 Next, we will take up optical instruments. Tell me one optical instrument which you use most often. Michael, you use it quite often. You have it. You know your eye is also an optical instrument. So, your eye is an optical instrument and the best part about eye is that you can change the focal length of the lens in the eye. Depending on what you are looking at, the focal length of your eye changes. So, a healthy eye is the eye which should be able to see the object which is as close as 25 centimeter. The least distance of vision for a healthy human being is 25 centimeter. And maximum how much you should be able to see? Infinity. That is correct. Your eyes are most relaxed when you look at objects that are at infinity. As in your further you look, the more relaxed your eyes will be. But if you put something very close your eyes, your eyes will be very strained. So, this is the healthy human. I mean healthy as in it is not that those who are wearing specs are not healthy. I mean by healthy means the normal functioning eye which does not need another device to look at the object. Now, why you need a lens in front of your eye? What is the need to correct what? To make sure the person who is not able to do this. Suppose a person is not able to look at objects which is at 25 centimeter. The lens will be able to correct this defect. Fine. So, if lens somehow ensures that you are able to see the object that is at 25 centimeter, then your defect is corrected. Fine. So, that is why we use lens. Fine. Now, let us see a numerical then it will be more clear. All right. Write down. You need to find out focal length. Focal length of the lens needed to correct the defect in an eye of least distance of distinct vision being 50 centimeter. You want to make sure that this person who is not able to see the object which is closer than 50 centimeter to see the object that is at 25 centimeter. Basically, you want to make sure the person who is able to see till 50 centimeter as in after 50 centimeter only should be able to see after 25 centimeter. So, what you should do? So, you have an eye like this. You put a lens in front of the eye. Your eye is able to see after 50 centimeter. This instrument can only see this is your eye can only see after 50 centimeter. So, if you do this thing that you put a mirror sorry put a lens like this so that the object when it is kept at 25 centimeter feels as if it is kept at 50 centimeter by the eye. Are you getting the point? The eye feels as if this object is not at 25. Eye feels this object is at 50 and you should know that the image of this image of lens is object of eye. Fine? That is what right? This will create an image that becomes object for eye. So, the object distance is 25. The image distance for this should be 50. Then only this will see at 50 because this is not capable to see till 50. So, now you are placing an object at 25 centimeter only, but eye will feel as if it is kept at 50. That is why you are able to see that object. So, if you use the lens formula 1 by v minus 1 by u equals to 1 by f, v is what? Minus 50 because it should be that side. u is what? Minus 25. This should be equal to 1 by f. So, f will come out to be 50. Now, when you have first time heard about optical instrument, what came in your mind? Microscope and telescope. What does microscope does? It magnifies. So, you have two artificial optical instruments in your syllabus. The first one is microscope and the other one is telescope. What microscope does? Microscope lets you see the object that is very, very small, very tiny. Our eyes are not capable to see the objects which are very, very small. What does microscope do? It magnifies it and then you are able to see what is happening. In fact, do you know that this green board or whatever object you take is mostly empty? The amount of empty space, percentage of empty space between a nucleus and electron is thousand time or in fact, I think 10,000 times more than percentage of empty space between earth and sun. That is how empty these entire objects are. But then we are not able to see it because of our constraint vision. But if we somehow keep on zooming this, then you will be able to see what is happening. You will be able to see that this surface is not smooth also. This is very, very rough surface. So, all that observation will come only when you will use microscope. Now, what is telescope? What do you use telescope for? Object at far distance. You have a telescope at your home. So, you see objects at very, very far distances. What is the problem with objects which are very, very far? Exactly. Your resolution is very, very less. You may be thinking that looking at a star, you may be thinking that there is only one star. But if you use telescope, probably your resolution increases and you may see there are multiple stars there. So, this is again something which helps you to observe things which you cannot observe using your just eye. So, let us take these one by one and understand them in a greater detail. The first one is microscope. Write down. There are two types of microscope in your syllabus. The first one is simple microscope. Another is compound microscope. So, we will take simple microscope first. Have you seen microscope? What it is? Okay, you are talking about some complicated microscope. Have you seen a very, very simple microscope? Just a magnifying glass or a convex lens. So, convex lens can be your microscope and that is what the simple microscope is. So, draw this. So, this is the convex lens. Here is the observer who is looking at the object. An object is kept at some distance. This is the object. So, where should the image be formed? Image can be formed anywhere depending on where the object is. But then when you are actually using microscope, what you want? Image should be at least formed at 25 centimeter. Isn't it? So, you have two cases here. Case number one, when image is formed, image is formed at D equal to 25 centimeter. Fine. So, from lens, the image should be 25 centimeter. So, it should be formed somewhere here. Let us say this is distance. This distance is D. Okay. Focal length is given as F. Getting it? So, this is case number one. So, can you find out magnification in this case? How much it is? Now, in terms of what is given? D is given, F is given. F into 1 plus, no, that is dimension incorrect. 1 plus 1 by D, you cannot add. 1 is different dimension. 1 plus D has a different dimension. You cannot add them. See, it is, you write your lens formula 1 by V minus 1 by U equals to 1 by F. Fine. Now, magnification is what? In case of lens, magnification is V by U. Multiply this with V. So, you will get 1 minus V by U equals to V by F. Fine. So, V by U is what? Which is magnification. This become equal to 1 minus V by F. What is V? Look at the diagram. Tell me what is V? No. Minus 25. Or you just write in terms of D. So, this is 1 plus D by F. So, this is the magnification. Okay. Now, magnification, this is a special case. The image is getting formed at D. This formula is not universal. So, if I ask you what is the magnification of a lens, you should ask me back in which situation. Fine. So, in a situation where the image gets formed at D, magnification is 1 plus D by F. Fine. There can be infinite formula for magnification. But this is only for this situation. Now, another situation is write down case number 2. Image is formed at infinity. If image is formed at infinity, where should be the object kept? At F. Right. So, object is kept at F. So, this distance is F only. Fine. So, if you draw a ray diagram, this is how it will be looking like. And here is the observer who will feel that the image gets formed at infinity. These two parallel rays won't meet. Or that you can say they meet at infinity. Fine. Can you doubt? Now, try to find magnification for this. Okay. So, you will not be able to find out magnification just like that. Okay. So, linear magnification doesn't make sense here. Fine. So, here what you will do, you will define magnification differently. Okay. You will not be using linear magnification formula. Okay. So, the way magnification is defined when this thing happens is this. Write down magnification will be defined as the angle made by image divided by maximum angle made by object. Isn't it? If this angle, can it denote how big the image is? Isn't it? If image is this much size. So, this ray will be like that. It will reach at the tip. Are you getting it? Okay. So, this angle is an indication of how big the image is. Fine. Let us call this as alpha. And how will you find maximum angle made by the object? Suppose you keep object like this. How will you find this thing? Maximum angle? It will make angle. It will make angle like this, like that, this one, this one. Which is the maximum angle? 90 degree. Right. But practically, you will not be able to look at it properly. You should put this object at least at a distance of D. Are you getting it? So, you put this at a distance of D and then you measure the angle. Okay. So, that is alpha and this is beta. Fine. Is beta the maximum angle? Beta is the maximum angle which is clearly comfortable for anyone to see. Okay. So, we will slightly modify this magnification. Okay. Here, we will say that magnification is nothing but tan of alpha divided by tan of beta. If alpha by beta is more, tan of alpha divided by tan of beta is also more. Okay. Because between 0 to 90 degree, tan is also increasing function. Okay. Tan of alpha is what? Suppose this distance is h. Tan of alpha will be h by f, tan of beta is what? This is the same object. Height is h. Tan of beta will be h by d. So, magnification becomes d by f. Okay. Can I say that magnification in this case is one less than magnification which was in earlier case? No. I cannot. Because the definition of magnification itself is different in both the cases. So, you cannot compare apples with oranges. Are you getting it? The way you define magnification itself is different. So, how can you compare? All right. So, this is about the simple microscope. But the problem here is that d will be around let us say 25 and f let us say is, let us say, you know, minimum to minimum 0.1. So, magnification becomes 250. But you want magnification of the order of 10000 or something. So, simple microscope would not be able to do that. So, then we use compound microscope.