 Now, the last thing we have to discuss is write on Bragg's law. What is Bragg's law? That is the equation of Bragg's law. What is Bragg's law? So, what happens in that? See, Bragg's law is the law we have through which we can find out the interplanar displacing. Interplanar displacing is what? It is the distance between the two layer in a crystal. Crystal has layer-laying structure. Suppose we have a layer 1, 2, 3 and so on we have. So, we must have some distance between these two layer. This distance d, we call it as interplanar displacing. And to find out this d, we use Bragg's law. The relation of Bragg's law is n lambda is equals to 2d sin theta. n lambda is equals to 2d sin theta. With this equation, you can solve all the questions of this. Whatever question they ask, whatever question this equation you can solve. Everything will be given one unknown detail. Use this formula and get the answer. I will discuss that. But how do we get this expression? n lambda is equals to 2d sin theta that we are going to discuss. Now, to find out this interplanar displacing, we use a light of certain wavelength. And that light will be in the order of that interplanar displacing. According to that, generally we choose x-ray because x-ray has penetrating power. So, that can penetrate into the crystal and then reflection. We have a receiver ring. We have a source of x-ray. That receiver receives light which gets reflect from the crystal surface. And then on the base of the image that you get, on the base of that image only, we will find out that beam. So, first of all, to understand this, we have to understand two properties of wave. And that is constructive and destructive. What is constructive? Interference. Properties of wave that is interference. That has two types of interference, constructive and destructive interference. What is constructive interference? When two waves of same phase. Suppose this is wave one and another wave is this. When these two waves combines, why they have same phase? Because you see they have same direction, right? This is the direction of the wave. The same wave, when these two combines, they will give you a net wave whose amplitude, suppose it is A1, this is A2. So, the net wave will have amplitude is equals to A is equals to A1 plus A2 of one. That is what Kea is. So, this is constructive wave. So, it will have to be same. Any multiple of them. That is possible. Basically, you will get, you have to add these two amplitude. When the wave is same, when the phase is same, when the phase is opposite like this, these two opposite phase. When these two combines, if the amplitude is same, then these two cancels also in each other. You will not get any wave. So, this kind of interference, we call it as constructive or destructive interference. What is diffraction? What is diffraction? This is interference, right? Can you see it is a bending of light? See, wave has two properties. Interference and diffraction. Interference, we have discussed constructive. We have the use of this interference only. Diffraction is nothing but the bending of light. It shines. It is an angle. It shines. That is diffraction of light. So, when the light or the, you know, light strikes at any sharp edge, it diffracts. And that, the shiny part when you tilt the blade like this, any shiny use, knife also if you, you know, tilt like this, at some different angle it shines. So, that is bending of light because of bending of light. So, that is diffraction, we call it as interference. We have use of interference here. Two types of interference, destructive and constructive. Now, to get a better image, we need constructive interference because you have nothing here, right? Our source of the wave is same, right? So, you will get obviously same wave you will get with same amplitude. And if the interference is destructive, you won't get anything. Receiver cannot, you know, receive this because you are not getting anything here. But here you are getting the larger amplitude wave, okay? To get the better picture, better image, we must require constructive interference for any experiment, whatever you are doing. So, here also for Bragg's law, or to find out the interference spacing, we require constructive interference or destructive interference, okay? Now, suppose the crystal we have this, this is the layer we have in the crystal. This side we have source of X-ray. Why X-ray we are using? Because it has penetrating power. It can go in a, like, it can go into the crystal action, okay? So, this is the source of X-ray. And this side we use, we take one receiver which can receive the reflected wave from this crystal, okay? So, this is the direction of wave we have in this section, it goes and it reflects, it goes like this. The angle of incident, this angle is theta. Okay? Now, since we require constructive interference, so the phase or the wave that you get here, that wave must have the same phase, okay? Then only we get constructive interference. Suppose this is the wave we have, okay? Same phase, so it should go like this, or then from here it should go like this. So, same phase we have, so here it should be. So, phase should be same, so it should go like this, okay? This one is, suppose we have path A, and this is, we have path B. This distance is the independent spacing, D, okay? Sir, let's see if we can touch it. Isn't it supposed to be like the surface which you should touch and then... Yeah, I am coming to this. Let me explain one point. Obviously, this wave goes like this. Okay. It goes like this, okay? But the point is, we should have here constructive interference. So, phase of the wave must be same. That's why I have problems, okay? Now, can you tell me path A and path B, two different paths we have. Which path the wave has to travel more distance, here B? B, correct? And what is the path difference? This distance is the same? This distance and this distance is same. Path difference is what? From this point to this point, okay? Now, suppose it is O, A, P and B. So, if I ask you what is the path difference? Path difference is nothing but A, P, plus D, B. Isn't it clear? A, P, plus D, B. Okay? What is this distance? It is D. And if this is theta, this one is what? What will be this one? 90 minus theta. What will be this one? Theta. And what will be this one? Theta. 90 minus theta. Okay, let's put theta down. If this is theta, then what is A, P in terms of D? Sine theta is what in this triangle? Sine theta is what? A, P by? O, P. O, P, right? A, P by O, P. So, what is A, P? A, P is D sine theta. Okay? A, P is D sine theta. Similarly, P, P is also D sine theta. Because if it is theta, this is also theta, right? Yeah. Theta? This is 90 minus theta. Take A, P, theta. T minus theta. Sir, O, P and A, P are parallel. No, no, it's not parallel. Okay, we say it's parallel. Okay, it's parallel. It's perpendicular, actually. It's perpendicular. This is perpendicular. I'm saying O, P and A, P. O, P and A, P. O, P and A, P. Yeah. O, P and A, P. O, P and A, P. Then if that is the case, then B, O, P should be 90 minus theta. If they are parallel. You are saying O, P and A, P. Yeah. If they are parallel. It is not parallel. I have just drawn perpendicular from this point to this point. This is the perpendicular. A, P, A, P. O, P should be a parallel. O, A, P is also 90. Okay. This will be 90 minus theta. This angle, this angle. 90 minus theta. See, this is theta. This should be theta. Take that. And this is also theta then? Yeah. This is 90 minus theta? Yeah. This is theta. This is 90 minus theta? This is theta. Since it is theta, this is parallel. A theta, A B theta over here? Yeah. A B theta over here? Yeah. These two angles must be equal. 90 minus 91 is theta. Sir, how can that be possible? That means 90 minus theta, theta. Okay. This is 90 minus theta? A little bit theta. Sir, A, P, B is the right angle. Yeah, A, P, B is right angle. A, P, B is the right angle. A, P, B. Yeah. A, P, B. How can this be equal? I don't know. But you're not assuming all that. No, no. This, the angle of whatever angle we have here, the same angle we should make in its reflection now. So, this angle and this angle must be same. Just like this. Okay. So, this angle is theta. This is 90 minus theta. And with the same angle it reflects. This should be theta. If this is theta, 90 minus theta, this should be theta. Okay. So, theta. Now, if it is theta, then what is P B then? Can you say P B? P B is again D sine theta. D sine theta. So, what is the part difference? A B plus P B. D sine theta plus D sine theta. That is 2 D sine theta. You'll get part difference. Now, if the part difference in terms of lambda is N lambda, then this thing is true. Okay. Now, you look at this, the part difference A B that you have. Suppose we have this A B. At point A, the wave is coming from the bottom and it is going from the top. So, at point A, the wave is coming this way and it is going this way. Now, for this thing to be possible, one possibility is what? It may go like this. This is one possibility. Another possibility is what? It forms two ways. Another possibility is what? It forms three ways like this. Okay. It is what? What is this distance? Lambda. What is this difference? Lambda plus lambda. That is 2 lambda. It is 3 lambda and so on. Then we can say the part difference must be an integral multiple of lambda. Okay. And that's why the part difference is N lambda is equals to 2 D. Is it clear? Part difference must be, must be the integral multiple of the wavelength of the light that we are using for this. And that should be equals to 2 D sine theta. Okay. Numerical questions you can solve under this. Mostly they are numerical only. Okay. They will give you the, no, all things will be given. Angle of incident. N is generally N, they like order. First order diffraction is there like that. First, second, whatever order they have written, it means that is the N value given. Okay. And whatever unknown you can find out from this. Sine 54.5, like this also they will give angle. But this value will be given in the question itself. Sine of 54.5 is this. Okay. Must you take care of what is the theta we have taken? Theta is this. Okay. If they have given you this value, then answer will be 90 minus theta. Okay. Sometimes they will give you this angle. Theta is 54.5. Okay. So, 90 minus this is that incident angle. Got it? So, how do you do 80 degrees or 80 degrees? I didn't say it... What is the point is... I didn't say it's 90. But here it is... Yeah, it is 90 also you can see. This is theta, right? So, this angle is this... A b b is 180 minus... 180 minus 2 theta. Depends on theta actually. See, we don't know about this angle. What is this A b b? But we are very sure that this angle should be this. Equal to this. Because if this is theta, this should be 90 minus theta. And the angle with which it is... The angle forms with this vertical line. Same angle it goes at the reflection. Same angle is an angle of incident or angle of reflection. These two angles must be same. That's what the concept is. Theta and theta. Okay.