 We will start the physics. This class would be regarding the chapter in your book which is light reflection and refraction and we will be discussing all important aspects of the topic. Considering that I have selected a good amount of questions in the presentation which I will be giving you later in the class, later after the class and during the class we will focus both on theoretical aspect of the topic and also on the numerical aspects. From numerical I don't only mean questions based on the quantitative ability, there are questions based on your theoretical knowledge also. So we will be discussing this topic in holistic manner with respect to or if I compare it with your grade 10 examination and if I look at this topic properly, if I give you a little bit of hint about what kind of questions that you get here from this topic, it is varied in nature because there are different formulas. So you get formula based questions and there is extensive theoretical part also involved in this topic. So mostly you get questions on the nature and size of image. So you will be given either of the two mirrors or either of the two lenses and you will have to find out a distance would be given to you and you will have to find out what kind of image would be found and you will have to specify with suitable diagram that nature and size of the image. That is one kind of question. Second kind of question is which more or less comes most of the time is that prism what is angle of deflection and then or you can get questions from rectangular slab and you will have to find out what is the deflection and what is the deviation and all those things. The easier questions are directly asked like what are the different laws of reflection and laws of refraction and then probably you will get questions. You can get questions from what do you say from numerical type of questions. So which are basically based on different formulas that we will be studying and deriving. See one very important part of the question of this topic is that none of the derivations are asked. I have not seen any time that derivation is asked but you have to understand that from where the formula is coming. So if time permits I would definitely like to get into a derivation of different topics different formulas and depending on that we will be taking numericals. So I think most of you have joined. There are a lot of people to join now also but I don't bother. Now they can join when they want and let me share the screen with you and then probably we can I hope you can see the screen now and here we go. So welcome again to this session on light reflection and refraction and we would be discussing this topic for next two hours. It's a comprehensive session for this particular chapter if you focus on this chapter now in next two hours properly I don't think any other revision would be needed. So this particular session would help you out to get full marks in all the questions which will be appearing in your examination coming February or March whenever the science paper that you are writing. So I would be starting with characteristics of light and if you look at this particular topic see this kind of question so my basic objective in discussing these this topic would be that what kind of question can arise from any particular subtopic that I'm discussing. So if I'm discussing this topic which is characteristics of light you there would be direct question that right to two properties of light or three properties of light or something like that and that kind of questions would not be more than one mark. So don't expect anything else from this particular subtopic. So there are different characteristics of light that we know first and the foremost which is most important is that it is an electromagnetic wave. The second one is it does not require medium from propagation. So when the light rays starts a journey from Sun to Earth in between in across the atmosphere there are different places where or across that journey there are different places where vacuum is also there and some kind of atmosphere is also there. So if it travels through all kind of I mean all kind of mediums even if no medium is there it travels through it. What is the speed? Speed in air or speed in vacuum is 3 into 10 to the power 8 meter per second. This is this we will understand the speed of light in different mediums in refraction we will understand this more properly till now we need to understand that speed of light is different in different mediums. So you will have speed of light that is why I have mentioned here speed in vacuum speed of light in air in water sorry in water in glass it will change and it will reduce. So if light goes to denser medium its speed reduces that's what I will tell till now then I'll explain it in the refraction part then colour of light is determined by wavelength so we know that a white light is made of Vibhgur seven different colours and it is determined by lambda so lambda increases from V2R that we need to understand and colour of light will be determined by the wavelength light travels always in a straight line if change in medium light doesn't change frequency this is very very important while speed and wavelength will change and speed of every colour light is different in different medium except vacuum. So what we need to understand from this point is that all these colours Vibhgur their individual speeds would be different in different colour in different mediums so when you will see when how this can be determined I have slide ahead for this if a white light is shown on a prism and it is refracted on the two different surfaces of the prism triangular prism and if you see the refracted rays you will see difference all seven different colours emerging out of this prism so this particular experimentation shows that the speed of the light is of different colours of light is different in different medium and in vacuum there's travel with same speed so this is the case or these are the properties these are the important properties these are not the only properties of light but these are the important characteristics of light that I wanted to discuss if you have to write any three you write these three or you write first second and and this travels in straight line don't make it complicated so these three points will do anywhere and that will fetch you a good enough marks so this is let's move to next slide and the next next slide is different type of beams so actually we study light in different manners so a combination of different light rays if they are parallel to each other they are called parallel beam if from a point source the light rays are emerging out of it they are called divergent and if they are trying to finish at one particular point merge at one particular point they are known as convergent beam now the question is that what happens when the light beam or any light from any particular source strikes with an object so if light from any particular source strike with an object there are three possibilities which which can happen and these three possibilities are it can be absorbed by the medium so if if light rays falls on a wall or on a wooden plank the wooden plank will absorb the light or it can be reflected what do you mean by reflect reflected reflected it doesn't mean anything else apart from it getting thrown back from the object so if it strikes it comes back directly from or it it is thrown back from this particular surface and the third one is refraction refraction does refraction is a part of process in which light goes from one medium to another medium so this second medium if light is going from one medium to another medium here in case of wooden plank if the light is going from air to the wooden plank wooden plank is absorbing it absorption means it doesn't let light particles or come out of its another surface so if wooden plank is this thick and if the light is coming from here the light rays will never appear on this side it will get absorbed inside this wooden plank the refraction is completely opposite the other medium will allow this light ray to travel through it completely and if it comes if there is another surface something like this it will come out like this and you will see that the light rays which is passing through or which is striking its top surface is coming out of the bottom surface it may be with a different speed inside this medium but the light surface will definitely come out so refraction means nothing but light ray traveling from one medium to another medium that's the meaning of refraction and reflection means getting thrown back to the same medium so I am writing here this is thrown back to same medium so here we discuss about only one medium in case of reflection and here it is it passes from one medium to another so this is what do you say this is about reflection refraction absorption of light when it falls on any particular object now let's move to something called lodge of reflection so as we know that reflection means bouncing back of light to same medium once it strikes the object or this object is called reflecting surface so I have written here reflecting surface what is the parameter of light getting reflected so it's generally it it generally gets reflected from glass objects and one of them is glass objects and it is mandatory that this glass object is you can say for reflection it is necessary that this glass object is painted on one side or silvered on one side so that it cannot pass through the glass so if we have a plane mirror for that matter if I draw a plane mirror over here and if you look at it from the perspective of reflection so I draw here I polish it here on the other side now what will happen if there is a light ray or if I am standing here if this is me standing in front of the object if I am standing here something like this and I want to know that how my image would be formed what is the process behind it to know this process or to apply the concept of reflection here it is important that we know lodge of reflection so the first law of reflection tells me that the incident ray incident ray is the ray which is coming from the object reflected ray reflected ray means when the incident ray will strike this mirror it will this mirror will reflect this particular incident ray and after bouncing back whichever ray is getting bounced back the rays which are getting bounced back are known as reflected ray and then normal to the tangent normal to the surface so if I draw normal here to this surface all these three this incident ray this reflected ray and normal to the surface they are in same frame and the most important point over here is that angle of incidence would be equal to angle of reflection so what is angle of incidence if I define angle of incidence angle of incidence is nothing but angle between the incidence ray and normal to reflecting surface point of incidence this is it so this is angle of incidence this is denoted by the small letter i angle of refraction is instead of incidence ray this changes to reflected ray so you look at here this is my reflecting surface the incidence ray falls here I draw this perpendicular line which is normal to the surface at the point of incidence the angle between this normal and the incidence rate theta 1 is angle of incidence so theta 1 is equal to i here and the angle between reflected ray and to the normal of surface theta 2 is nothing but angle of reflection so this is denoted by small letter r so i is angle of incidence r is angle of reflection and both of them are equal in case of reflection so this is one thing you need to understand now sometimes there may be a question which asks you that draw the diagram of reflection through a plane mirror so what how do you draw it so I want to show you this you draw this plane mirror and from this plane mirror you you you put this line this line is a sign that you have painted it on the other side then you draw your object your object suppose is something like this so you have drawn your object from the object what you will do is is you will draw a perpendicular to the surface here suppose a ray goes like this so if a ray goes like this try to understand what would be angle of incidence so i here would be zero why i would be zero because incidence ray is also making 90 degree with the surface and normal will also make 90 degree with the with the surface so if you look at here if the incidence ray is along to the normal to the reflecting surface then the theta one becomes what zero this side will go and match with this so here i is zero if i is zero then r would also be zero r zero means it will come back in the same direction so I just draw these line like this and I will draw one more line like this which is normal to the surface which is parallel to this now my incidence ray would be something like this this is my incidence ray this is not at 90 degree i this angle is suppose i so now I will have angle of reflection equal to angle of incidence so this angle will also be i so I'm writing i is equal to r now whenever you are making an image please listen to this point very carefully very very important point whenever you make any particular image we need at least two incidence rays and with respect to those two incidence rays I need two reflected rays so wherever those two reflected rays would be cutting each other at that particular point I will have my image so this ray will go here somewhere here it will cut here and if I draw this this will come like this so my image would be somewhere here now what would be height of my image if this image is h and if the height of the object is h suppose this is a this is b and this is c this is d this is e and this is h dash now we need to understand that if this is r this is also r because they are opposite angles and i is equal to r this is 90 degree this is also 90 degree so all three angles are same if all angles are same then we know that the triangle would be what then we can prove that the time triangle is similar and if there's sorry the triangle is congruent and if they are congruent angle opposite sorry side opposite to equal angles would be equal so i and r are equal opposite to them the sides are a b and d so their lengths would be equal so h would be equal to h dash so that is your calculation here so if you understand this now let's move to because reflection is not only related to plane mirrors reflection is also related to spherical mirrors so if it is related to spherical mirror let's understand what is spherical mirror and then we will move to image formation by spherical mirrors so see here spherical mirrors as you can see here there are two kinds of a spherical mirror one is concave one is concave there is some kind of noise can we stop that thank you so there is some there are two kinds of concave spherical mirror one is concave which is this what do you mean by concave painted on the cave side or painted on the other side if the name is yes so there's a doubt in the comment box okay i'll clarify it what is the doubt sir it's asked by shreyas if for a brief description of for brief discussion of diffraction so i'm coming to those topics later this this class is only for reflection and refraction so those topics would be covered later so this is only for reflection and refraction so those things would be covered don't worry about it in different class so what i'm trying to say over here is that the names of mirror are kept looking at where the reflection is happening if reflection if the incidence rays are falling on the cave side of the spherical mirror what do you mean by spherical means these glasses have been taken from a sphere if a sphere is something like this and i take out a part of this particular sphere and then paint it on one side it converts into a spherical mirror so if the painting is done on non cave side it so it means that you are leaving the cave side for the reflection and that if the cave side is left for the reflection it means that if the light incident ray falls on the cave side it is concave mirror and if it falls on the other side if the cave side has been polished then it means that it is a convex mirror now what are the different important terms so different important terms of any particular mirror is first one is aperture so the aperture over aperture is nothing but i'm writing here please if you want to write with me write it down aperture means portion available for reflection so first one is portion available for reflection so if you look at here the portion available for reflection is mpn so it is nothing but mpn so this is it the second one is pole pole is nothing but geometric surface sorry geometric center of reflecting surface second one is center of so here what is the pole pole here is p so if you look at the reflecting surface the midpoint of it which is the geometric center is denoted by p now the third one is center of curvature what is center of curvature center of the sphere of which the mirror is a part so could you define aperture properly aperture is the portion available for reflection so if this is the mirror what portion is available from this point to this point this is the complete portion available for reflection so this particular portion is known as aperture so aperture of this spherical mirror is suppose this point is m and this point is n so this this complete peripheral mn is known as aperture is it fine did you understand yes sir okay center of curvature is nothing but center of sphere from which mirror has been taken so if mirror has been if the sphere is something like this and mirror is a part of it at and its center is over here so this particular point c which is the center of the sphere from which this mirror has been taken out is known as center of curvature then there is something called principal axis principal axis is nothing but a line joining the center of curvature and the pole so this line pc is known as principal axis then we have radius of curvature so length of pc is nothing but because p is a point on the circumference of the sphere and and c or or on the surface of the sphere and c is center of the sphere so distance between the distance between two points or distance between center and any point on the surface of the sphere would be radius so which is pc in this case so pc is nothing but radius of the curvature and what is principal focus so principal focus is very very important and look at here that's why i have taken this diagram to explain you what is principal focus principal focus is nothing but if the lights are or or there are parallel beams so you see here both for the case of concave mirror this is your concave mirror and this is your convex mirror both for the case of concave and convex mirror there i have taken combination of parallel beams now wherever after reflection wherever these reflected rays of incident parallel beams wherever they meet each other that particular point is known as principal focus so the parallel beams i can write that the parallel beam beams after reflection converges in case of con concave mirror here see they are converging or diverges in case of convex mirror at one particular point one point that particular point is known as focal point now what is focal length so distance between and and focal point is denoted by f capital f so distance between pole and focal point is known as focal length and it is denoted by small f now try to understand whenever you are measuring distance from the lens all the distances are taken along the principal axis from the pole so the initial point or from or or the reference point with which i measure all the distance is the pole of the spherical mirror so if i have to calculate the center of curvature it would be pc if i have to calculate focal length it will be pf so all the distances are measured from the point p this is a very important point here that you should be noticing now so this is how different terms related to a spherical mirror is defined i hope you understand these things the next point is cartesian sign and then i'll go for rules for constructing images so i'll tell you what are the different rules for constructing images first let's understand the cartesian sign of convention so whenever you want to find out that if i keep an object in front of any kind of mirror what kind of image would be found you need to place the object on the left hand side of the mirror so the object is always placed to the left left left side of left of the mirror this implies that the light from the object falls on the mirror from the left hand side second thing the distances parallel to principal axis are measured from the pole of the mirror which i was just discussing all the distances measured to the right of the origin are taken positive while those measured to the left of the origin are taken negative so what do you mean by positive x-axis and positive negative x-axis this pole is actually origin because you are calculating or you are measuring all the distances from here and this pole is considered to be origin if you go towards the right hand side of the pole so that particular thing is positive that distance is positive if you go on the left hand side of the pole that is negative there is another way to define it if i am keeping an object on the left hand side and the incidence ray would be falling like this so you can always see that the distances measured in the direction of the incidence ray i am writing here the distances measured in the direction of incident ray is positive and opposite to it is negative so if you are going in this direction it means that you are going in the opposite direction to the direction of incidence ray hence in this direction look at the arrow in this direction the distances would be negative if you are going in this direction you are going in the direction of the incidence ray hence the distances measured would be positive so actually point three and the point which i have written on on on the board is actually same one and the same so question number and why i discussed because in most of the books that you will be studying what i have told is given and not not exactly what you are studying here distances measured perpendicular to the uh uh to and above the principal axis so you know that if this is x axis this would be positive y and this would be negative y and this is just convention so by convention it is it is like this so this is positive above exact above the principal axis below the principal axis this is negative then uh uh distances measured perpendicular and below to the y axis is taken as along the y axis is taken as negative so this is this particular thing if if a question asks you that what is the Cartesian sign convention for reflection you need to write these five points these are the five extent five points extensive so you don't need to write anything else if you write these five points you get get your marks fully now what are the difference different rules for constructing images so i have told you that for construction of image two reflected rays are required in case of refraction when we will be studying refraction two refracted rays would be required here we are studying reflection so two reflected rays would be required at least now if i need at least two reflected rays it means that i need to have two incident rays which incident ray there can be infinite incident rays which would be falling on the reflecting surface which incidence ray out of those infinite rays to be selected so that my image construction is is easy and it it it does not create any problem for me uh it's very very simple and what is it try to understand the first rule is if if the light ray passes through the center of curvature this is the first one through the center of curvature then there is no reflection sorry there is no deviation it gets reflected in the same direction or in in direction opposite to the incidence ray so try to understand if this is my center of curvature what happens we understand that radius is always perpendicular to any particular point on the surface so if i draw this line from this center of curvature it means that this is 90 degree so if a light ray is coming in this direction it means that the angle between the light ray and the normal to the point of incidence is actually zero so i is equal to zero if i is equal to zero r is zero r is zero means it will get reflect reflected in opposite direction exactly opposite direction to the incidence ray so it means that there would be no deviation it it will be coming in the direction going in or deviation of 180 degree you can say so you will not be able to separate out uh the two rays and second thing is second thing is that any ray parallel to the principal axis after reflection we know that if light beam is parallel after reflection it converges or diverges on focal point so it will get converged or diverged on the focal point the third one is that any particular light ray passing through the focal length after reflection will become parallel to the principal axis so this is nothing but actually the same thing that if if it is going in this direction the reflected ray would be like this if incidence ray is like this then the reflected ray would be parallel to the principal axis why because i is equal to r so it has to prove it's this is nothing but principle of reversibility that i would be discussing in the next slides so these are the three different rules which we would be taking care of or or with the help of these three rules we will be finding out what kind of images would be formed depending on different distances of the object from the spherical mirrors so let's finish those things off here are six conditions so in these six conditions i have taken both uh the position of the object if the position of the object is infinite what does it tell you if the position of the object is infinite all the rays falling on the reflected ray would act like a parallel beam and if it acts like a parallel beam it will get uh converged on the focal length so it it is getting converged on the focal length so you look at here the size of the object would be highly diminished it means that it will be a point it will be real and inverted then if it is beyond c you look at here condition b so beyond c means between infinite and c so i am drawing these two lines one is going here passing through parallel uh uh focal length uh focal point and and one going through center of curvature so then returning again 180 degree here the image formed you look at here is nothing but diminished real and inverted if you go through all these points if it is at c the image would be formed at c only and real and inverted and of same size if it is between c and f look at here so image would be real inverted but the height of the image would be more than the height of the object this is called condition of enlarged image again if it is at f so i know that uh if uh any particular light ray passes through f after reflection it becomes parallel to the principal axis and hence they all you look at here they are all uh going through f something like this center of curvature and they never meet each other so highly enlarged they meet at infinite real and inverted if any particular object is kept between the uh pole and the focal point then the virtual what do you mean by virtual image virtual image means the reflected ray does not mean actually they appear to meet at certain point they in in reality they never meet each other so real image means remember this real image means reflected or refracted rays meet at points in reality virtual image means they don't meet in reality but appear to meet at one point so this is it so these are the different conditions in which you will have to find out now this particular slide is very very important these six points i can make you sure that these six uh points and the upcoming two points at least you can expect one question from here every year out of these eight different uh figures you will have to draw one and you will have to write uh the position of image size of image and nature of image so this is for the convex mirror uh there are only two types if it is at infinite so you know that the light beams would be parallel to the principal axis and they appear to be uh meeting at the focal point hence virtual and erect image is formed which is highly diminished because it is a point size image and between pole and infinite anywhere you put you see that a diminished image which is virtual and erect would be formed here so for virtual and erect there are only three cases the two cases are in convex mirror which is infinite and between pole and infinite anywhere in case of concave mirror if a virtual image is formed you need to know that the distance between the object and pole distance between object and pole is denoted by letter u and distance between image and pole is denoted by v so u is or distance is between pole and focal length so if between f and p there is an object in case of concave mirror of virtual erect and uh diminished image would be uh sorry enlarged image would be formed in case of concave mirror here in both the cases you will have diminished image here in case of concave mirror you will have virtual erect and enlarged image so you need to understand these eight points properly if you understand these eight points if you remember these eight points i can guarantee that at least one question would appear from here now uh um excuse me sorry is there any doubt yeah uh it's me charan sir yeah like uh can you use uh like uh the concave mirrors and convex mirrors in real life um sorry i'm not getting your question applications of concave mirrors and convex mirrors in real life like uh concave mirrors like some when the object is at infinity it's used in a cinema theater in a projector or something like that so actually concave mirror and convex mirror uh we both use these kind of mirrors uh one thing that you need to understand that the convex mirror is diverging in nature so you look at here the reflected lights are getting diverged is it okay and the concave mirror is actually converging in nature except one case so looking at this uh diverging and converging effect of con uh concave uh and convex mirror uh different uses of concave and convex mirror are there in real life so if you look at the mirror used in in vehicles what kind of mirrors are used in vehicles so you look at here for concave mirror because it is converging in nature if you have to look at any particular point very minutely for that matter if there is some problem in your in your teeth and the doctor uses torch over there what kind of mirror is that that is concave mirror for saving uh shaving we use a concave mirror so inspection then for the sake of uh shaving then large concave mirrors would be used to concentrate because this is a converging kind of mirror to concentrate sunlight at at at at one point in order to produce heat so if you are able to uh produce heat uh sorry concentrate sunlight at one particular point um you will uh see that uh a large amount of heat is generated and and and this this is a natural source of uh heat uh being concentrated at one particular point now let's go to uses of convex mirror so uh uses of convex mirror you you you can use it in in cars so the rear view mirrors in the car are actually convex mirror why because it is diverging in nature so you can you can cover more area to look backwards then in your sunglasses you don't want concentration of light at one particular point at your eye so it gets uh dispersed in different directions in some glasses in the context in rear view mirrors in class huge convex mirror there are different depending on whether you want divergence or convergence there are different usage of uh vertical this particular formula i'm not deriving you need to understand that um so there's a lot of micro forms of silent relation which one is a like before the in the previous like class the convex the usage of convex see the usage of concave mirror is for inspection so torch for that matter then uh shaving cleaning wherever you want convex mirror is diverging in nature so rear view mirror of cars your sunglasses so this is the uses now relation between r and f this i'm not deriving nobody will ask derivation of this do i derive the other formulas uh looking at the time uh whatever time we have so uh r would be equal to 2 f so always remember that in case of suppose this is a concave mirror and this is center of curvature see this is the focal point f and this is the pole p then understand that p c is always equal to 2 times p f or you should understand that focal point is in exactly at the mid point of uh distance between the center of curvature and the pole so uh relationship between these two are r is equal to 2 f or f is equal to 2 by r now let's go to another topic which is um uh known as mirror formula now this is mirror formula in mirror formula we have v minus u uh uh one by v plus one by u equal to yes sir in the magnification formula yeah in the magnification formula the left it purposefully once i derive the uh mirror formula from there i will take magnification formula is it okay yes sir i was just talking because it was in the previous slide okay no issues absolutely no problem i have left it purposefully i'll i'll i'll i'll do it here so uh try to understand when we uh go to derive this formula first we need to know to know that what is v u and f so f is nothing but focal length u is distance between object and the pole v is distance between image and the pole so if we look at here um there are different triangles over here so so let me take triangle a a p b and triangle a dash b dash and p so these two triangles are and i'll prove why they are um um similar so if you look at here if i take triangle a b p and triangle a dash b dash p this is 90 degree excuse me and yes sir you are previously you told in sunglasses we use convex mirror yes um but in convex mirror only one side like one side is polish and another side is therefore reflection but how how will that reduce the concentration of sunlight in our eyes i'm i'm i'm i'm saying sun do you think sunglasses are polished sunglasses are not polished actually sunglasses are of different color and if you look at the formation of the sunglasses the sunglasses is something like this so uh actually the filming of the sunglasses is actually done on the inside so that the light rays will fall from here the sunlight will fall from here and it will get diverged from this side are you understanding so the filming is done on this particular side so that the divergence happen at the outer surface over here are you understanding yes sir okay so it's a virtual indirect image then yes actually i our eyes also make the same kind of image so look at here when i discuss human eye in the next class in which i will take other topics also like diffraction and all so actually optics is a bigger topic in which i have i have separated in two parts one is reflection and refraction and the other part is the other phenomenon the wave phenomenon of light and and human eyes so those things would be covered in a different talk lecture so i'll tell you how the exact image is formed in the brain there i discuss it is it fine okay so look at here these two are similar because this angle all three angles are are are are same actually so this is this if this is i and this is our i is equal to our this is 90 degree this is 90 degree so you can write that ab divided by a dash v dash is equal to pb divided by pb dash and this is nothing but so if you look at pb dash pb dash is equal to nothing pb is equal to nothing but formation of or place of object so this is minus u and pb dash is where image is getting formed so this is minus v so it is nothing but u divided by v so ab divided by a dash b dash is equal to u by v similarly i will take another triangle so that triangle would be abc and triangle a dash b dash and c so these two triangles are also similar because these two are opposite angle this angle is 90 degree third angle has to be same when two angles are same so i can write that ab divided by a dash b dash is equal to bc divided by b dash c so bc is nothing but pb minus pc divided by a b dash c is nothing but pc minus pc minus b dash c b dash p so what is pb pb is nothing but minus u and pc is nothing but r which is in negative direction so minus minus r divided by pc so pc is again minus r and minus b dash p is nothing but v so minus minus v so this gives me r minus u because minus minus is positive divided by v minus u so if you look at here ab divided by a dash b dash is u by v here and ab divided by a dash b dash is r minus u divided by v minus u so if you put u v is equal to r minus u divided by v sorry this is v minus r so this is v minus r and if you cross multiply it so you get u v minus u r is equal to r v which is check the chat box for a minute we have a few doubts okay fine i will check it now two u v comes out to be r u plus v so you bring on that side two by r is equal to u by u v plus v by u v so this gives me two by r is equal to one by u plus one by v and two r can be written as two f so one by f is equal to one by u plus one by v one second i am just checking the chat box what is there in the chat box shrey s s the question that you are asking that how sunglass is a convex mirror first of all it's not a lens it is a mirror because it's if you look at you you take a sunglass and try to look at the construction of the sunglass it's it's it's it has been taken from a sphere where there is only one cover something like this something like this this is how the glass now it's is the same material here there is a filming done over here on the glass is not painted so that you can't see there is a colored film or or black film or blue film through which light ray cannot pass so what happens over here this is particular the divergence happens from this particular surface why do you use sunglass for that matter why not a because it's just a filming it's just a filming i'm saying it is convex it is it is bulged on the other side it is bulged on the other side and light comes here and and diverges here how do you see your image try to understand how do you see your image in the plane mirror the thing is listen let me explain this image formation has nothing to do with with the polishing image formation happens because the reflected lights would be appearing at that particular point so for eyes the image formed by this particular mirror will act as the object and i will make an image of image with respect to image formed by this convex mirror so even if i'm filming it here it doesn't mean that image would not be formed and i can't see anything you look at here in case of plane mirror i have done this particular polishing if polishing has been done image is not formed image is formed light will not inter directly fast whenever in front of the eye look at here actually i'm forced to discuss how human i make image which i want to discuss it in the next class when i'm discussing human eye what happens is when you put a lens forget about most of us use eye lenses or or or some kind of a spectacles specs what i'm trying to say is is is that when we use this spectacle what happened first the light falls on this spectacle this is a lens this lens will make an image this image made by this lens will act as an object for the eye now the image made by this particular lens is acting as an object for this eye now this image would be seen by the eye as an object and i will make image with respect to image made by this lens similarly here in case of convex mirror which is diverging which is the sunglass image would be made by this particular this this particular spherical mirror which is convex i will look at the image made by this spherical mirror and then i will make image with respect to image made by this spherical mirror so that is the nature of formation of image and that is why this question is coming and that's why i was telling you that let me not explain this this now because in human eye when i'm discussing human eye and with respect to lenses when i discuss different when i discuss different lenses and myopia and hypermetropia i'll let you know that in myopia why concave lens and and and in hypermetropia why convex lens and all those things so i'll let you know that so don't worry about that in this in in in in this class let me discuss what i'm discussing so i've done this particular formula now somebody was asking me okay no issues if you keep on asking doubts but wherever i'm saying that i will discuss it please trust me i'm gonna discuss it so size of object you look at here i have written magnification formula size of image divided by size of object so it is defined something like this size of image divided by size of object which is nothing but here a dash b dash divided by ab and a dash b dash is also equal to pb dash divided by pb now pb dash or try to understand this this is if i take this as hi and ab adds ho we write what this hi is actually negative so we write minus v divided by minus u and this hi is negative so this negative negative gone hi by ho is equal to minus v divided by u are you understanding this yes or no these microphones on silent there is something called refraction of light so let's move to refraction of light and let's finish it fast so that we can solve few questions from there so guys let me know in the chat box if you have any further doubt about convex mirror how the image is formed if there is any doubt let me know in the chat box i'm not getting anything so so probably there is no doubt here and there so that's fine actually okay so now let me go to refraction of light refraction of light is nothing but i've already explained passes of light from one medium to another medium from one medium to another medium now what is this so there is something called optical density and optical density is decided by ability to control the speed of light now what is the ability to control the speed of light please look at here if speed in air vacuum is three into ten to the power eight then if any particular medium reduces it from here then it is called denser with respect to vacuum or air so i'm writing only air so this optical medium the rarer or denser is with respect to this is respective with with respect to other medium for glass refractive index i'll explain what is a refractive index is 1.5 for what a water it is 1.33 what does it mean there is 3 by 2 this is 1 by 3 with respect to what this is with respect to air and this particular with this particular these particular numerical values i have no value no meaning until and unless i say that these are the measure of their optical density with respect to air if i say only 1.5 and don't say with respect to air or vacuum they have no significance so they are respective values so if i look at these values then what happens it's it actually it basically tells me that glass is glass has higher refractive index and water has lesser refractive index it means that with respect to water glass is more dense or glass is denser with respect to water and water is rarer with respect to glass so rarer and denser has meaning in relative sense it does not have any absolute sense here so whenever we are discussing whether an optical medium is rarer or denser we need to have a reference point now if medium one is air and medium two is glass so i know that air is rare and glass is denser so there are two things one is which i am discussing about direction of bending the rule is that when rarer to denser rare to dense refracted ray refracted ray will bend towards the normal denser to rarer it will move away from normal i'll again explain it with numerical values also so till now you need to write this after this let's move to yes ask me your doubt okay so if you are not asking that out here it is so yes so basically if it goes from the rarer to denser medium it will move towards the normal so can you write that again rarer to dens towards the normal and dense to rare away from the normal is it fine okay now look at here what are the different laws we studied the law of reflection now it's time for law of refraction so law of refraction the first point is same incident ray refracted ray and normal to the point of incidence lie in same plane and there is something called snails laws dense law tells me that a refractive index of a medium sign value of the angle formed between the ray and the normal or you can say multiplication of multiplication of refractive index of a medium and sign value of the angle formed between ray and the normal is constant so it's the definition which i'm giving is absolutely different from you have studied and and and remember it this way so what i'm saying is mu sin theta is constant and i'll give you the definition of the book also so what is this value what is this value for air so it's mu of the air multiplied by sin i and what is this value for glass so mu of the glass and what is the angle formed here sin r now this is constant it is always same so this is equal to k this is equal to k it means that mu a sin i is equal to mu g sin r so i can write that sin i divided by sin r is equal to mu g divided by mu a mu g by mu a is nothing but refractive index of glass with respect to air and now from here books gives you books give you definition that snails law is such that ratio of sign value of incidence angle and refracted angle is equal to the refractive index of medium in which the light is entering so this is the actual definition which is given given in your in your book so refractive index of the medium is ratio sorry snails law is one second so snails law second law of sense is the ratio of sine of angle of incidence to the sine of sine of angle of refraction is constant for a given pair of media and for a given color of light and this is equal to mu this mu is nothing but a refractive index now what is a refractive index the refractive index is nothing but the ratio of write down if you want to write down I am I am I am telling I am orating it refractive index is nothing but refractive index of a medium is a ratio of velocity of light in air so velocity of light in air which is denoted by C divided by velocity of light in that medium in medium which is denoted by V so it is nothing but mu is equal to C by V and this is called absolute refractive index what do you mean by absolute refractive index absolute refractive index is nothing but refractive index of any particular medium with respect to air and definition is refractive index of any medium is the ratio of velocity of light in air or vacuum to its velocity in a given medium so if I am not asking you absolute refractive index if I am asking you a reference please don't talk if I am asking you refractive index of one medium with respect to other medium you need to write that refractive index of reference medium divided by refractive in sorry you understand here if this is medium one suppose this is water and this is air sorry this is glass so refractive index of glass with respect to refractive index of water I have to find out so that would be equal to velocity of air in velocity of light in in water reference velocity always goes in the numerator divided by velocity of light in glass so this is refractive index of glass whichever one is in the denominator refractive index of that has been calculated so this is refractive index of glass with respect to what water so for whichever one I have to find out refractive index I write it on the right hand side and the reference medium is written on the left hand side so refractive index of glass with respect to water is nothing but velocity of light in the water divided by velocity of light in the glass it can also be calculated like this so if velocity of glass with respect to air is c divided by velocity in glass and velocity of refractive index of water with respect to air is c divided by velocity in the water so refractive index of glass with respect to water is nothing but absolute refractive index of glass divided by absolute refractive index of water and a mu g is nothing but c by vg and divided by so I can write that vw divided by c so c and c gone vw by vg so you see here I have written here vw by vg so you can write it in any way so absolute refractive index is nothing but velocity of light in air divided by velocity of of light in that particular medium so this is how you have to define things I hope you are understanding everything I can see some murmuring I will have to please don't take it otherwise but if this is not stopping then guys sorry I have to block a few of you who are talking continuously now refractive index of two mediums with respect to each other so for glass and air suppose it is this is c by vg and suppose for water it is c by vw so refractive index of glass with respect to water is absolute refractive index of glass divided by absolute refractive index of water c by vg into vw by c so this and this is on it is vw by vg so that's how you have to do it now what is principle of reversibility principle of reversibility is nothing but so look at here if a ray of light travels from medium one to medium two along a certain path it retraces the path when it travels from medium two to medium one uh and then we can see that the path of the light is reversible in nature so try to understand here if it is going in this direction from medium one to medium two so I write mu one sine i is or theta one let me write this as theta one so mu one sine theta one is equal to and this suppose is theta two mu two sine theta two now if it is coming in this direction if it is going in the opposite direction so if this becomes mu two sine theta two in this here and mu one suppose this angle becomes theta three here so mu one sine theta three now this and this are equal so mu one sine theta one is equal to mu one sine theta 3 so this and this gone from here theta one comes out to be theta three it means that if it is going in this direction and if this is the path if the refracted ray becomes incidence ray incidence ray becomes refracted that is what principle of reversibility is so that's how you need to say so this is it now let's go to another topic let's finish it fast so that at least we can solve some six seven eight questions that should be more than sufficient now another topic is so refraction through glass slab so refraction through glass slab is what type of question would be asked so the type of question which would be asked from here is that what is this lateral shift so later why there is a lateral shift because look at here if this angle is I and this angle is R for this refraction now this line is coming here this refracted ray and and and this mn and this m dash n dash here or this n n dash and m m dash are parallel to each other because they are perpendicular to a parallel surface so this angle and this angle would be equal if this angle and this angle is equal then this angle and this angle would be equal how because if it is mu 1 sine i1 here so this is what mu 2 sine r1 and this is equal this and this mu 2 sine r1 here then what it would be it has to be equal to mu 1 sine i1 because it is constant so this angle and this angle is equal it means that incidence ray and refracted ray are making same angle with this normal it means that this incidence ray if I am retracing like this and this refracted ray they are parallel to each other with just certain lateral displacement so what would be this lateral displacement you will you may have to calculate this this is what the question which can come from here or the easiest question that would come from this topic is that they'll tell you that with the help of suitable diagram or neat diagram show the refraction through recrangular slab that's it and then not they will not ask you to derive the formula of lateral displacement so look at the question read the question very carefully and then try to answer the question if derivation of lateral displacement has not been asked don't derive it most of the times if you will never be asked what is lateral displacement I mean how to derive lateral displacement you will be asked what is lateral displacement derivation will never be asked yes some question was coming please go ahead and put it forward somebody was asking me certain sir could you read that what what lateral displacement is okay I'm saying that if there is no slab then this is the incident ray yes or no this ray will move in FP direction see here P is given and here F is given so this incident ray if there is no glass slab will go in FP direction like this this dotted line is it okay but because there is a glass slab and light is going from denser medium to rare or medium this light ray will change its path and will come nearer to the normal so see here if this is the incident ray refracted ray is coming nearer to the normal now this refracted ray will go and strike with the second surface and here the light is coming from denser medium to rare or medium hence the light will go away from the from the normal so this light is nothing but final refracted light and this dotted line is nothing but actual or original direction of the incident ray so it in this phenomenon it is seen that the final refracted light is at certain distance from the it from the original direction of incident ray and distance the perpendicular distance between these two rays the incidence ray the original direction of incidence ray and the final refracted ray is known as lateral displacement are you understanding yes or no yes so any doubt tell me okay so look at here there is one question which is asked that what are the different factors on which the lateral displacement depends so a lateral displacement is nothing but you look at here you draw this line here let me calculate it this is 90 degree and this if this is the thickness T so I write that cos r is equal to this oh dash sorry this suppose this is x so oh x divided by oh dash so oh dash is equal to oh x by cos r and oh x is nothing but your thickness so P by cos r and this complete angle is I and this angle is R so this angle here is I minus R so in this triangle oh oh dash and L triangle oh oh L oh dash and 90 degree at L if this is lateral displacement y so this is a right angle triangle sin I minus R is equal to oh dash L divided by this line oh oh dash so oh dash L is nothing but y which is a lateral displacements and oh dash is nothing but P by cos r so y is equal to P by cos r sin I minus R which is nothing but P secant r sin I minus R now the motive of deriving this particular formula for you is so that you don't mug up or you don't get confused that why what I am saying about the factors on which the lateral displacement depends the lateral displacement y depends on T what is T thickness of the slab it depends on R what is our refractive index because R will depend on refractive index you know that mu 1 sin I is equal to mu 2 sin R so I can write that sin R is equal to mu 1 by mu 2 sin I and R can be written as sin inverse mu 1 by mu 2 sin I so R will actually depend on angle of incidence and refractive index so it depends on T it depends on refractive index mu and it also depends on angle of incidence I so lateral displacement will depend only on three factors which are your T mu and I is it okay yes no so this is about lateral displacement now let's go to real and apparent depth and measurement of normal shift the formula is very clear the refractive index of the medium this medium so if this is me medium 2 and this is medium 1 so mu 2 with respect to 1 is equal to real depth what is the real depth suppose an object is here now if my eye is here original ray is not reaching my eye refracted ray is reaching my eye hence I will not see this object where it is actually placed I will see this object where the image of this object is getting found so that is why there is a difference between and it only happens in case of in case of try to understand in case of when it is going from rare or medium to sorry denser medium to rare or medium why because if it is not going because the light ray will go away from the normal hence this image would be formed above this particular object if it is going from the rare or to denser medium then it the refracted ray would be something like this and this will meet this line somewhere here which is not possible so you'll never be able to see the image so this is only possible when it is going from rare or medium to denser sorry denser medium to rare or medium because the refracted rays goes away from the normal hence the image is formed above the particular object like this as it has been displayed displayed in this particular figure so the refractive index of the medium depends on of the medium is real depth divided by apparent depth apparent depth can be written as real depth divided by mu so this depth is nothing but h by mu then somebody asks you what is the vertical shift so this is the depth is always taken from the surface top surface vertical shift would be taken from the object so if this height is is if this depth is h and this apparent depth is h by mu the vertical shift shift would be h minus h h by mu you take h common 1 minus 1 by mu so vertical shift is h multiplied by 1 minus mu what is vertical shift shift in the position of the object not object where the image is formed so where it is from distance between the object and the image is vertical shift h 1 minus 1 by mu and apparent depth is nothing but depth from the top of the surface which is h by mu so please remember these things I have explained it pretty clearly questions are asked from this topic regularly only you need to write sorry could you explain vertical shift again what this is your apparent depth h by mu vertical shift is distance between image and the object so which is nothing but if this is h so distance between image and object would be h divided by h minus mu which is h 1 minus 1 by mu vertical shift is nothing but where actually and where the object is visible to me object is visible to me in the form of image so where that image is formed above the object so distance between object and image is nothing but vertical shift is it fine okay next topic is lens lens you just need to know these six things Cartesian sign remains same important terminologies remain same center of curvature and focal point and all those things nature and position of image I have gathered here so these are the six different points this is for convex lens and at infinite we know that it will be on the focus then highly diminished real and inverted actually this is something convex lens is equivalent to concave mirror so you see here in five cases it is real and inverted this will also be similar when the object is between focus and the pole then inverted image is getting formed sorry virtual image is getting formed which is enlarged in this particular position so if you remember one and you have a little bit of idea about how the things are getting done then you will probably be able to solve these things for concave mirror it's something like this so there are two cases as it was in case of convex mirror so if it is at infinite you will have virtual erect erect and highly diminished which will be a point side between infinite and optical center O you will have diminished virtual erect image which will be something like this here so this is it now I have derived the formula for mirror so lens formula is similar you have 1 by V minus 1 by U is equal to 1 by F please remember in case of mirror formula it was 1 by V plus 1 by U is equal to 1 by F lens formula is 1 by V minus 1 by U is equal to 1 by F now magnification is height of image divided by height of object so height of image you see here it is negative so minus H I divided by H O and that is equal to V by U here so V is positive and U is negative so from both side negative negative one M comes out to be H I by H O that is equal to V by U so that's the formula in case of mirror it was minus V by U and what is power of lens now a lot of people do mistake here power of lens is nothing but 1 divided by focal length in meters so always remember that these focal lengths why meter centimeter is required because if you take it in centimeter the formula becomes 100 by F centimeters so if focal length has been given to you 80 centimeter don't just write 1 by 80 and and write the formula as 0.1 by 8 that is 0.0125 diopters so it is written by capital D so unit of power is diopter which is written as capital D so don't make this mistake I've seen I've checked a lot of copies I've seen a lot of people doing this mistake they don't realize that the focal length has been given in centimeters if it has been given in centimeters write it 100 by the focal length in centimeter if not then write it in terms of meters which is 1 by focal length in mirror sorry yes so the focal length for a convex lens will be positive right yes this is the focal length so for convex length this focal length is positive for concave lens because it goes like this so the focal length would be negative so also okay let me add here also don't forget sign convention here so if it is a concave lens put F in negative and say that the power is negative or if somewhere power has been given to you as negative you have to understand that the question is asked about concave lens if power has been given as positive you have to understand that the question has been asked about convex lens now let me go to another topic what is total internal reflection now total internal reflection is nothing but you look at here suppose this is the refracting surface and here I have the so look at here suppose this is denser medium and this is rare or medium and this is incidence angle I and this is refractive angle of refraction are why I am taking incident angle in dense incidence re in denser medium is that total internal reflection is only possible when the light rays goes from denser medium to rare or medium why because only in that case R would be greater than I so I know that mu 1 sine I is equal to mu 2 sine R now sine I by sine R is equal to mu 2 by mu 1 now if if it is suppose this is rare or so this would be denser first case so rare or means mu 1 is lesser than mu 2 so it means that if mu 2 is greater than mu 1 it will be greater than 1 it is greater than 1 means sine I is greater than sine R it means that I is greater than R if I is greater than R it means that the refracted ray is going towards the normal in another case when mu 1 is greater than mu 2 so sine I by sine R would be less than 1 it means that sine R is greater than sine I and R is greater than I it means that the refracted ray is more than I more than incident refracted angle is or angle of refraction is more than angle of incidence hence it is going away from the normal now what will happen in that particular case is that at certain angle this at certain angle of incidence this R will become 90 and that is called condition of total internal reflection now if a light ray you understand or you think that when a light ray goes from rare or medium to denser medium R can never be 90 because for R to be 90 I has to be greater than 90 because in case of rarer to denser I is greater than R if R is more than 90 I if R is 90 I has to be more than 90 which is not possible I more than 90 that you are going in the another medium this is becoming like this I more than 90 that it is going in the another medium not a possible case so it is only possible when the light rays goes from denser to rare or medium because total internal reflection is a condition when the refracted ray or sorry angle of refraction becomes 90 degree or refracted ray is parallel to the surface for this I can write that mu 1 sine I is equal to mu 2 sine R when R becomes 90 degree that incidence angle is known as IC critical angle so mu 1 sine IC is equal to mu 2 sine 90 is equal to 1 so I'm not writing that now I can write that sine or let me write it here sine IC is equal to mu 2 by mu 1 so IC is equal to sine inverse mu 2 by mu 1 that is the case of total internal reflection so critical angle is the angle of incidence for which the angle of refraction is equal to 90 degree which means that it is parallel to the refracting surface also if I becomes more than 90 degree then and angle of refraction will become sorry I becomes more than and critical angle R becomes more than 90 degree and in that particular case the refracted ray will keep on coming to the same medium something like this so that is only called total internal reflection so this is the concept of total internal reflection I've given you the relation between refractive index and critical angle one of its application is optical fibers so if communication signals have to be sent to the far of distance it's actually sent through the optical fiber in which signals are in the forms of wave they are if total internal reflection happens and it travels through a longer distance so that's the case now let's go to another topic okay so solve this question now questions solve this question quickly quickly solve this question have you done let me know once you are done let me know okay so answer to this particular question is here so see how you have to write the answer if the image found by a spherical mirror for all positions of the object placed in front of it is always erect and diminished what type of mirror is it important keyword over here is always erect and diminished in case of concave mirror it is not always erect in diminished it is only in one case that it is always erect and diminished which is in case of concave mirror when object is placed between the pole and the focal point in case of convex mirror it is always erect and diminished hence I need to write that convex mirror always forms erect and diminished image I need to make a neat diagram of the convex mirror to support your answer actually when I will have to make I'll make make both the images here only one image has been formed so I'll make both the images and I'll say that when it is parallel so it the virtual erect and highly diminished images formed at the focal length and when it is between infinite and pole anywhere then a diminished erect and virtual images formed like this so and that's how you need to write now when you are writing the size nature size and nature of the image you definitely write this very prominent manner so that it is visible to the examiner because they look at the keywords so if you don't write virtual erect diminished your marks would be deducted so write it properly okay next question just write it do the second question second question let me know I've just done it second question and write it in a sense that you are writing you are actually writing your examination so quickly write it so that all the keywords at least all the keywords are covered and then I will identify the keywords for you and you can probably match your answer when I'm discussing the keyword for this answer have you done it so now I'm discussing the answers the two law of refraction are incident ray refracted ray and normal are these three are keywords here and point of incidence lie in same plane so this you have to write same plane which is very very important and ratio of sign of angle of incident to the sign of angle of refraction at a point in a medium is constant absolute refractive index if you don't make a diagram of this incident ray and reflected ray like this and you don't write new one new two marks would be deducted if this is a three marker you have to make this diagram if you don't make it some mark would be deducted here and there always remember if you draw a neat diagram of any any anything even if one one or two words here and there is a mistake you will get marks absolute refractive index it is the ratio of speed of light in vacuum to the speed of light in the given medium I've already discussed it with you so this this is second question third question just do it question number three let me know the answer of the lens is nothing but measure of convergence and divergence of the lens if anywhere this question is coming you need to write power of lens is measure of convergence or divergence of the lens excuse me sir yes sir in our exam like according to our school I like write wrote something similar to that and ma'am did not give a marks and she told we have to write power is the reciprocal of focal length so what should we do what should we write in the board exam power is first line I have written second line you have to write that power of the lens is defined as reciprocal of focal length in meter is it okay so then you need to write p is equal to 1 by f the first line convergence or divergence measure of convergence or divergence and then is defined as reciprocal of the focal length measured in meters and p is equal to 1 by f these three lines would be complete answer you will get the answer you will get the marks anyone checks will get the marks thank you sir okay next one have you done this question no sir give us two minutes okay okay take one more minute okay enough time for this question look at here the power of a lens is measure of degree of convergence or divergence of light falling on it it is also defined as reciprocal of its focal length in meters and then you need to write that p is equal to 1 by f and here you in bracket you need to write meters this is the complete answer then you need to write that the SI unit of power is diopter then you need to go to this question as student uses a lens of focal length 40 centimeter and another of minus 20 centimeter find the nature and power of each lens so focal length first it has been given in centimeter so 40 by 100 is equal to 0.4 meters so p is equal to 1 by f 1 by 0.4 is equal to plus 0.25 diopter now you look at here even if the answer is positive there is a positive sign used here purposefully please don't forget to use this positive sign so whenever you are writing power right power either with positive or negative sign if it is a positive number don't forget the positive sign there additional positive sign and when it is 20 centimeter so it is nothing but 1 divided by 0.2 and a negative here so which gives me minus 5 diopters so if you have to write the nature of the length because the focal length is positive it is convex lens and because the focal length is negative it is concave lens yes any doubt there is no question asked so I'm not replying it if you have any particular questions just write it I will yes you have to write both the definition always write proper definition don't leave anything on the wish of the examiner suppose an examiner wants to know that whether you know or not the divergence and convergence point perhaps you can deduct the marks if examiner wants only 1 by f and if you have written 1 by f you will get the mark so add everything write unit everything should be written that is why I'm time and again focusing on key keywords solve this question have you done this question okay so look at the answer here or let me solve for you an object is placed at a distance 30 centimeter from the concave lens of focal length 15 centimeter list four characteristics of the image formed by lens so concave lens lens formula is 1 by v minus 1 by u is equal to 1 by f now this is nothing but first of all I have to find v so 1 by v minus 1 by u u is always negative because it's on the left hand side divided by 1 by f for concave lens it is minus 15 so 1 by v plus 1 by 30 is equal to minus 1 by 15 so 1 by v is equal to minus 1 by 30 minus 1 by 15 which gives me 30 this is nothing but minus 1 and this is nothing but minus 2 so this is nothing but minus 3 divided by 30 which gives me minus 1 by 10 so v comes out to be minus 10 now I know that v is minus 10 it means that it is virtual in nature position is minus 10 centimeter on the left hand side of the concave lens 10 centimeter from the optical center now size of so what is hi but size has object size of the object has not been given but you can you can find magnification so you can write that hi by h o would be equal to minus v divided by minus you both gone so it will be 10 divided by 30 which is 1 by 3 so you can see that hi is equal to h o by 3 it means that image would be diminished image would be diminished and one third would be diminished and one third of total so that's the case of the or of the size of the object so that's how you have to write it so this was the answer for this question let's solve one more question before we finish the session and this PPT would be available to you pretty soon so all the PPT is along with other materials would be uploaded by so CV is minus 10 centimeter image is virtual erect size of image is formed diminished from 10 centimeter now solve this question and then then probably will stop have you done this question okay so I've given you two minutes for this question which is more than enough now you look at here if the image found by lens for all positions of object placed in front of it is always erect and diminished you know that it is a concave lens so you need to write that it is a concave lens draw a ray diagram to justify you have drawn the ray diagram to justify it P is equal to 1 by F so this particular part P is equal to or power has been given as 10 after numerical value of the power has been given that is why it has been taken as positive so because it is asking you that what kind of lens so it can't give you the power of lens positive or negative so f is equal to 1 by P so you can write that 1 by 10 and 10 is equal to 0.1 meter but once you're writing your answer right that negative has been inserted to to show that the focal length belongs to the concave lens from the focal length belongs to the concave lens so P is equal to minus 0.1 meter or you can convert it into centimeter and write minus 10 centimeter so that's the answer to this particular question now this slide along with other questions would be available to you in next next two days so this is all from me in the chapter light reflection and refraction I hope you understood these things I am available for doubt clarification by any one of you on your groups personally or if you have my number you can you can send me a message so any particular doubt related to the chapter can be clarified later also what I would advise you is that once you have done this chapter go to your book open your book start revising solve few questions from there and also the questions which I would be uploading in a day or two and it will be informed to you in in in your groups so what I want you to do is to write few questions to write few theoretical questions answer of theoretical questions to solve few questions so that once we have revised it if you do self-revision at home it'll it'll clarify your concepts better it will make you better prepared for your examination any way your pts are going on we are conducting tests so different tests would be I mean we would be conducting tests so different tests are coming your way and you will have to write these things in your tests also in the coming time in next next 10 15 days so once you are done with these things this particular chapter which which cover ups good amount of questions in physics portion of the science paper will be very beneficial to you so I will recommend self-revision revise it in maybe today tomorrow whenever you have times write few theoretical questions also few numericals and if any doubt get in touch with us thank you so much thank you from my side for attending this class and I hope I was able to do justice to your time so thank you so much and wish you all the best thank you