And the focal length, let’s call it f. Pretty simple right? So let’s move this aside right now and let’s kind of take it up here and let’s see how we reason this whole thing out. And you’ll have plenty of examples where you understand how this is really useful. \right)}{\left( {{u}_{2}}-{{u}_{1}} \right)}\); If object is small, \(m=-\frac{dv}{du}={{\left( \frac{v}{u} And the other ray that’s going through the center of curvature is going to come back that way. In fact most of the countries in the world do it in the right side. focal length of the mirror and this formula is valid in all situations for all It can be artistic sometimes. So we found one particular set of similar triangles. So write it down in mathematical form that way and let’s now look again. Those two quantities are going to be equal. Lots of people can do things in many, many ways. All we can do is just take 2 rays, extend them, reflect them back and find out where the object image forms, from where the object forms. Because they have an opposite angle and they have right angles. {{m}_{s}}={{m}^{2}}=\frac{{{A}_{i}}}{{{A}_{o}}}\). And what is the origin? Two angles same for two triangles, what does that mean about those two triangles? Look around. That’s how it will be stored in your mind. \(m=\frac{I}{O}=-\frac{v}{u}=\frac{f}{f-u}=\frac{f-v}{f}\). Have to remember this mirror formula. Concave or convex. Or let us see what happens and where the image forms by our known method. But the first thing we need before we talk any math is to define something called a convention. What strikes you? From the origin, which is the pole of our mirror, everything else becomes very simple and it’s just this. Could we do that? And that’s the top part of our image, this is the bottom part, so that’s where the image is going to be. Object distance is the distance of the object from the pole of the mirror; denoted by the letter u. Now, at some length and the image might be at some other distance. Because the object is at some length from the mirror. We’re looking for something that relates to those quantities. What do we do? So that’s what we are going to do today, or in this couple of minutes that we’re going to spend. Pretty simple. So right and up – positive. Divide the whole thing, the entire equation by uvf. See most of us sit together and decide okay this is how we’ll do it. Now, we all know that there is a mirror. And what are those two triangles? So write that equation. Right? And if you have already been accustomed to what’s called the Cartesian coordinates, then we know something. Mirror formula gives the relationship between image distance, object distance and the focal length of the mirror and this formula is valid in all situations for all spherical mirrors for all positions of the object. It’s called the mirror formula. perpendicular to principle axis and then its areal magnification is: \({{m}_{s}}=\frac{Area\,of\,image\left( {{A}_{i}} Of course you’re going to use math and physics right? It would be pretty pissing off if we all wrote A’s in our own ways and then we had to translate stuff. Right, becomes a very simple thing. So once we’re done with these 3 we’ll see how they are related for mirrors. It’s very simple right now. If you know where the image is it will tell you where the object is. What are we connecting? All of us get together and say, okay fine. What do you know about those two triangles? Now write the same very similar equation for them and if that’s the object size this is also going to be equal to the object size. Magnification produced by a We can do the same thing just by using some math and let’s see what we can do. Draw a diagram and figure out. Because before this there was a pretty difficult convention where you measured this way in a particular manner, that way, no. So that for you is the mirror formula. Now there are some countries where they do it in the right side of the road. So now that we have the sign convention in place what do we do to use it? Second Formula for Magnification There is another formula of magnification Note : - If magnification (m) is positive , It means image formed is virtual and erect If magnification (m) is negative, It means image formed is real and inverted Questions Example 10.1 - A convex mirror used for rear-view on an automobile has a radius of curvature of 3.00 m. 1 by v, plus 1 by u equals 1 by f. Right? Pretty simple right? For make‐up and shaving mirrors the most common ratings are 3X, 5X, 7X and 10X. The sign convention for spherical mirrors follows a set of rules known as the “New Cartesian Sign Convention”, as mentioned below: a. All needed was a scale, maybe a pencil, protractor also not required right? Wouldn’t it be nice if we were able to do that? Range of Expressions using Trigonometric Substitution, AYUSH Counselling Schedule for NEET AIQ GOVT./ GOVT. That side by this side equals this side by that side. Just like that. d. All the distances parallel to the principal axis are measured from the pole (p) of the mirror. 3) For most users a 3X or a 5X mirror works very well. Great. Now till now what did we need? It could either be this way or it could be that way. We don’t want to use even pencil, scale, nothing. So let’s take, now you can watch there and you can see, I want you to notice that there are two triangles there that have a very special property. What we are going to do is figure out how exactly do we measure these lengths? c. The object is always placed on the left side of the mirror which implies that light falling from the object on the mirror is on the left-hand side. Two triangles that seem to be similar. \right)}^{2}}\). If I’ve given you a mirror, we found out if we keep an object somewhere, where is the image going to form? \right)}^{2}}={{\left( \frac{f}{f-u} \right)}^{2}}={{\left( \frac{f-v}{f} 4) Areal Magnification: If 2D – object is placed with its plane Now why we are doing this don’t ask me okay. And why do we need it? Anything down is negative, and anything up is positive. Take one ray, and draw, that’s right, the parallel ray is going to go through the focus. So now what we are going to do is just define some distances. Let’s say we all drive, we all in India have decided to drive on the left side of the road, right? its axial magnification is: \(m=\frac{I}{O}=\frac{-\left( {{v}_{2}}-{{v}_{1}} 2) Lateral Magnification: When an object is placed perpendicular to the So we all love formulas don’t we? We will all write A this way and not in some other way. As a demonstration of the effectiveness of the mirror equation and magnification equation, consider the following example problem and its solution. So that’s one of the things we’re going to do here right now. See all arguments in physics need not just be for utility, it can also sometimes be for beauty right? A mirror formula may be defined as the formula which gives the relationship between the distance of image v, distance of object u, and the focal length of a mirror. Left and down – negative. We’ve a very simple looking expression right now and divide the whole thing by a product. Example Problem #1 A 4.00-cm tall light bulb is placed a distance of 45.7 cm from a concave mirror having a focal length of 15.2 cm. We know u, we know v, we know f. How can we relate them? CBSE Previous Year Question Papers Class 10, CBSE Previous Year Question Papers Class 12, Lakhmir Singh Solutions For Class 8 Science, NCERT Solutions For Class 11 Business Studies, NCERT Solutions For Class 12 Business Studies, NCERT Solution For Class 12 Accountancy Part-1, NCERT Solution For Class 12 Accountancy Part-2, NCERT Solution For Class 12 Micro-economics, NCERT Solution For Class 12 Macro-economics, NCERT Solutions For Class 6 Social Science, NCERT Solutions For Class 7 Social Science, NCERT Solutions For Class 8 Social Science, NCERT Solutions For Class 9 Social Science, NCERT Solutions For Class 10 Social Science. It’s the place from which we start all out measurements. We’re going to understand what this mirror formula is. We’re going to drive something that’s very favorite you know, it’s pretty weird to most of the people who’ll ask you a few questions. So let’s see what happens now. What’s a convention? There’s one more there. 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