Assuming that the car, the steering wheel isn't telling it to turn or anything, the car would just go straight in this direction. But what happens right when--which wheels are going to reach the mud first? Well, this wheel. This wheel is going to reach the mud first. There's going to be some point in time where the car is right over here. Where it's right over here. Where these wheels are still on the road, this wheel is in the mud, and that wheel is about to reach the mud.
Now in this situation, what would the car do? What would the car do? And assuming the engine is revving and the wheels are turning, at the exact same speed the entire time of the simulation. Well all of a sudden, as soon as this wheel hits the medium, it's going to slow down. This is going to slow down.
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But these guys are still on the road. So they're still going to be faster. So the right side of the car is going to move faster than the left side of the car. You see this all the time. If the right side of you is moving faster than the left side of you, you're going to turn, and that's exactly what's going to happen to the car. The car is going to turn.
Reflection and refraction
It's going to turn in that direction. And so once it gets to the medium, it will now travel, it will now turn-- from the point of the view from the car it's turning to the right. But it will now travel in this direction. It will be turned when it gets to that interface.
Now obviously light doesn't have wheels, and it doesn't deal with mud. But it's the same general idea. When I'm traveling from a faster medium to a slower medium, you can kind of imagine the wheels on that light on this side of it, closer to the vertical, hit the medium first, slow down, so light turns to the right. If you were going the other way, if I had light coming out of the slow medium, so let's imagine it this way. Let's have light coming out of the slow medium. And if we use the car analogy, in this situation, the left side of the car is going to-- so if the car is right over here, the left side of the car is going to come out first so it's going to move faster now.
So the car is going to turn to the right, just like that. So hopefully, hopefully this gives you a gut sense of just how to figure out which direction the light's going to bend if you just wanted an intuitive sense. And to get to the next level, there's actually something called Snell's Law. Snell's Law.
And all this is saying is that this angle-- so let me write it down here--so let's say that this velocity right here is velocity 2 this velocity up here was velocity 1, going back to the original. Actually, let me draw another diagram, just to clean it up. And also that vacuum-water interface example, I'm not enjoying it, just because it's a very unnatural interface to actually have in nature. So maybe it's vacuum and glass.
That's something that actually would exist. So let's say we're doing that. So this isn't water, this is glass.
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Let me redraw it. And I'll draw the angles bigger.
So let me draw a perpendicular. And so I have our incident ray, so in the vacuum it's traveling at vand in the case of a vacuum, it's actually going at the speed of light, or the speed of light in a vacuum, which is c, or , kilometers per second, or million meters per second--let me write that-- so c is the speed of light in a vacuum, and that is equal to it's not exactly , I'm not going into significant digits-- this is true to three significant digits million meters per second. This is light in a vacuum.
Light in vacuum. And I don't mean the thing that you use to clean your carpet with, I mean an area of space that has nothing in it.
Refraction and Snell's law
No air, no gas, no molecules, nothing in it. That is a pure vacuum and that's how fast light will travel. Now it's travelling really fast there, and let's say that--and this applies to any two mediums-- but let's say it gets to glass here, and in glass it travels slower, and we know for our example, this side of the car is going to get to the slower medium first so it's going to turn in this direction. So it's going to go like this. We call this v2. Maybe I'll draw it--if you wanted to view these as vectors, maybe I should draw it as a smaller vector v2, just like that. And the angle of incidence is theta 1.
And the angle of refraction is theta 2. And Snell's Law just tells us the ratio between v2 and the sin-- remember Soh Cah Toa, basic trig function-- and the sin of the angle of refraction is going to be equal to the ratio of v1 and the angle--the sin of the angle of incidence. Sin of theta 1. Now if this looks confusing at all, we're going to apply it a bunch in the next couple of videos. But I want to show you also that there's many many ways to view Snell's Law.
You may or may not be familiar with the idea of an index of refraction. So let me write that down.
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Index of refraction. Index, or refraction index. And it's defined for any medium, for any material. There's an index of refraction for vacuum, for air, for water. For any material that people have measured it for. And they usually specify it as n. And it is defined as the speed of light in a vacuum That's c. Divided by the velocity of light in that medium.
So in our example right here, we could rewrite this. We could rewrite this in terms of index of refraction. Let me do that actually.
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Just cause that's sometimes the more typical way of viewing Snell's Law. So I could solve for v here if I--one thing I could do is just--if n is equal to c divided by v then v is going to be equal to c divided by n. And I can multiply both sides by v if you don't see how I got there. The intermediary step is, multiply both sides times v, you get v times n is equal to c, and then you divide both sides by n, you get v is equal to c over n.
So I can rewrite Snell's Law over here as instead of having v2 there, I could write instead of writing v2 there I could write the speed of light divided by the refraction index for this material right here. So I'll call that n2. Right, this is material 2, material 2 right over there.
Right, that's the same thing as v2 over the sin of theta 2 is equal to v1 is the same thing as c divided by n1 over sin of theta 1.
And then we could do a little bit of simplification here, we can multiple both sides of this equation--well, let's do a couple of things. Let's-- Actually, the simplest thing to do is actually take the reciprocal of both sides. So let me just do that. So let me take the reciprocal of both sides, and you get sin of theta 2 over cn2 is equal to sin of theta 1 over c over n1.
And now let's multiply the numerator and denominator of this left side by n2. So if we multiply n2 over n2. We're not changing it, this is really just going to be 1, but this guy and this guy are going to cancel out. And let's do the same thing over here, multiply the numerator and the denominator by n1, so n1 over n1. A Bend in the River's Salim is a bad guy. He's a bully and a coward. He doesn't know that he's a bully and a coward, and VS Naipaul doesn't seem to know either. He seems okay with it.
She calls him later. The road is quite empty. I can be back in twenty minutes. Oh, Salim. I look dreadful. My face is in an awful state.