13.5 Total Internal Reflection

Ok, today we're going to continue with refraction and reflection, but we're going to sort of look at special cases. The first topic we're going to look at is what we call total internal reflection. Total internal reflection only occurs when we go from a high-density object to one that is less dense than the object. An example of this would be light going from water to air. If we look at the first example, it shows the red ray. As you can see, the red line comes in, and when it hits the air, it's going to speed up. Something that's going to happen is that it will bend away from the normal, as shown in this picture. Now, let's look at the second example at the bottom. It's the blue ray. All we've done is increase our angle. Originally, the angle there is approximately 20 degrees, but now it's about 40 degrees. If we increase the angle, the same thing occurs. However, because that angle is bigger, it means our refraction angle is going to be bigger. As well, okay, so that's still basically just normal. So, what happens then if we increase it to the point where the refracted angle is exactly 90 degrees? If we have a pretty big angle of incidence and then it refracts, and if that angle of refraction is 90 degrees, that means that light's never really going to leave the surface. So, it just sort of goes straight along the surface of the water. Basically, we wouldn't see anything. So, we call that angle the critical angle. The critical angle is what is the angle of incidence so that the refracted angle is exactly 90 degrees. So, when we do calculations like that, all we gotta do in our formula, if we have sine theta 1 over sine theta 2, we just put in 90 degrees for our surface, number 1 or 2 doesn't matter which one. So then, the question then is what happens if the angle's less than the critical angle? If we get anything smaller, that's like our first two, which are just. Normal situations: if we have an angle larger than the critical angle (as shown here), when this angle becomes really big, like 50 or 60 degrees, you can see that the refracted angle is below the surface. So, it never truly leaves the surface; it just reflects inside. This is why we call it total internal reflection. All of the light never leaves the surface; it just reflects inside and stays within the first surface. This is the key idea for fiber-optic cables. So, if we have a chunk of fiber-optic cable, which is usually made of clear plastic or glass, all we need to do is shine a light into it. The way it is set up is that the light travels through the high-density plastic and reflects back and forth as it travels down the length of the cable or line, even if there are bends in it. Let's suppose we have. Bend in the wire, it would still just reflect as it goes through. So total internal reflection works really well for anything that's fiber-optic. It also works in cases where we can create the signal. So, in terms of computer lines, it looks like we can get better quality, faster transmission, and no loss. The other thing I just want to mention is that you may have all seen this before when we look at this greenery again, where we're right at the critical angle. What happens in that situation is if you're driving down the highway on a hot day and you look far in the distance, you sort of see a mirage or something that looks kind of watery on the road. The reason for that is it's sort of the same thing. We actually have hotter air right next to the surface of the road because of the heat of the pavement. So, the heat rays or light rays that come off the pavement actually come up and... Then, when they hit cooler air, they actually refract, just like they would if it were water to air or something like that. So, if we're driving our car and we're at a long distance away and we were looking at this, basically what's happening is: when we see a mirage, we're at the perfect distance where that light wave is at a certain angle, and we end up getting the critical angle. So, that's why we don't see the road - it's refracting right at the perfect angle, so we just sort of see that water shiny, sort of looking surface. And that's the same thing when people think they see a mirage in the desert - it's the same thing. The heat coming off the sand at a certain distance makes it look sort of like water. Now, our last little topic we're gonna look at is how a prism works. And remember, a prism is just basically a clear glass, but it's in a triangular shape. And the reason for that is so we can use it to get white light. Because each wavelength that's going to refract slightly different, we can actually split the white light apart. So, You can see the white light go into the prism. It sort of splits inside of it, and then at the other angle, because we've got two different angles, it causes the white light to refract differently. And it's due to those angles that's how we get our rainbow or hue-give colors. So, pretty cool how prisms work. And if we had another prism, let's suppose we put another prism right there, and it refracted through it, it would come out back as white light again. So, two prisms, and you can recombine light back into white. So, we call it recomposition. If we put white light through a prism and it breaks apart, we call it dispersion because light disperses apart into its individual colors. So, nothing fancy about a prism. Just like this, it's just a triangular piece of glass. But water, it doesn't have to be triangular. Round works as well too, but we typically would then get a round sort of rainbow color. And that's how we see rainbows. We have water droplets, light enters the water droplet, and it actually disperses it. Just like a prism would, that's how we see our rainbow coming out of the water droplets. So, they have millions of them, all working together at roughly the same angle. When they all do it together, we get our big, massive rainbow. To have a rainbow, we need mist in the area, water droplets, and a bright light source. So, it has to be a sunny day. In the picture at the bottom, you can see a rainbow up in the sky. It's actually round, but we only see it as a semicircle because the ground cuts off our vision from the rest. If you look closely, you can see a full circle, and you can actually see the second ring below it at a distance. One key thing to note is that the second rainbow basically splits the original back up and reverses it. So, we sort of have Reggi Biv on the first rainbow too. But if you look at the other ones, it actually goes the... The other way? Red is on the inside and violet is on the outside, and it would keep going on and on. There's actually going to be a third and a fourth rainbow, and so on. But usually, the light's not bright enough. We can only see usually just two, and that's it.