Concave mirrors

there is a famous building in London called the walkie-talkie building it's shaped like a walkie-talkie so it's called like that and it's famous for melting things and putting things on fire one of the story says that there was a driver parked his car on the road in front of this building somewhere and when he came back he saw that the side view the rear view mirror the side mirror was melted another story says that there was a doormat again somewhere in front of the mirror front of this building and again and it was found that it caught fire certainly and so many such incidents has happened and we're pretty sure it's caused by this so somehow this is setting things on fire in front of it so why does it do that well we will be able to answer this question satisfactorily at the end of this video now to answer this question we need to talk about curved mirrors and one of these curved mirrors are called concave mirrors and that's what we will do in this video we'll explore what these concave mirrors do we'll understand the properties and finally we'll be able to answer our question before we start with concave mirrors let's start it off we already know what we might already know you might have some experience with flat mirrors plane mirrors so imagine we have a plane mirror where the right hand side is the reflecting side and let's say we incident some rays of light let's incident a parallel ray of light so that parallel rays of light so that is easy to analyze what do you think will happen to these rays after reflection well you may have already studied the rules of reflection the angle of incidence always equals the angle of reflection so to use this we always draw in normal so let's draw the normal we draw a normal a normal is just a perpendicular that we draw at the point where the incident ray is hitting the mirror so we draw the normal grow the perpendicular and then the angle between the incident ray and the normal becomes the incident angle or the angle of incidence and that is zero over here everywhere and therefore from the rules of reflection even the angle of reflection must be zero because angle of incidence always equals angle of reflection which means the reflected ray will just go just retrace its path and so if you could see the reflected rays it would be somewhat like this it would have retraced its spot okay so this is something that we might have seen before now the important thing to note over here is that the incident rays were parallel and after reflection even the reflected rays are parallel to each other that is there is something to note over here okay now let's see in contrast what happens if we have a concave mirror so let's look at a concave mirror a concave mirror is a curved mirror and if you look at carefully you see it's the inner part that is reflecting since this inner part is sort of like a cave we call this mirror as a concave mirror you can think of a spoon and the part of the spoon that you use you know the stuff that you put inside the spoon the inner part that is the concave part of it all right so this is a concave mirror and so the question we want to think about is what's going to happen if we incident some rays of light on a concave mirror again let's incident parallel rays of light I like to draw pile rays because they're easy to analyze you can draw any rays actually but powder is they're pretty easy to analyze so let's draw them and so the question now is what would happen to these rays of light after reflection well we don't have any experience with curved mirrors so far but we know what happens to flat mirrors so I'll tell you what I like to do what we can do is we can wherever wherever the rays of light are hitting the mirror we zoom in over there we'll take a very tiny patch of that mirror and we'll assume it's flat okay so let me just show you what I mean so we'll do is so if I want to know what happens over here I'm just going to zoom in zoom in as much as possible as much as this software allows me to do it allows me to all right so here it is and I'm going to assume this to be a flat part of the mirror so let's say this is flat like this okay let's zoom back out and we can do the same thing everywhere else if I look at this over here this part over here I can pretty much assume it's a flat mirror isn't it this looks pretty much flat to us any curve you take and if you zoom enough on it if you take a very small patch of a curve you can approximate to be flat we do the same thing with earth also right earth is a curve but when you look at a small part of it it looks flat to us and the reason we are doing that is because if you think in terms of flat mirrors we know what to do we can draw normals and then we can figure out where the reflected light will go so let me go back here it is so we have three tiny flat mirrors and we can now draw normals I should have drawn normal so let me go back and draw now let's draw a normal over here so a normal is perpendicular to this so let's draw perpendicular to this it's not exact but you can sort of see now can you can you visualize what the angle of incidence is the angle of incidence is over here which means they're reflected so this is the incident ray so the reflected ray must go somewhat like this all right so let's do over here and see what happens over here again if you draw a normal normal is going to look like this the incident ray and the normal line that means the angle of incidence is zero so the reflected ray will just go back because the angle of reflection will also be zero and similarly we can do the same thing at the top and I want you to pause the video now and try to visualize this yourself can you visualize this and think where the reflected ray will go just pause and see alright let's do this again we'll draw a normal normal must be perpendicular to this surface so if it drop in normal this is what the normal looks like and here is the angle of incidence and so we can we can see the reflected ray to go somewhat like this again the angle of reflection must be the same as angle of incidence so if we zoom back out let's zoom out what do you see well notice that after reflection the rays of light are no longer parallel to each other but if we extend these rays of light and I have not drawn this properly but if I did draw it properly you would see let me just rub this a little bit okay if you had drawn this properly you would see that this Rays these three rays of light are actually actually going to meet at one single point all right and when the rays of light meet at a point we say that they are converging converging at a single point and after converging the rays of light will just continue on their paths which are not shown but what's important is that after reflection there is of lighter no longer paddle but they're converging to a single point and the beauty of this shape is that if you get this shape right we'll talk more about the shape in the future videos but if you get this shape right then we will see that even even if we draw more parallel rays of light and if you can do the same thing you will find out if you again zoom in and you draw normals and if you draw it carefully not like the way I've drawn it if you draw it carefully you will see even these reflected rays will converge to that same point and if we draw even more rays of light regardless of how many parallel rays of light you draw you will see all the rays of light will meet up at that single point and that point where the rays of light are being focused being concentrated we give a name to that point we call that as focus just a nice name it's called as the focus of this particular mirror all right so now we can go back to that initial question and see if we can answer it so if you look at this front face of this building you can sort of see through it right that's because it's made of glass and it's important to understand is glass can reflect light not all of light not like a mirror it can reflect some of it but but since we're dealing with such a giant piece of glass even some small amount of light that it reflects becomes significant okay and and so so basically this is this is acting like some kind of a reflector and more importantly look at the shape of the building it's not flat if you look at it carefully you see it is curved inwards look at this curve look at this curve it's inwards so it's acting like a concave mirror and that's why when you when you have sunlight okay let me just draw when sunlight hits that particular glass face or the front face of the building the rays of light from the Sun are pretty paddle and we'll talk a little bit about that don't worry we'll talk about that but anyways after reflection just like what happens here all these rails get focused at a single point and of course of course it turns out that this point of focus really depends on I mean the location of this focus really depends on at what angle these rays of light are coming in all of that let's not worry about that what's important is it does get focused on a single point and at some particular part of the day that that look that focal point lies on the road and so if you've parked anything at that location then all the sunlight is being concentrated I mean all the light that has been hitting this particular glass piece most of its getting concentrated at one single point producing a very high intensity spot over here and that is enough producing a lot of temperature and increases the temperature producing a lot of heat and that's why things are getting melted and what's mind-boggling for me is that notice that this is pretty flat it's not all that curved but it is curved even that small curvature is enough to focus that sunlight and caused enough problems that's pretty amazing okay before I wind up we just want to show you one thing why did I say that the rays of light from the Sun are parallel to each other that's all I want to show you so let me quickly go to another screen let's say we have a tiny bulb which is giving out light in all the directions and what we'll do is we'll dim this light let's dim that light and now let's keep a mirror in front of this let's say it's a concave mirror itself and we only concentrate on the rays of light that are hitting or there are being collected by the mirror now notice when the mirror is close to the bulb right now the rays of light that are hitting the mirror are pretty much trying to go away from each other you can pretty much see that however if we take that same mirror and we keep it far away from the bulb now notice if you were to look at these two rays of light and you forget about everything else you just concentrate on those two rays of light which are hitting the mirror mm-hmm yeah if you only look at these two rays don't they look pretty much parallel to each other even though these rays are actually originating from the same point so long story short what's happening is when we keep our mirror close to the bulb or close to the source the rays of light don't look paddle but when you keep it far away and what do we mean by far away far away means the distance between the mirror and the source must be much larger compared to the size of the mirror that's the whole idea I hope you'll agree that if the size of the mirror was large then a lot of rays would hit and then again the rays will not be paddled but if the size of the mirror is much smaller than the distance then there is a flatter paddle and if this was the Sun then earth would be extremely tiny it would be pretty much a dot over here and so since the size of the earth is much smaller than the distance between the Earth and the Sun or the source we can pretty much very nicely assume that the rays of light from the Sun is parallel when it comes and hits the earth all right so now let's let's go back so to quickly summarize what we learned over here is that when you take a mirror and you curve it in such a way that the inside part is reflecting we call it as a concave mirror and what do concave mirrors do well we so logically that they can focus a parallel beam of light to a single point and it concentrates that light and we call that point as the focus and that's why the walkie talkie tower which acts like a concave mirror ends up burning things when you keep things at the focus of that particular of the particular building