 Hi, I'm Zor. Welcome to New Zoroaducation. We talk about phenomena of light. Now, today's topic is just yet another phenomenon, phenomenon, probably I should say, in the singular, which is called dispersion. Now, dispersion is really a rather large topic, which I have decided to break into parts. Today we will talk about dispersion on a flat surface. So, it can be a glass, let's say, a window glass, for instance. So, the light goes into the flat surface, then there is this dispersion, and at the second half of this lecture I will talk about what happens when it goes through another flat surface, like into the glass and then from the glass back into the air. So, that's today. The next lectures will be about dispersion on a prism, and eventually maybe we will talk about rainbow, because we all know about rainbow, rainbow is beautiful, but question how actually it appears on the sky after the rain or maybe above the waterfall. By the way, recently I was in Victoria waterfall in Africa, and that was a beautiful rainbow. All the sky was actually covered with it. Anyway, this lecture is part of the course called Physics for Teens, presented on Unisor.com. I do suggest you to watch this lecture from the website. Not only because the website is completely free and there are no ads, no strings attached, but also because every lecture has a textual part, which is basically presented right near the video, video and textual part, notes, whatever, which is actually like a textbook. So, consider that the whole textbook is divided between different lectures, and each piece of this textbook is attached to the video. Plus there are exams, which I think are very, very useful to take, because it's precisely the problem solving where your creativity, your analytical skills are developed. And as I said, the website is completely free, there are no advertisement, no strings attached. Okay, so, well, I mentioned rainbow, and just let me just start from this, since it's such a beautiful topic. The reason for rainbow is refraction, and basically know a lot about refraction from the previous lectures. So, we are talking about dispersion of light, in this case, on a flat surface, which is caused by refraction. Now, let me just remind you what refraction actually says. Well, if there is a boundary between two different substances, let's say air and glass, and there is a ray of light, which comes at incident angle theta 1. Then in this particular case, the light as it comes after this border into the glass would be at different angle to a, perpendicular to a normal to a surface. And these angles are related using this law, where V1 is the speed in this case in the air, and V2 is the speed in the glass. Now, because this speed is higher than this, sorry, vice versa, this speed is lower than this, speed in the glass is less, the light is slower. This ratio will be greater than 1, which means theta 1 would be greater than theta 2. So, if V1 is greater than V2, we have theta 1 is greater than theta 2. And if it's less, obviously it's less. Now, the problem is that these numbers are huge actually. The speed of light is very, very big, even in such substances as glass. Now, here is the fundamental property of light, which is causing this dispersion phenomenon. Different lights have different wavelengths, we know about that. Different colors, I'm talking about visible light only. So, we have red, for instance, with the longest wavelengths and the violet with the shortest wavelengths. And this wavelength is very, very important for refraction. So, if you remember when we were talking about refraction, especially in Huygens model, we were talking about front of the light front. And then it just turns, this is turning of the wave front of the light. And obviously, it should depend somehow on the wavelengths. The shorter waves might actually do something different than the longer waves. And that's exactly true. It looks like the speed of light depends not only on the substance where the light actually propagates, but also on the light itself. The longer light waves, like red color, have slightly higher speed in any substance except vacuum. And the shorter ones, like violet, they have lower speed. And it's really related with the wavelengths. It's kind of difficult for me right now to explain this, because I do have to go into some quantum mechanics and stuff like this, which, quite frankly, I'm not sure I understand right now myself. But this is the fact which you just have to take as given. The wavelengths also affect the speed of propagation of the light in any substance but vacuum. In the vacuum all the wavelengths have exactly the same speed. But in some substance, even the air, obviously the glass or water or whatever the transparent substance is, the wavelengths really affect the speed of light. The longer the waves, the higher the speed. Now, we used to have another expression for this particular thing. We were using the refractive index of the substance, which is N is equal to C over V, right? So this is the other way around, I'm sorry. So this is refractive index. This is the speed of light in the vacuum, and V is speed of light in any particular substance. So their ratio is actually called the refractive index. Now, if we use this instead of the speeds, we will have N2 divided by N1, reverse. So the lower speed corresponds to higher refractive index. Now, if it's vacuum, then V is equal to C and vacuum is equal to N is equal to 1, right? If it's air, it's not 1. For air, it's something 1, 0, 0, 0, 3, blah, blah, blah. It's greater than 1 because the speed of light in the air is less than the speed of light in the vacuum, but so little that it's almost 1. So in our calculations, which we will probably carry up to a second or third decimal point, you can consider air to be practically equivalent to vacuum as far as the speed of light is concerned. But for glass, for instance, it's 1.525, if I'm mistaken. So that's a lot. You see, 1.5, it's 50% less. So this is like 300,000 kilometers per second. Then for light, it would be about 200, 2 thirds of this, right? 200,000 kilometers per second inside the glass. So whenever we were talking about these numbers, they're very big and kind of difficult to participate in calculations. These numbers are completely equivalent, proportional, but it's easier to deal with small numbers like 1.525 rather than huge like 200,000 kilometers per second, etc. So we will probably deal with this and using this type of thing, we can rewrite it as sin theta 1 times n. 1 is equal to sin theta 2 times n2, right? Same thing. And 1 and 1, 2 and 2, from which we see, again, very similar law. If n1 is greater than n2, like air and glass, then the sin of theta 1 should be, I mean, glass. Let me start with this. n1 is less. So it's air has about 1 and 2 is about 1.5, right? So the relationship between sines will be opposite. If this is greater than this, this should be less. If this is less than that, this should be greater than this, right? So if it's greater, then this is less. So if light goes from substance with a smaller refractive index into the side, into the substance like glass with a greater refractive index, then the angle of incident should be greater than angle of refraction. So this is the right picture. This angle is greater than this because this, because n1 and 2, because n1 is about 1 and n2 is about 1.5, so we have this. So that's why this angle should be greater than this angle. Okay, now, here is a really tricky thing. How did we calculate the n, the refractive index, based on this ratio? If v in some substance, in any substance, is not a constant, it's basically a range between the speed of the red light, which is higher, and speed of the violet, which is lower. Well, obviously it means it's not really the right kind of exactly mathematically right thing we have to approximate. Well, the thing is that the difference between the speeds of light from red to violet is really small. It exists, but it's really small. And so what physicists have decided, they took the light which is right in the middle, which is yellow. It has the middle wavelengths between the red color and the violet, and they took its speed. So this v is actually a speed of yellow light in any particular substance. So it gives you approximation, but it's approximation precise enough for calculations which most people are doing. Whenever it's not, people kind of make modifications. So we will consider this to be as a given thing, so this will be the refractive index of yellow light, but we will use it for all lights in both substances, in air and in the glass. Okay, so this is just a small nuance that n is actually varies based on the speed of particular color, but physicists have decided to use only the yellow color for this particular definition. Okay, so that's done. Now we will do an experiment and we will just use the white light as the ray of light which is coming down onto the surface between air and glass. So what happens with white light? Well, let's just use this law. We know n1 and n2, and one is air, which is about 1, and 2 is about 1.5, let's say 1.5 whatever, 2, 0, doesn't matter. So let's just have a concrete, let's just take concrete angle of incident and see what happens with the angle of refraction in this particular case. Okay, so now I know the following. When this thing is used in general considerations, calculations, etc., we are using the yellow light, but since we are talking about dispersion right now, we need a concrete value of n for every particular color. What is it for each particular wavelength? So I will exemplify it on two, the red and violet, because they are on different edges of the spectrum, everything else will be in between. So n1 for red is equal to 1.520 if I am not mistaken, yes, and violet equals 1.538. You see, this is higher because the wavelength is shorter. As I was saying, the wavelengths, the slower light goes inside that particular substance, whatever the substance is. How much slower obviously depends on the substance, but this is for the glass. We are talking about, well, there is a special kind of glass, like crown glass if I am not mistaken. For our purpose, it doesn't really matter. So these are numbers which I took from the internet, basically. I did not invent them. Real numbers. So this is for glass. Now, for air, I would consider it to be 011. Actually, it's some other numbers after the decimal digits, but since we are talking about thousands, I just cut them out. It's too real, like three and something else. So we have this table. How can we, from this table, derive what happens with the white ray of light, which comes down, let's say, at angle of 30 degree, in incident angle. Well, let's just use the formula. So we have, let's say this is alpha and this is beta. It's easier than having indices. So sine of alpha is equal to sine of 30 degrees, which is 1 half. Now, this end of air is always 1, so n1 is equal to 1 and 1 is over there. So on the left, we have 1 and 1 half. 1 half times 1. That's on the left. On the right, we have sine of beta. Beta is same as theta 2. It's a refractive index times. And now let's talk about color. If this is red, it will be 1.520. If it's violet, it will be 1.538. So sine of beta is equal to 1 half divided by this, right? So it's 1 divided by 2 point either 1.520 or 1.538. So we have two different angles. And the result is that red light, beta equals for red. It would be 19.21 degree. And for violet, it would be 18.97 degree. Look, difference is not really such a big one. It's about what? 20 something hundreds of 1 degree. And the whole circle is 360 degree. You can imagine how small this angle is. But it exists and that's what's important. So red light would go... So if this is just a continuation without any kind of refraction. So red light would be closer to it. That would be red. That's 19.21. It's further from the normal, from the perpendicular. And the violet would be a smaller angle so it would be closer. And the closer it is to a perpendicular to the normal, the greater deviation from the original direction. Deviation is basically difference between this angle which is same as alpha. They are vertical and this angle. So alpha minus beta, alpha being this vertical angle and beta being refractive angle. It's a deviation from the original direction. So red would be less deviated because it's refraction angle would be greater and closer to the original direction. Violet would be deviated more because it's refraction angle would be less. So that's basically all about this particular phenomenon of refraction on one particular surface between air and glass. Now what happens when we are talking about window glass for instance? There are two surfaces. First from air to glass and then from glass back to air. So what happens? Well let me just draw a picture which actually would be more descriptive. I'll use a different scale of this thing. So we have two surfaces. So this is glass, this is air, this is air. Now this is perpendicular. Now we have angle about this third degree angle. And we will continue it as the line of original direction of the white light distribution. Now this is white light which means it consists of all the different components. So red component will go this way and violet component will do this way and everything else like green, yellow, etc. will be in between them. So what happens now? So let's talk about red for instance. Here is perpendicular. Now the angle of refraction on the top border between air and glass becomes the air of incident on the bottom. So before I had alpha and this word beta. So I had sin alpha times n air equals sin beta and glass. Now the same angle beta. You see? Why is it the same? This is perpendicular, this is perpendicular. And this is the line which basically crossed them both. So these angles are equal. So now sin beta times n glass should be gamma. Should be equal to sin gamma times n air. Right? So beta becomes from the refracting on the top. It would be an incident for the bottom surface. But now we are talking from glass to air. Whenever we are talking from glass to air, from a greater index, refractive index to a smaller refractive index, you remember how angles are related. It's just an opposite. In this case, this n of air is less than this. So this angle will be greater than this. In this case, this index of refraction is greater than this. So the angle should be smaller. Incident should be smaller than refracting. Okay. And what follows is, you see this is sin beta times n of glass. And this is the same thing. This is the same thing, which means sin alpha times n air equals sin gamma times n air. So this would be equal. Well, this is n air and n air. From this we have alpha is equal to gamma. So this angle, the deviation from the vertical, is exactly the same as this one, original one, from which follows that this ray will be parallel to this one. So what I'm saying is that after the second refraction, if these are two parallel sides of whatever substance is, in this case, glass, the resulting ray will be parallel to the original direction but shifted. It will be shifted a little bit for the red, a little bit more for the violet. So after the light goes through both surfaces, one ray of white light would be split into many different rays of different colors. So that's basically, already if you put some kind of screen here, and this is a relatively narrow ray of light, you will see maybe just a little bit. I mean, the deviation is really very, very small, but in theory you will see different colors here. But the colors inside will be still mixed together, but on the edges you will still have the colorful lights, red on one end and violet on another. So that's why the result of the white light going through these two parallel surfaces with glass in between would be that it will be wider, and at the edges you will have the red and violet picture. That's what's very important actually for photography because it's really a color aberration which needs to be somehow dealt with and it's not easy because it really completely changes the picture, at least on a detailed scale. So that's why it's very difficult actually to do the good camera. That's why the cameras which are good, they are big and bulky and there are many different things inside including electronics things which fight this problem of light aberration. On the other hand, rainbow is beautiful and this is also the result of it. But we will talk about rainbow in another lecture. So basically that was all I wanted to say about dispersion on flat surfaces. Now obviously if it's something like window it's very thin basically and the difference between left and right deviation of the red and the violet is tiny, it's hundreds of millimeters. The textual part of this lecture contains some more numbers for different colors and including this calculation of this difference between these two edges between the red edge and the violet edge. If you have a single line, just line, mathematical line of the white light then we will have the spectrum here which will have certain widths and the width is hundreds of fractions, not hundreds of hundreds of millimeters but hundreds of parts of one millimeter, which means it's not noticeable at all. That's why we see basically the white light as white light going through the window. But if this glass is thick enough then these rays will spread actually along a bigger distance. So that's why it would be more noticeable for thicker glass. Alright, that's it basically for today. We were addressing this dispersion on a flat surface only. And next lectures will be about how the dispersion going when we are talking about prism and the light goes through the prism. It will also, in this case, the result is parallel lights of different colors. In this case they will have angular deviation as well, not only linear deviation but angular as well. And then maybe we'll talk about Wrangler. After we will prepare ourselves to all the different forms and shapes of pieces of glass or pieces of caplets of water, then we'll talk about Wrangler. Okay, I do suggest you to read the notes for this lecture because the pictures are much nicer over there and there are some tables which basically give you exact numbers of what are these reflective indices are and what's an exact linear deviation of the single ray of white light whenever it goes through the window glass, let's say. Alright, that's it. Thank you very much and good luck.