.760 --> 00:00:54.950
So let's think about
that a little bit.

00:00:54.950 --> 00:00:56.934
So if we have a
supermassive black hole

00:00:56.934 --> 00:00:58.350
at the center of
a galaxy-- so let

00:00:58.350 --> 00:01:00.807
me draw that right over here.

00:01:00.807 --> 00:01:02.390
So that's our
supermassive black hole.

00:01:02.390 --> 00:01:04.629
And maybe that's the
surface of the event horizon

00:01:04.629 --> 00:01:06.070
of the supermassive black hole.

00:01:06.070 --> 00:01:08.190
The actual mass
of the black hole

00:01:08.190 --> 00:01:11.160
is in the center of
that event horizon.

00:01:11.160 --> 00:01:14.314
If there is material that's
passing by this black hole,

00:01:14.314 --> 00:01:15.730
it's going to get
attracted to it.

00:01:15.730 --> 00:01:19.020
And it's going to form an
accretion disk around it.

00:01:19.020 --> 00:01:21.590
This material is going
to start rotating

00:01:21.590 --> 00:01:22.580
around this black hole.

00:01:22.580 --> 00:01:25.680
And some of it, if it
doesn't have enough velocity,

00:01:25.680 --> 00:01:27.840
is going to actually
fall into the black hole.

00:01:27.840 --> 00:01:32.320
So you have all of this material
going around the black hole.

00:01:32.320 --> 00:01:35.060
And some of it, if it doesn't
have enough angular velocity

00:01:35.060 --> 00:01:38.310
and not enough to orbit
around the black hole,

00:01:38.310 --> 00:01:41.300
it's actually going to fall in.

00:01:41.300 --> 00:01:42.216
Let me label this.

00:01:42.216 --> 00:01:43.340
This is the accretion disk.

00:01:47.590 --> 00:01:51.810
So as things are getting faster
and faster as they fall closer

00:01:51.810 --> 00:01:53.590
and closer to this
black hole, and bumping

00:01:53.590 --> 00:01:56.910
into each other more and more,
that gravitational potential

00:01:56.910 --> 00:01:58.725
energy from things
falling into it

00:01:58.725 --> 00:02:02.950
is being turned into actual
energy, actual temperature.

00:02:02.950 --> 00:02:05.170
And so what you
have is things start

00:02:05.170 --> 00:02:12.600
to get really, unbelievably
hot near the surface.

00:02:12.600 --> 00:02:15.280
They get hotter and hotter as
they fall closer and closer

00:02:15.280 --> 00:02:17.200
to that event horizon.

00:02:17.200 --> 00:02:19.140
And so near the
event horizon itself,

00:02:19.140 --> 00:02:23.670
things are so intense
that they're actually

00:02:23.670 --> 00:02:27.100
releasing high-frequency
electromagnetic radiation,

00:02:27.100 --> 00:02:30.740
mainly in the X-ray
part of the spectrum.

00:02:30.740 --> 00:02:32.230
Now, I want to been very clear.

00:02:32.230 --> 00:02:33.730
So there's two things here.

00:02:33.730 --> 00:02:36.790
One is when you
learn about quasars,

00:02:36.790 --> 00:02:42.060
or when I first was exposed to
quasars in like a Nova special,

00:02:42.060 --> 00:02:44.940
they make you think that the
quasar, that the radiation is

00:02:44.940 --> 00:02:48.230
somehow being released
by the black hole itself.

00:02:48.230 --> 00:02:50.280
And I would scratch my
head because I was just

00:02:50.280 --> 00:02:53.830
told that nothing can escape the
event horizon of a black hole,

00:02:53.830 --> 00:02:56.410
including electromagnetic
radiation.

00:02:56.410 --> 00:02:59.176
So how could that be being
emitted by the black hole?

00:02:59.176 --> 00:03:00.550
And the answer
is, it's not being

00:03:00.550 --> 00:03:02.260
emitted by the black hole.

00:03:02.260 --> 00:03:05.710
It's being emitted by the matter
in the accretion disk that

00:03:05.710 --> 00:03:08.720
hasn't quite gotten to
the event horizon yet.

00:03:08.720 --> 00:03:11.990
Once it's inside of
the event horizon,

00:03:11.990 --> 00:03:14.450
any electromagnetic
radiation that it might emit

00:03:14.450 --> 00:03:17.320
will not be able to escape
the black hole anymore,

00:03:17.320 --> 00:03:20.270
will not be able to escape
the actual event horizon.

00:03:20.270 --> 00:03:22.460
So all of this is from
the accretion disc

00:03:22.460 --> 00:03:27.367
around the supermassive
black hole.

00:03:27.367 --> 00:03:29.450
And the other question
that used to pop in my mind

00:03:29.450 --> 00:03:34.210
is why does it come out at
these kind of perpendicular,

00:03:34.210 --> 00:03:40.100
orthogonal to the plane of
the actual accretion disk?

00:03:40.100 --> 00:03:42.800
And at least my logic
tells me, well, things

00:03:42.800 --> 00:03:44.370
aren't going to pop
out-- they're not

00:03:44.370 --> 00:03:46.650
going to pop out along the
direction of the accretion disk

00:03:46.650 --> 00:03:48.360
because then they're going to
be absorbed by other things.

00:03:48.360 --> 00:03:50.734
In fact, that's what's going
to cause other things to get

00:03:50.734 --> 00:03:55.170
heated up closer to the
actual event horizon.

00:03:55.170 --> 00:03:57.840
So any energy that's going
out in that direction

00:03:57.840 --> 00:04:01.100
is just going to be absorbed
and make other things hotter.

00:04:01.100 --> 00:04:04.860
And only when you go roughly
perpendicular to the plane

00:04:04.860 --> 00:04:06.960
of the accretion
disk is that energy

00:04:06.960 --> 00:04:10.115
allowed to kind of go and
transmit freely into space.

00:04:10.115 --> 00:04:11.710
Now, I want to be very clear.

00:04:11.710 --> 00:04:15.750
Quasars, these are the
most luminous things

00:04:15.750 --> 00:04:17.555
that we know of in the universe.

00:04:26.310 --> 00:04:29.220
The brightest-- or
actually, many quasars

00:04:29.220 --> 00:04:32.260
are on the order of a
trillion suns in luminosity.

00:04:32.260 --> 00:04:35.050
So they can be brighter
than an entire galaxy.

00:04:35.050 --> 00:04:37.510
And that's just
coming from material

00:04:37.510 --> 00:04:41.070
around a fairly small
region of space,

00:04:41.070 --> 00:04:43.590
much, much, much smaller
than an actual galaxy.

00:04:43.590 --> 00:04:44.500
It's the very center.

00:04:44.500 --> 00:04:46.660
It's kind of just
the galactic core.

00:04:46.660 --> 00:04:49.680
Now another interesting
thing about quasars,

00:04:49.680 --> 00:04:51.960
and this kind of gives
credence to this notion

00:04:51.960 --> 00:04:53.890
of a constantly
changing universe,

00:04:53.890 --> 00:04:56.790
and even to some degree
the Big Bang itself,

00:04:56.790 --> 00:04:59.380
is you have these
supermassive black holes that

00:04:59.380 --> 00:05:01.850
may be formed shortly
after the Big Bang.

00:05:01.850 --> 00:05:04.950
Now you can imagine, at an
early stage in the universe's

00:05:04.950 --> 00:05:08.117
development there would
have been a lot of mass that

00:05:08.117 --> 00:05:10.700
would have been near these black
holes, that didn't have quite

00:05:10.700 --> 00:05:12.710
the velocities to be
able to escape them or be

00:05:12.710 --> 00:05:14.250
able to orbit around them.

00:05:14.250 --> 00:05:15.640
And so these would
actually start

00:05:15.640 --> 00:05:17.920
falling into the black hole.

00:05:17.920 --> 00:05:19.780
And then over time,
all of the mass that

00:05:19.780 --> 00:05:22.770
had to fall into the black hole,
into the supermassive black

00:05:22.770 --> 00:05:25.450
hole, will have fallen into
the supermassive black hole.

00:05:25.450 --> 00:05:27.550
And if you imagine at some
future period of time,

00:05:27.550 --> 00:05:30.820
you should still have the
supermassive black hole.

00:05:30.820 --> 00:05:34.260
But all you should see is mostly
things orbiting around it.

00:05:34.260 --> 00:05:35.710
Anything that had
to fall into it,

00:05:35.710 --> 00:05:37.440
would have already
fallen into it.

00:05:37.440 --> 00:05:40.400
So you're just going to see
things orbiting around it.

00:05:40.400 --> 00:05:43.062
And this is actually what
we see if we look around us.

00:05:43.062 --> 00:05:44.520
If we look at our
Milky Way Galaxy,

00:05:44.520 --> 00:05:47.060
we don't observe a lot
of things falling in.

00:05:47.060 --> 00:05:51.310
For example, the
Milky Way Galaxy

00:05:51.310 --> 00:05:55.750
does not have an active
nucleus, an active core.

00:05:55.750 --> 00:05:58.760
It is not currently a quasar,
the center of the Milky Way

00:05:58.760 --> 00:05:59.260
Galaxy.

00:05:59.260 --> 00:06:02.030
The supermassive black
hole there is not,

00:06:02.030 --> 00:06:06.020
I guess we could say, digesting,
is not digesting or consuming

00:06:06.020 --> 00:06:06.520
material.

00:06:06.520 --> 00:06:09.450
But you could imagine at some
point in the Milky Way's past,

00:06:09.450 --> 00:06:11.320
there might have been
a lot of material

00:06:11.320 --> 00:06:15.160
that didn't have quite the
velocity to be able to orbit.

00:06:15.160 --> 00:06:16.360
And so that was consumed.

00:06:16.360 --> 00:06:21.520
And as it was consumed, it
would emit all of this X-ray

00:06:21.520 --> 00:06:24.330
radiation and could be
observed as a quasar.

00:06:24.330 --> 00:06:25.870
And that's actually
what we observe.

00:06:25.870 --> 00:06:27.750
The closest quasars--
and we've observed

00:06:27.750 --> 00:06:32.170
more than 200,000 quasars--
the closest quasars are

00:06:32.170 --> 00:06:39.032
on the order of 780
million light years away.

00:06:39.032 --> 00:06:39.990
So what does that mean?

00:06:39.990 --> 00:06:43.350
We don't observe quasars closer
than 700 million light years.

00:06:43.350 --> 00:06:46.260
So what that tells
us is, at least

00:06:46.260 --> 00:06:49.730
in our region of the universe,
the most recent quasars

00:06:49.730 --> 00:06:53.960
were 780 million
years in the past.

00:06:53.960 --> 00:06:57.750
When we look at closer parts
of the universe-- let me draw,

00:06:57.750 --> 00:07:00.010
let's say this is the
observable universe.

00:07:00.010 --> 00:07:01.100
This is us.

00:07:01.100 --> 00:07:03.160
So we only start
to observe quasars

00:07:03.160 --> 00:07:05.280
at a certain distance
away from us.

00:07:05.280 --> 00:07:06.750
And that distance
is actually also

00:07:06.750 --> 00:07:08.140
a certain time in the past.

00:07:08.140 --> 00:07:10.920
Because it took the light 780
million years to get to us.

00:07:10.920 --> 00:07:12.680
And actually, most
of the quasars

00:07:12.680 --> 00:07:15.550
are more than 3 billion
light years away.

00:07:15.550 --> 00:07:18.380
Which tells us that they
only existed more than 3

00:07:18.380 --> 00:07:22.430
billion years in the
past, at a younger

00:07:22.430 --> 00:07:25.250
stage of the actual
universe, when there

00:07:25.250 --> 00:07:28.810
was actual material for these
supermassive black holes

00:07:28.810 --> 00:07:30.970
to consume at the
center of galaxies.

00:07:30.970 --> 00:07:34.410
You move closer in time to
us, and most of that material

00:07:34.410 --> 00:07:36.840
has actually been consumed.

00:07:36.840 --> 00:07:38.550
And we just have
material orbiting

00:07:38.550 --> 00:07:42.020
around these supermassive black
holes, which we call galaxies.

00:07:42.020 --> 00:07:45.009
And so we don't observe
quasars anymore.

00:07:45.009 --> 00:07:46.050
And just to give an idea.

00:07:46.050 --> 00:07:49.000
I mean these are, as everything
we learn in cosmology,

00:07:49.000 --> 00:07:50.680
kind of these
mind-bending concepts,

00:07:50.680 --> 00:07:54.100
unbelievable distances,
unbelievable masses,

00:07:54.100 --> 00:07:57.020
unbelievable brightnesses, I
guess you could think about it.

00:07:57.020 --> 00:07:59.430
But just to give a sense,
the brightest quasars,

00:07:59.430 --> 00:08:02.600
the brightest known
quasars, devour

00:08:02.600 --> 00:08:11.160
on the order of 1,000
solar masses per year.

00:08:11.160 --> 00:08:16.200
So that's on the order of 10
Earths, 10 Earths per second,

00:08:16.200 --> 00:08:19.490
if I did my math right.

00:08:19.490 --> 00:08:23.530
10 Earths per second
are being devoured

00:08:23.530 --> 00:08:25.340
by the brightest quasars.

00:08:25.340 --> 00:08:30.040
And it's that energy of that
mass that's acreting around it

00:08:30.040 --> 00:08:32.595
that's generating
all of that energy.

00:08:32.595 --> 00:08:34.470
And actually, I should
say-- I shouldn't even

00:08:34.470 --> 00:08:36.909
talk about it in
the present tense.

00:08:36.909 --> 00:08:38.200
This happened in the past.

00:08:38.200 --> 00:08:40.299
We're just observing it now.

00:08:40.299 --> 00:08:42.220
For all we know, the
rest of the universe

00:08:42.220 --> 00:08:44.820
looks fairly similar to
the way our universe does.

00:08:44.820 --> 00:08:47.010
And so there really aren't
that many quasars around.

00:08:47.010 --> 00:08:49.550
Although the other side
of the coin might be,

00:08:49.550 --> 00:08:51.560
even though most of the
material has already

00:08:51.560 --> 00:08:54.400
been consumed, maybe even by
our own supermassive black hole

00:08:54.400 --> 00:08:58.260
in the center of the Milky Way,
at some point in the future,

00:08:58.260 --> 00:09:01.720
maybe it will be able to consume
on some more stellar material,

00:09:01.720 --> 00:09:06.070
some more-- well, any type
of material in the future.

00:09:06.070 --> 00:09:08.070
And that might happen
about 4 or 5 billion years

00:09:08.070 --> 00:09:10.690
in the future when we actually
collide with the Andromeda

00:09:10.690 --> 00:09:11.670
Galaxy.

00:09:11.670 --> 00:09:14.750
So anyway, hopefully that gave
you some food for thought.