 Hi, I'm Zor. Welcome to InDesert Education. Continue talking about dispersion of light. Today's lecture will be about dispersion when the light goes through a prism. We are talking about triangular prism. Right, regular triangular prism, where the bases are regular triangles, equilateral triangles, and the edges are perpendicular to the bases. Now, this lecture is part of the course called Physics for Teens, presented on Unizord.com. I suggest you to watch this lecture from the website. Well, not only because it's completely free and there are no advertisements and no strings attached, it's because it's a course. So, this lecture is part of the topics and topics are part of the bigger parts. And then there is a prerequisite course called Maths for Teens on the same website. Maths knowledge is mandatory for studying physics. Like today, for instance, we will talk about some trigonometric properties. And what else? So, the website also has exams, which you can take as many times as you want. So, in any case, it's really much more advantageous for you to go through the website and through the menus one after another, one lecture after another. You choose, in this particular case, from the home page, from the Unizord.com, you go to Physics for Teens course, for example, go to the part called Waves, and then Phenomenal Lights. This is one of the lectures about Phenomenal Lights. So, anyway, let's go back to our dispersion things. Now, in the previous lecture about dispersion, we will talk about dispersion against the flat surface, flat glass. And then we basically explained how different colors having different wavelengths are going through the border between, let's say, air and glass. And they are dispersed. There is an angular dispersion. Why? Because we are dealing with different wavelengths and because of that, different wavelengths have different speed of propagation in certain substances. Well, in all substances except absolute vacuum, different wavelengths of light have different speeds. Only in vacuum all the speeds are the same. Why? It's a different question. It's kind of complicated. But anyway, that's the fact. And the longer the wavelengths, like red, for instance, has a longer wavelengths than violet, the faster the light travels. The difference in speed is not really significant, but it exists and that's what's very important. The risk, however, is a big difference between the speed of light, let's say, vacuum, or in air, which is almost like vacuum. There is still some dispersion. There is still some differences in speed between different colors in air, but very, very insignificant. But when you go to something like glass or water, the speed significantly diminishes. Speed of light is like 1.5 times less in glass, generally speaking, than in vacuum. And basically that's why we have a deviation from the original direction of the light when the light crosses the border between, let's say, air and glass. And we all know the law of refraction, which is sin of theta 1 times N1 is equal to sin of theta 2 times N2, where theta 1 and theta 2 are angles of refraction. And N1 and N2 are refractive indices of the substances before and after the border. Let's say this is air and this is glass. And basically they are ratio between the speed of light and vacuum to speed of light in that particular substance, whatever the substance is, air or glass or water or anything like this. So this is something which we have learned before. And we also have learned that when the light goes through glass, which has two surfaces, so this is N1 again, so air, glass, air, like going through the window glass, it deviates here and then it goes back to original direction but with a shift. So that was in the previous lecture. So this is the flat glass. Now today we will talk about prism. Okay. So let's get rid of this picture and we will draw another one. So I will draw the section of the prism. So the light goes to a side of the prism. So let's consider the prism goes like this. So it goes this way. This is the base. Or a section which is parallel to a base. And then there is a ray of light which comes at certain... So this is the white light. Now the white light has the components which we kind of conditionally call red, orange, etc. up to violet. And again my point was that different colors have different speed and that's why, since the speed is different, so the refractive index is different for different colors. Then we have different angles of refraction. So again, this is a perpendicular. So this is our angle of incident of original white light. Now let me just put it a little bit here. This is original direction. This is not the direction this white light propagates but I will compare it with this one to know the deviation. So where the light actually is going? Well, it will not go straight. It will undergo certain refraction. Now you see from here that if the speed is greater the sign is should be less. So whenever you have a difference in speed, let's say this speed is greater than this one, then this sign should be less than this one. So basically what kind of deviation we will have? We will have using this particular thing. So N1 is approximately one, more or less, because this is air, okay? This is air and this is glass. So on this border the red light would go this way and blue light and violet light goes this way. Now why? Well, since the refractive index for red is less than refractive index for violet, then the angle of diffraction will be correspondingly greater than this equality, right? Equality should always be there. So if N2, let's say this is violet and N2 is greater than N1. So it means that the theta 2 should be less than theta 1. In this case I am using alpha and this would be beta red or beta violet. So red would be greater than the violet. Okay, so far so good. Now all other colors would be in between basically. So we have already split our original white light into a certain angle where red and orange and other colors are kind of separated. Well, obviously it's not like exact separation between colors. It's a gradual change from one to another. But now we have another border. Now this border is from higher speed to lower speed, which means that our angle of incident would be greater than angle of refraction. Now we will have here an opposite situation. We are going from lower speed to higher speed, which means we are going from higher index of refraction to lower index of refraction, which means that the angle of incident would be less than the angle of refraction. So what happens here is a little perpendicular. This would be an angle of... I'll put it like beta prime. This is for red. And this would be for violet. So this is beta prime. Okay, now we are talking about refraction being given greater than incident in this case. From air to glass, refraction is less than incident. From glass to air, refraction should be greater than incident. So if this is an incident angle, then this should be greater. And again, if this is an incident angle, which is even greater than this one, that would be even greater here, right? So this is qualitative picture. Now let's talk about numbers. Let's just assume that this is how our prism is oriented, and this is the direction of the white light, and alpha is equal to, let's say, 30 degrees. Now why do they choose it? Because it's easy to take the sign of 30 degrees. So our left side would be sine of alpha, which is sine of 30, which is one-half, and one we are talking about air, so it would be approximately one. So on the left I will have 0.5. On the right I will have... Okay, for red. For red, and red is equal to 1.520, and violet is equal to 1.538. I do remember it. So for red I will have the angle. So if I will calculate left side as this, right side is sine of unknown angle times... So it would be x times 1.520, and for violet it would be x times 1.538. So I will find x from here, now this is a sine, and then I will find the angle by sine, and the angle will be 19205 degree, and 18.971 degree. So these are... So BR would be greater than beta... BR would be greater than beta V. Beta R is refraction for red, and beta V would be refraction for violet. Slightly, slightly greater. Very slightly, mind you. It's like less than 3 tenths of a degree, which is a very, very small difference, but it exists, which means that our white light is splitting into different rays. Each ray will have its own color. Okay, now considering this is a very small difference between the biggest and the smallest angle within the visible spectrum. We are talking about only visible light, obviously. We might not even just peel it or see it with our eyes, this split. But then, as we go further, the split will increase more. Now, for the next one, I have these calculations also done. The split would be calculated based on these angles. But you see, we don't know these angles, beta prime. We know beta. How can I get beta prime from beta? Well, that's actually very easy. It's just plane geometry. Look at this A, B, C. Let's say this is P and this is Q. This point is Q. Now, if I know beta, let's talk about R, red. So I know beta R. That means, since this is perpendicular, that means that angle B, P, Q is 90° minus beta. I'm not using index R or D because the calculations are the same. Now, this angle is 60°. So from this angle, from B, P, Q and this angle, I can derive the value of B, Q, P because the total should be 100° degree. If I subtract from 180°, I have to subtract this and I have to subtract 60. And that would give me angle B, Q, P. And my beta prime is 90° minus this one. So I have to do 90° minus this one. So what would be the result? So this would be 90 plus beta minus 60. So that would be 30 plus beta 90 plus beta. 90 minus this would be 60 minus beta. And this is beta prime. So knowing this angle, the refraction, alpha we know, so we did this calculation so we know beta, beta R and beta B for red and for violet. From this, we know the angle of incident on another side of the prism. So the angles will be beta prime R would be equal 60 minus this, which is 40.795 and beta V prime, that's this angle would be 41.029°. Now I can do exactly the same thing as before using the law of refraction. Now I know the incident angles and I can find these guys. Now in this case N1 is something like 1.5 and if I will multiply sign of this times 1.5 whatever, for red it will be 1.520, for violet it will be 1.532. Now in this case N2 will be equal to 1 because the outgoing ray goes to air so it's almost 1. From which I can basically derive sign. And here we have a very interesting condition which I myself was first surprised a little bit but then I started thinking about this and found that it's actually how it's supposed to be. Here it is. If you will do sign of this times this and divide by 1 actually you will have something which is very close to 1. Sign of 40 times 1.520 would be something like 0.99 whatever. Very close to 1, which means what? Which means that the angle will be very close to 90 degree. So this angle deviation from this perpendicular to this this will be my gamma R. Very close to 90 degree. When I multiply sign of this by this I had one point something greater than 1 and sign cannot be more than 1. And I was again surprised a little bit let me tell you honestly. Now what actually happens is that's how it's supposed to be. Under certain conditions like this one for example this is a practical example by the way when you know your initial angle of incident you calculate everything you see this will be this angle of incident of this violet ray of light will be significantly large well greater than some boundary value. When this light will be completely horizontal and a little bit more than that it will not really go out it will reflect here and that's what actually happened here. The violet and actually blue as well if you do all the calculations and I have it in my textual part of this lecture blue and violet will not go through the angle will be sufficiently large which multiplied by this will give a sign which is greater than 1 which does not exist and it will be a total internal reflection. So that's what's interesting. The red light will go through and orange and green but the blue will not and red and violet will not because their angle would be too large to go through. Now but this is a very known property you have heard about fiber optics fiber optics you have a very thin something like a glass or maybe plastic I don't know a thin tube and if you send a light signal along it it will be really not very it will not really penetrate the wall because it will always reflect within the wall and it will go because of this property because this law dictates that after certain critical value whenever the angle is large enough angle of incident which means angle with the perpendicular to a surface it will not go out it will be within this thin tube and actually if you are interested you can go and internet and there are some demonstrations the person took a laser pencil whatever it's called put it at the edge of the glass or plastic tube and you will actually see how the light you will see the trajectory of the laser light it will go through reflecting from the walls but not penetrating the wall and everything goes through the edge that's what fiber optics actually are so in this particular case since blue and violet will not go out the whole color of this visible color will be towards the red light it will be not exactly white it will be little reddish white now the last thing which can be calculated very easily it's a deviation of the final ray of light from the original direction after two reflections well basically it's very easy first you calculate the deviation of this this angle since you know this and you know this is alpha and this is alpha as well because they are vertical and this is my beta minus beta with the initial deviation the secondary deviation from this would obviously be gamma minus this is gamma and this is continuation of this so this would be vertical with this this would be beta prime and we know that beta prime is 60 minus beta so I can just replace it with 60 minus beta and if you will add these two deviations which would be alpha plus gamma minus beta and that would be plus beta so minus 60 so this is the total deviation by the way in case of red I have calculated that gamma red is equal to 83.3 degrees very close to 90 degrees we were talking about very close to 90 degrees but whenever I was calculating gamma for violet sinus was greater than 1 so basically you know gamma you know alpha let's say alpha is 3 gamma is 83 minus 60 it would be what about 50 something degree so the final red light would be deviated from original direction by 50 something degree so that's all about double reflection from both sides of the triangle prism so obviously everybody saw that whenever the sun goes to some kind of a triangle or some kind of a prism you definitely see all the colors like a rainbow now in the very beginning I think on the previous lecture I mentioned that rainbow is also a result of this reflection and dispersion of the light I did not really talk about this this is something like dispersion on a sphere because every little drop of water or vapor or whatever it is from which basically rainbow is formed is a little sphere but that's subject of the next lecture so I do suggest you to read notes for this lecture so if you will go to unison.com physics14 waves properties phenomenon of light and this lecture is about dispersion and a prism so the notes for this particular lecture contains some tables with numbers for all different colors these angles and a little bit nicer picture so I do suggest you to go to the website and see the textual part of this they are always together visual and textual that's one of the advantages you have a textbook basically and the lecture as a presentation ok that's it thank you very much and good luck