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Studying for a test? Prepare with these 3 lessons on Geometric optics.
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In the last couple of videos we talked about reflection. And that's just the idea of the light rays bouncing off of a surface. And if the surface is smooth, the incident angle is going to be the same thing as the reflected angle. We saw that before, and those angles are measured relative to a perpendicular. So that angle right there is going to be the same as that angle right there. That's essentially what we learned the last couple of videos. What we want to cover in this video is when the light actually doesn't just bounce off of a surface but starts going through a different medium. So in this situation, we will be dealing with refraction. Refraction. Refraction, you still have the light coming in to the interface between the two surfaces. So let's say--so that's the perpendicular right there, actually let me continue the perpendicular all the way down like that. And let's say we have the incident light ray coming in at some, at some angle theta 1, just like that...what will happen--and so let's say that this up here, this is a vacuum. Light travels the fastest in a vacuum. In a vacuum. There's nothing there, no air, no water, no nothing, that's where the light travels the fastest. And let's say that this medium down here, I don't know, let's say it's water. Let's say that this is water. All of this. This was all water over here. This was all vacuum right up here. So what will happen, and actually, that's kind of an unrealistic-- well, just for the sake of argument, let's say we have water going right up against a vacuum. This isn't something you would normally just see in nature but let's just think about it a little bit. Normally, the water, since there's no pressure, it would evaporate and all the rest. But for the sake of argument, let's just say that this is a medium where light will travel slower. What you're going to have is is this ray is actually going to switch direction, it's actually going to bend. Instead of continuing to go in that same direction, it's going to bend a little bit. It's going to go down, in that direction just like that. And this angle right here, theta 2, is the refraction. That's the refraction angle. Refraction angle. Or angle of refraction. This is the incident angle, or angle of incidence, and this is the refraction angle. Once again, against that perpendicular. And before I give you the actual equation of how these two things relate and how they're related to the speed of light in these two media-- and just remember, once again, you're never going to have vacuum against water, the water would evaporate because there's no pressure on it and all of that type of thing. But just to--before I go into the math of actually how to figure out these angles relative to the velocities of light in the different media I want to give you an intuitive understanding of not why it bends, 'cause I'm not telling you actually how light works this is really more of an observed property and light, as we'll learn, as we do more and more videos about it, can get pretty confusing. Sometimes you want to treat it as a ray, sometimes you want to treat it as a wave, sometimes you want to treat it as a photon. But when you think about refraction I actually like to think of it as kind of a, as a bit of a vehicle, and to imagine that, let's imagine that I had a car. So let me draw a car. So we're looking at the top of a car. So this is the passenger compartment, and it has four wheels on the car. We're looking at it from above. And let's say it's traveling on a road. It's traveling on a road. On a road, the tires can get good traction. The car can move pretty efficiently, and it's about to reach an interface it's about to reach an interface where the road ends and it will have to travel on mud. It will have to travel on mud. Now on mud, obviously, the tires' traction will not be as good. The car will not be able to travel as fast. So what's going to happen? 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. So what's going to happen? 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. 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. So what's going to happen? 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. 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. 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. 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 v1--and 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 300,000 kilometers per second, or 300 million meters per second--let me write that-- so c is the speed of light in a vacuum, and that is equal to 300-- it's not exactly 300, I'm not going into significant digits-- this is true to three significant digits--300 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. 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. 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. 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. That guy, that guy, and that guy are going to cancel out. And so we get n2 sin of theta 2 over c is equal to n1 sin of theta 1 over c. And now we can just multiply both sides of this equation by c and we get the form of Snell's Law that some books will show you, which is the refraction index for the slower medium, or for the second medium, the one that we're entering, times the index of the sin of the index of refraction is equal to the refraction index for the first medium times the sin of the angle of incidence. The incident angle. So this is another version right here This is another version right there of Snell's Law. Let me copy and paste that. And if this is confusing to you, and I'm guessing that it might be, especially if this is the first time you're seeing it, we're going to apply this in a bunch of videos, in the next few videos, but I really just want to make sure, I really just want to make sure you're comfortable with it. So these are both equivalent forms of Snell's Law. One deals with the velocities, directly deals with the velocities, right over here, the ratio of the velocity to the sin of the incident or refraction angle and here it uses the index of refraction. And the index of refraction really just tells you it's just the ratio of the speed of light to the actual velocity. So something where light travels really slowly where light travels really slowly, this will be a smaller number. And if this is a smaller number, this is a larger number. And we actually see it here. And you're going to see a little tidbit of the next video right over here. But here's a bunch of refraction indices for different materials. It's obviously 1 for a vacuum, because for a vacuum you have the refraction index is going to be c divided by the speed of light in that material. Well, in a vacuum it's traveling at c. So it's going to be 1. So that's where that came from. And you can see in air, the speed is only slightly smaller, this number's only going to be slightly smaller than the speed of light in a vacuum. So in air, it's still pretty close to a vacuum. But then for a diamond, it's traveling a lot slower. Light is travelling a lot slower in a diamond than it is in a vacuum. Anyway, I'll leave you there, we're going to do a couple more videos, we're going to do more examples using Snell's Law. Hopefully you got the basic idea of refraction. And in the next video, I'll actually use this graphic right here to help us visualize why it looks like the straw got bent.