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Current time:0:00Total duration:10:10

Video transcript

let's explore sign convention in this video basically we're going to talk about the rules that we're going to use to apply positive and negative signs to measurements now you may be having a lot of questions in your mind as in what measurements are we talking about why are we applying science certainly all of a sudden and where are we going to use them so what we'll do is you'll first look at what the rules are let me look at some of the examples and then hopefully it'll kind of sort of make sense why are we talking about it and where it's going to be useful and one last thing before we begin although in this video we only want to talk about mirrors if you are watching this video while studying about lenses then the same rules are gonna be applied even for lenses as well just wanted to clear that out and by the way if you are not studying lenses or you haven't studied them yet don't worry about it so let's start with the rules and to understand these rules let's take one example let's say we have a concave mirror with us and by the way this is called as a concave mirror because the reflecting side is forming a cave so what are the rules now rule number one is that all the distances are measured from the pole recall what polis pole is the center of this mirror now when I say all distances honestly there are only three distances one is the focal length how far the focus is then object distance how far the object is and the image distance how far the images all the three distances are measured always from the pole that's rule number one which I will not write down now rule number two is when you measure these distances these distances can be measured either in front of the mirror or it can be measured behind the mirror to give you an example images sometimes the images will be formed in front of the mirror and you may have seen that sometimes it can be formed behind the mirror so to differentiate between the two distances we're going to call one of this measurement as positive and the other measurement is negative so the second rule is to figure out which distances should recall positive all right and let me write this down the rule is we always choose incident direction as positive incident Direction is always chosen as positive so what do we mean by this well if we come back over here not is that because this is the reflecting side over here the incident light will always be to the right side because you know you would keep an object over here notice where the incident ray would be incident ray if you were to draw an e would always be to the right and so since incident direction is positive in this example right side is positive and what do we mean by right side a right side of the pole because all measurements are done from the pole so any measurement which is towards the right side of the pole in this particular example will be positive measurement and any measurement which will do to the left side of the pole would be negative measurement so to take an example imagine we are given the focal length of this mirror as 2 centimeters everything is in centimeters let's say there's an object kept at 3.5 centimeters from the pole and let's say once we draw ray diagrams we figure out that the image is formed at 5 centimeters from the pole these numbers may not be accurate I don't know but just take an example now let's assign science to them that's not with the object distance notice that the object is lying on the negative side therefore this object distance would be negative similarly look at the focus the focus lies on the negative side of the pole therefore this focal length would be negative similarly look at the image the image lies also on the negative side so here the image distance would be negative all right let's take one more example and it would be great if you could pause the video and see if you can try this yourself so just pause the video and apply science to these three distances remember incident Direction is always chosen as positive all right so insulin Direction is taken as positive over here this is the reflecting side and our object is over here so the incident rays will be towards the left therefore you start from the pole and all the measurements to the left are considered as positive this time does that make sense because we are choosing because our incident ray is to the left and all the measurements to the right side now will be negative and so the object is on the negative side so it'll get a minus sign the focal length however notice is on the positive side the focus is on the positive side so this focal length is positive and similarly if you look at the image it's on the positive side so that image distance would be positive all right now there's one more rule and that rule has something to do with Heights sometimes when you consider objects and images the heights will be above the principal axis and sometimes the heights will be below the principal axis again you differentiate between them we're gonna call as 1 1 of them as positive the other one as negative so again the rule that we're gonna fall over here is you're gonna choose above principal axis or electricity I'd like to just say up is positive all right so if there's any height which is above the principal axis we'll call it as a positive height and if there's any height below the principal axis we'll call it as a negative height so if we knew the height of this object I don't know maybe say the height of this object was 5 centimeters then that would be a positive height all right and whatever is the height of this image that would be a negative height I'm pretty sure how is here you can understand this since this object height is above the principal axis it would be a positive height whatever the height is and look at the image again the height is above the principal axis this would be a positive height as well and that's it for sign conventions so we have three rules all the distances are measured from the pole then you start from the pole and you go in the incident direction that's chosen as positive and when it comes to Heights any height above the principal axis is chosen as positive and by the way this rule is your honor name this particular convention that we are following it's called as the Cartesian sign convention Cartesian signs and the word Cartesian might remind you of a graph and the reason behind it is because that's what we do in graphs as well right in graphs we start from the origin and we choose the right side usually as positive left side as negative upwards as positive downwards is negative that's basically what we're doing over here as well we are treating the pole as the origin because you're measuring all the distances from the pole and instead of choosing right side as positive the only difference is you are choosing incident direction as positive that's it but pretty much everything else is the same as graph that's why it's called the Cartesian signs now one small thing is that in some textbooks they follow this a little differently it's pretty much the same so the only different thing that they would do is while drawing the diagrams they will always make sure that the incident direction is drawn to the right okay they'll always make sure this is true then automatically the right side will always be positive all right for example they would recommend never to draw like this because over here incident Direction is to the left they'll always recommend you make sure that your object lies on the left side of the mirror so we have to flip this whole image so basically they say that you know you always draw in such a way that the incident direction is to the right all right and then we can always choose right side as positive which is what we do usually in any graph so it's more aligned to the graphical system okay and you can follow that obviously but in general what I like to remember is you draw however you want just take incident direction as positive so anything you can follow it's pretty much the same thing so the last thing we'll talk about is why do we even consider science and for that let's take an example where we have already done this before so an example of things falling under gravity you may recall that whenever things are falling under gravity usually when an object is falling down we would say it's velocity is negative and when it's going upwards you'd say it's velocity is positive if we didn't use that sign we might have to explicitly say in English that velocity is downwards and velocity is upwards but we don't like that we want to reduce English and use maths as much as possible so science tell us what direction the ball is traveling mathematically and the idea were here is exactly the same without science we have to explicitly mention we're dealing with a concave mirror or a convex mirror or the images in front of the mirror or the images behind the mirror but with science these these things are done mathematically for example if I just say negative focal length it automatically means it's a concave mirror positive focal length convex mirror if I say the object distance or that say the image distance is negative automatically it means it's in front of the mirror it's positive automatically it means it's behind the mirror so long story short science help us differentiate between the directions in which we are doing the measurement mathematically