Convex & concave mirror ray diagrams

in this video we're gonna take a convex and a concave mirror and then we'll take an object and we'll move it at different locations and we'll find out what will happen to its images where its images will be what will be the nature of the image and all of that so let's begin with a concave mirror and let's start with an object which is placed far away far behind or beyond the center of curvature of this mirror to figure out where its image is going to be all we have to do is pick a point on this object so let's pick the topmost point pick a point on this object draw a bunch of rays of light from this which goes and hits the mirror and see what happens to them after reflection you see this point is emanating it is giving out rays of light in all the directions we'll pick a few which will go hit the mirror and see what happens to them if we take an ear and Ondrej it becomes difficult to trace that we like for example if you take a random ray that goes and hits over here then you become difficult to figure out what the angle of incidence is and you figure out what the angle of reflection is in a draw that but if you pick few particular rays as you'll see it becomes easier to trace them so one of those rays that we're going to draw over here is the one that goes parallel to the principal axis the reason we picked this is because we already know what happens to this ray all parallel rays which hits this mirror goes through the focus after reflection so this ray has to go through the focus after reflection so this is one and this is one another ray we can draw through the focus or maybe we can also draw another ray through the centre of curvatures they will also do but I usually like to draw another ray of light which goes which is targeted at the pole so let's draw a ray that is shot all the way from here and goes to the pole and I'll tell you why I do that I like this because because you see the principal axis forms the normal at the pole because the the principal axis passes to the center of curvature and so we can easily see the angle of incidence and so after reflection the ray of light will just go somewhat like this keeping the angle of reflection the same so it go somewhat this way there we have it so the two rays incident rays after reflection intersect at this point in fact guess what if we were to drum more incident trace then it would looks a lot like this if it drum more incident Ares I had it'll take more time but if you did it then you find something like this all right the picture looks scary but what's important is that all those rays are not is being focused at this particular point the point of intersection all of them intersect at the same point and as a result now if you were to put a screen right at this point the point where all of them are being focused then you will see a sharp image a sharp image of this point over here and you only get that at this point if you were to put your screen over here notice they're not intersecting at the same point and as a result you'll get a blur and over here also notice you'll end up getting a blur it's only at this point you'll get a very very sharp image so let's get rid of this screen so to figure out where the image is form we need to figure out where all the rays are going to intersect but since they all intersect at the same point we don't need lots of phrase it's enough if we just draw two rays of light and that's why we're going to ignore the rest of them and so we can comfortably say now that the image of this point is going to be at this point over here so we'll find an image over here and similarly if you take another point on the subject and draw the rays like this you would see they will get focused somewhere over here and another another point over here would get focused over here this bottom most point on the principal axis would get focused right at this point over here and as a result we could now say that we could now construct this image the image would look somewhat like this and again if you were to bring our screen we can capture this on our screen which means not is very getting first of all the image between F and C it's inverted it's real because we can capture it any image that can be captured on the screen or which is being focused is called real and it's diminished in nature here is that exact setup we have the concave mirror this dude in the phone is acting like the object and we have the screen notice that the object is kept far away from the center of curvature and if you now draw a rays of light from here they're gonna get focused but I've kept the screen says that it's focused right at that point and we can actually see its image over here and so if we dim the lights so there's a screen if you dim the lights notice you can see a beautiful inverted image a sharp image that is being focused at this point this is really cool stuff if you directly look at these rays by keeping a giant eye over here then your brain will tell you that these rays are emanating from this point and as a result you can actually see that with your own eyes or with the camera and so here it is if we directly look into the mirror also we can see that real inverted image and that's smaller in size it's diminished all right now using the same technique let's see what happens if we were to bring our object closer let's say we were to bring our object somewhere over here whoa now where would now the image be I want you to pause the video and try to draw a ray diagram yourself for this all right for me it's very easy to do this on the app first of all notice the paddle Ray's gonna look exactly the same the only thing I have to do is get rid of this part over here but look at the ray that is being focused right at the pole this ray now starts making a bigger angle at the pole can you see that because it it originates from here so the angle of incidence at the pole has increased and as a result the angle of reflection will also increase so the reflected ray will go somewhat like this somewhat like this right and as a result the Rays are not intersecting at this point that means to obtain a sharp image I have to move my screen away from the mirror and so my image as a result we could now say is also moving away from the mirror but notice the image is now getting bigger because the top part is over here and the bottom part would be over here so the image will be now this big over here again we can see that over here as we move the object closer to the mirror notice we have to move the screen backwards of away from the mirror can you see that and the image is getting bigger and bigger and bigger and bigger I hope you can see this if we continue this and let's say we bring our object right at see now the image will deform at sea at sea they'll meet each other the beauty of this part over here is that you will find that the image height will be exactly the same as the object height here it is the object is right at sea and not as the screen is right below it and again you can notice that the two have exactly the same size let's bring the object now even closer let's say we keep it between F and C somewhere over here well now if you draw the ray diagram we'll find that all the Rays of light is going to intersect or somewhere over here beyond C so image will be beyond C and it will be huge it will be humongous in size again let me show you that now the object is between F and C and where is the screen well now the screen has to be behind over here and again if we dim the light there it is look at that beautiful magnified inverted image that's just beautiful right and the closer you bring this farther the image will be and the bigger it will be eventually we can bring our object right at the principal focus right at the principal focus and now you will see that the two rays become exactly parallel to each other and result they will never meet each other which means you will never see an image there is no image anymore some people like to say there is no image is formed at infinity at infinitely far away so at the principal focus no image is formed but you know what we don't have to stop there we can go even further and bring this object between P and F somewhere over here well now the rays of light after reflection are being divergent they are going away from each other which means again there'll be no real image form you cannot capture this on a screen because it's not being focused however if you were to keep a giant eye somewhere over here you see your brain will tell you that these two rays of light are emanating from somewhere back over here so if we're to move this thing a little bit since the two rays are divergent it as it appears as if the two rays are appearing from somewhere over here that's what your brain will tell your brain is being fooled into thinking like this and as a result what will now happen is that you will see the image of this point at somewhere over here somewhere over there similarly if you take the image of this point it'll appear to be somewhere over here image of this point on the principal axis will be appearing to be somewhere over here and as a result your brain will tell you that these rays of light are emanating from back over here even though in reality they are not notice the rays of light are not really originating from this point they're actually originating from here that's what your brain will tell you and as a result even though it's not real image you can still see it so we call this as a virtual image you can think that one is that it's erect in nature notice it cannot be captured on the screen it's magnified that's another property it's magnified compared to this and it's called virtual because the rays of light are not really emanating from this point it just appears to be emanating from that point over there again we can see that notice over here now I have brought the object very close to the mirror inside the principal focus and as a result we will see first of all there is no screen the screen is no longer needed but now if we directly look into the mirror you can see a giant virtual image look at that see here you can clearly see the erect image it is no longer inverted and that's a giant image can be seen so concave mirrors can produce magnified virtual images and this is why they're used as shaving mirrors our makeup errors and as the object gets closer you'll find the image stays virtual it comes closer but little less magnified so this is the story of concave mirrors the key somebody over here would be something like this as long as the object is outside the principal focus the image will be real inside the principal focus it's virtual and closer the object it is to the principal focus bigger with the image P and I don't want to write this down because I don't want you to remember this all of this stuff can be worked out just by drawing ray diagrams so now let's quickly go ahead and do cases for convex mirrors here it is the only difference now is that this is the reflecting side and as a result we'll have to move our object on this side of the mirror somewhere over here and now to figure out what will happen where the image will be we're gonna do the exact same things so again would be a great idea to pause the video right now and try to do this yourself first all right let's draw one ray of light from the top of this which goes and hits the mirror parallel to the principal axis and we know what's going to happen this rate will not go through the focus like this it doesn't go into the mirror but it appears as if it's emerging from the focus so it's gonna get it's gonna go up this way and it's gonna appear as if it's gonna start from here so I'm gonna start this all the way from here let's do that appears to start from here and then one more ray of light we are going to shoot straight at the pole same thing exactly the same thing over here at the pole and this ray well this is the angle of incidence so the angle of reflection will be exactly the same so what we find after reflection the two rays are diverging away from each other which means no real image but if we kept our giant eye over here I'm not gonna keep that but you can imagine a giant eye then the brain will tell you that these two rays are emanating from somewhere over here it appears to be coming from somewhere over here another result you'll see the image of this over here you end up with a virtual image and the whole thing will be constructed like this and so you end up with a virtual image which is diminished in size and between the pole and the principal focus and what's something that you can confirm is regardless of where you keep this object you will always get a virtual diminished image when it comes to a convex mirrors since I didn't have a convex mirror I went to a parking lot and looked at the image of a parked truck look at the image of this parked truck carefully and you can see that the image of this truck is smaller in size and in fact because this is the images and the convex mirrors are smaller you can fit more of them and as a result you can see more in this mirror and that's why these mirrors are used usually in parking lots to see around the corners so the super duper final key summary of all of this is that don't ever remember any of these cases if you are ever tested in any of this all you have to do is draw ray diagrams and you can figure out all the properties of the images