Compound microscope

let's explore compound microscopes we'll first understand the logic behind it and then we'll build it so let's say you were looking at a tiny amoeba with your naked eye will imagine this is your eye and your cornea and your islands are together over here the schematic okay now how big this amoeba looks to you really depends on the size of the image form in your retina and that depends on this angle which is the same as this angle this angle we'll call that as theta naught and if the angle theta naught is small enough which is which is the case in the case of an amoeba then we can approximate that angle as being equal to this height hatch divided by this distance D now for the case of amoeba this angle is very tiny because amoebas size is very small making this height extremely tiny and for the naked eye we cannot come any closer than about 25 centimeters that's our near point and as a result this angle becomes very small and so this size in the retina becomes very small so we can't see it clearly now in order to magnify this image we somehow have to increase the size in the retina but the question is how do we do that so we have to increase this angle right so how do you increase that angle theta knowledge first just let's look at mathematically how do you increase the value of theta naught well we can do two things one we can somehow increase the height of the amoeba itself if you would somehow that's a stretch that amoeba and make it say ten times bigger and I'm pretty sure you agree with me that even this angle would become ten times bigger making this size in the retina also ten times bigger another thing we could do is decrease this value of D so decrease this which means if you could go closer then also theta naught would increase suppose we could go about ten times closer let's say than the near point of course with our naked eye it's going to be absolutely blurred but somehow if we solve that problem of blurring and if you could go ten times closer then again theta naught will increase again by a factor of ten which means there will be a total increase of a factor of 100 you see that hundred times more this size will be you know retina now and guess what that's exactly what a compound microscope does so our compound microscope does two things one it stretches the height or the size of the object that's one stage of magnification the second stage is it allows your eye to go much closer than your near point giving you a second stage of magnification together giving you a huge magnification so all we need to figure out is how do we practically build something that does this and this all right let's make some space to build our microscope so let me keep this thing down somewhere over here I want this for our reference this is what we're seeing with the naked eye and let's minimize this excellent so first step is to increase the size of the amoeba say about ten times as an example how do we stress this amoeba and make it ten times larger well actually you already know how to do that so say you hadn't had a convex lens with you and say you kept that same object somewhere between F and 2f say very close to F but in between F and 2f now if you draw the Rays we can clearly see that the topmost point is being focused somewhere over here the bottom will get full so focus somewhere over there which means you're gonna end up with a huge magnified image and inverted real image like this now the closer you bring this object to the principal focus you will see if you draw the ray diagrams the bigger this will be so by choosing a suitable distance over here we can make this image about about ten times H if you wanted so you can do that so we have received the first stage of magnification we can treat this now as our new object even without the second stage say you were to directly look at this just like how you would look at this object say you will directly look at this by breaking this point right at your near point can you see now this object this image is going to subtract here it's going to something ten times bigger and as a result if you draw a reference right through the optic center notice that the image size inside your retina is already ten times as big as you got over here that's why we have achieved the first stage of magnification now one small detail is you may be wondering well the rays of light are coming down over here right so how could you see it over here well in reality remember these angles are extremely tiny so all these rays are pretty much paddle to the principal axis all right so we have exaggerated over here but what's important is already with the first stage we have gotten ten times bigger image in our retina but we're not gonna stop over here oh no no we need to make it even bigger to increase this angle even more we are going to do the second stage of magnification the second stage we are going to go closer and in our example we are going to go about ten times closer so the current distance is about 25 centimeters that's seven air point which means to go ten times closer I have to bring my eye about 2.5 centimeters from this image but how do we do that because if we do it right now with our naked eye then the rays of light will not be focused on our retina it'll be a blurred image so we are going to make use of a convex lens we are going to get help from a convex lens in fact you know what let's bring in a convex lens which has a focal length of exactly 2.5 centimeters and now with the help of this convex lens we can bring this entire system our eye and the lens all the way till here so that the object the new object for us is actually the image so I'm talking about this image which is the object for us that comes right at the principle focus because when it comes at the principal focus what's going to happen is that these rays of light are going to be parallel to each other and now our eyes I can focus these paddle beam of light on the retina now as a result can you see that the MU angle subtended is about ten times larger let me just show that there it is notice now the angle subtended is further ten times bigger and the rays of light after refraction are pretty much parallel to each other again these rays of light will fall on our eyes because these rays are pretty much parallel we have exaggerated over here and as a result they will all get focused at this point now so this this point will get focused at this point and as a result our image now is going to be humongous further ten times bigger so the e-rate sizes increased further ten times which means compared to this what we had before the image has increased a hundred times more we have we have achieved hundred times magnification and so this is what our compound microscope looks like now before we continue any further a small thing this second stage of magnification we got by bringing a convex lens right next to your eye and coming closer this is actually the principle of a simple microscope so this lens is just acting like a simple microscope and we've talked a lot about this in previous videos in great detail so if this part was not super clear to you or you need more clarity on this the second part where we went closer then it would be a great idea to go back and watch those videos and then come back over here anyways we can see that our microscope consists of two lenses want to achieve this and another one to achieve this and we give names to these lenses the one that is close to the object we call that as the objective so this lens we often call as objective so the purpose of the objective is to create a large magnified image and this lens which is kept close to our eye which acts like a simple microscope is called the eyepiece again it's called eyepiece because it's kept very close to our eye and it's job is to do this let me show you this in reality so here I have drawn a tiny amoeba on my computer screen and with my naked eye this is what I'm seeing right now that's it now to increase the size we need to magnify this so we're going to build a compound microscope so first stage of magnification will be by using an objective lens and here you can see I'm using an objective lens over here so this is going to create a real image it's a convex lens it's going to create a real image and so if I look at that again directly with my naked eye have to look from here somewhere and if I look directly from my naked eye this is what I pretty much see this is the first stage of magnification and if we compare it to what we had before you can clearly see it's a little bit magnified it's little bit quicker it's not ten times it's a little bit because I'm not having a perfect lens over here all right so anyways you can see it's magnified first stage of magnification now to further magnify this we are going to use our eyepiece which is just a magnifying glass a simple microscope if we now bring this magnifying glass right next to our eye we can go even closer and get that image even bigger in our retina this is the final image a little bit more magnified again not much because again we don't have perfect lens system over here and now we have simulated our compound microscope so the final setup looks pretty much like this here's our objective here's our eyepiece and this is our compound microscope in fact it's called compound because it's made up of two lenses now lastly we look very quickly look at the magnification produced by our compound microscope in our example we got it to be a hundred texts right we got we found that with the microscope the image in the retina is hundred times more than we get without the microscope how did we get the hundred well ten was produced by the objective and further ten was produced by the eyepiece so it's the product so in general we can write the magnification produced is the magnification of the objective times the magnification of the eyepiece this in simple is the total magnification of a compound microscope