Convex mirror & applications

if you take a look at the side view mirror the rear view mirror of a car or a bike and if you touch its surface you'll find that it is not a flat mirror its bulged out a little bit it's curved why is it a curved mirror why don't we use just a normal regular flat mirror over there and why are the objects in the mirror closer than they appear we're going to answer these questions satisfactorily in this particular video so to understand or to answer this the secret lies in understanding curved mirrors now before we begin we've already seen in a previous video one kind of curved mirror a mirror in which the inner part is reflecting and we call such a mirror as a concave mirror and we saw what it does we saw that if you were to incident paddle beam of light or paddle rays of light and they all from after reflection get concentrated a single point called as the focus so a concave mirror can converge a beam of light but this time we're gonna talk about what will happen if you were to make the outer surface reflecting that's the focus of this video what happens if you make the outer surface reflecting so let's do that let's get rid of these rays and let's make the outer surface reflecting so when the outer surface becomes reflecting now the reflecting part is bulged out can you see before the reflecting parts are over here the reflecting part was big forming a cave so this was called as a concave mirror but since now the reflecting part is bulged out we call it as a convex mirror the word vex literally means bulging out all right so the question now is what does a convex mirror do that's what we want to figure out and again we will do the same thing what we did earlier we will shoot parallel rays of light onto this mirror and we'll use rules of reflection and see what happens to these parallel rays of light after reflection all right so let's do that let's incident parallel rays of light let's do that so here they are rays of light and which was parallel rays because they are easy to analyze it's easy to understand what you're concave or convex mirror is doing if we choose parallel rays of light you can choose whatever is you want the physics remains the same but it's easier for parallel rays all right so how do we figure out what happens to the rays of light after reflection well the trick is we zoom in at every point of incidence we zoom in so much and we only concentrate on the tiny patch we assume that tiny patch to be flat and why do we do that because we know how to deal with flat mirrors we draw a normal then we use the rule of reflection and then we figure out where the reflected light is all right so what I want you to do is pause the video and see if you can try this yourself just draw a rough sketch and just see if you can drop normals at every point and try to you know sort of get a rough idea of what the reflected light looks like all right let's do that let me do that over here okay so I'm gonna do it for a couple of places and then I'll just show you what it looks like so let's zoom in somewhere over here let's go here so if i zoom in at this point okay at this point over here notice that this I can approximate this to be a flat mirror like this okay and once I know the flat mirror is like that the next thing I do is drop a normal in fact if you have done this in previous videos as well so if this is not super clear to you you can just go back and watch that video where we did that but anyways we're gonna do the same thing over here so here is the angle of incidence because this is the incident ray and so the reflected ray will go like this how do I know it goes like that because the incident angle must be the same as the reflected angle I should remain like this all right let me do that one more place somewhere over here let's do over here let's zoom in okay now if I consider it over here the flat mirror looks somewhat like this oriented this way isn't it again I'm gonna drop in normal a normal means just remember it's a perpendicular that we draw and now we have this as the angle of incidence so the reflected ray will make sure that the reflected angle should also remain the same all right let's zoom back out let's go back to the original view let me just zoom out over here and that's what it looks like all right and this is not very accurate because they're not used rulers or whatever but I've done an accurate picture so let me just show you what it looks like for all these places so highly encourage you to first try it yourself place it all in do it at all places and try it yourself if you've done it let me show you what it looks like what it looks like for everywhere slice over here here it is this is what it looks like and if you notice you can see that after reflection the rays of light are no longer parallel they're all going away from each other which means your convex mirror diverges rays of light after reflection that's the property of a convex mirror and in contrast just to remind you in contrast when we were dealing with a concave mirror what was happening a concave mirror I'm just gonna show you this way over here a concave mirror converges a beam of light to a single point but a convex mirror diverges a beam of light and you know what's interesting interesting is if you were to back-trace these I mean if you were to extend these rays of light let me just do that if you extend these rays of light then these rays of light appear to start from that same point focus that we defined earlier and so even for a convex mirror we can define a focus for a convex mirror the focus is a point from there the rays of light appear to diverge from okay it's not really diverging from that point but it appears to do that and and when we define it when the incident rays are parallel to each other so in short a convex mirror as you if we saw a convex mirror diverges a parallel beam of light appearing to be from a single point focus and a concave mirror converges that parallel beam of light to a single point so convex mirrors can diverge rays of light excellent but what's the application of this where can we use this I mean I can't think of a you know a direct application of divergence of rays of light I mean we use that well there is an application and to understand that we need to remember something about these ray diagrams remember that these rays are reversible meaning we can just reverse the arrow marks we can make the reflected rays the incident ray and then the incident ray becomes the reflected ray why is it reversible well because the rules of reflection still hold true I mean let's concentrate on this ray if we were to reverse this this becomes the incident ray this becomes the reflected ray and we and we can draw in normal somewhere over here and when we reverse this the incident angle becomes the reflected angle and the reflected angle becomes the incident angle but they're still equal to each other the rule of reflection still is valid isn't it and that's why even if I were to reverse this race let's do that let me just do that here even if I were to reverse these rays of light rules of reflection still is valid which means this is also a valid diagram and this will help us understand what's the application of this let me just make this a little bit smaller all right in this reverse ray diagram what you can see is that rays of light from various wide angles can be reflected towards you what I mean is say you are standing somewhere over here this is this is uh this is the top view of a head okay I have drawn specs over here drawing eyes was a little difficult anyways imagine you were standing in front of this mirror and let's say there was there's something over here there's some tree over here and there is some bike over there or something like that now what's important to understand is that the rays of light from this tree and the bike after reflection can come straight towards you which means just by moving a little bit you can see a lot of stuff at a much wider angle that's behind you compared to what you can see with a plane mirror so if you had a plane mirror let me draw that over here if you're a plane mirror and if you have that same ray of light I'm drawing the same Ray over here notice it would have gone down after reflection because it would have missed you as a result it would have missed you but because we have a convex mirror you can see a lot of stuff behind you so in other words we can it gives you a wider field of view you can see what's behind you at a much wider angle then what a plain mirror allows you to do and you can actually see that in this photo that I took this is a convex mirror it's bulged out the mirror is curved like this it's a convex this mirror was kept near a parking lot somewhere over here and notice when you look into it you can see it a much wider angle you can see pretty much at this end of the road you can also see pretty much at this end of this end of the road this is almost a 90 degree 90 degree angle and you can see all of it over here sure it looks a little destroyed but you can see it and so if you were to come from this side even if you're riding in a vehicle from this side you can just look into a mirror in this convex mirror and you can also see what's on this side and so based on that you can avoid collisions and other stuff that's why these mirrors are pretty important they're almost there there are there install a lot in these parking lots and now we can answer our original question it's for the same reason the sideview mirrors of vehicles are also curved they are convex same reason so that when you look into it you can see a little bit wider you can you can see what's what's there behind you at a little wider angle then if you had a plain mirror over here I just like to end this video now with one last thing why are the objects in the mirror closer than they appear this is really interesting so think about this if you come back over here let's look at this picture if this was a flat mirror of say the same area imagine you had a flat mirror of pretty much the same area I hope you agree now that inside in that mirror we won't be able to see as much as we can see over here we just discussed that isn't it which means a convex mirror can fit more things compared to what a flat mirror can fit in that same area correct but in order to fit more things the things have to become smaller think about it if you want to fit more things in that same area shouldn't they all become smaller right so things in a convex mirror images in a convex mirror look much smaller than in a plane mirror and of course we look at this in great detail in the future videos but as of now hopefully from this reasoning you can understand that things in a convex mirror or images in a convex mirror are always smaller than in a plane mirror but we don't have an experience with convex mirrors we have experience with plane mirrors and so when we look into these convex mirrors and we look at these small images our brain automatically thinks that these are far away because only when things are far away they look very tiny and that's why we feel that these things are pretty far away from us for example it looks like this truck is far away from this mirror isn't it but it's not it's not really that far away and that's why there's always a reminder over here to tell you that the objects in the mirror are actually closer than they appear they appear to be far away because they are smaller and therefore there's a good chance that we might do a misjudgment over there we might take a sudden right turn thinking that these these vehicles are far away and therefore there's always a reminder to make sure that we take into the accounts this is pretty important when we are driving and so to quickly summarize then you have a curved mirror where outer surface is reflecting we call that as a convex mirror VEX means it's bulged out the reflecting surface is bulged out and if you insert in power parallel rays of light on this mirror then they diverges so convex mirrors end up diverging rays of light and their major application is in the fact that they give a much wider field of view when you look into it