Today we are going to discuss the topic which is optics and I'll try to cover every portion of reflection, refraction, everything in this session, which I am going to take today. So I'll start with basic property of light. So what happens is if I talk about characteristics of light, it's an electromagnetic wave. So first of all, let's discuss what is light So light is a form of radiant energy which excites vision. So it's a form of energy. First of all What happens if I talk about source of light? We have natural source of light which is Sun and We have artificial source of light or man-made source of light. So which are your bulbs You can say candle tube lights So all these things now There are two These sources of lights are divided into two specific Categories one is called point source So if you see a lot of questions are asked specifically numerically in your examination Where you are asked that a light beam or a ray of light is coming from point source What do you mean by point source? So point source is Defined like this. So suppose there is a source of light which has been kept over here and there is an Observer who is sitting over here with respect to observer if the dimensions or the size of this source of light is negligible this source of light for this observer would be considered to be point source of light and What happens if with respect to observer this Source of light is not negligible or size of source of light is not leg negligible Then what will we call it? We will call it extended source of light so I define two kinds of sources point source and Extended source so point source was where the size of the Object emitting light is negligible with respect to observer that would be point source if it is not negligible If it has some dimensions it is comparable with respect to observer then it would be extended source of light now, let me move to the actual Electromagnetic wave so light is called electromagnetic wave though. It does not have any charged particle It does not represent or it does not Have any magnetic particle even in that condition light is supposed to be Electromagnetic wave because it it is in form of wave where electrons if you put electron in that source It'll it'll show some kind of oscillation. So let's not get into much deeper details of it. So Light is known as electromagnetic wave. What is the next property? So I have seen a lot of question based on characteristics of light So I have seen a two marker question or a three marker question best on right two properties of Two characteristics of light or three characteristics of light or five characteristics of light So that's why I have jotted down all the points for your reference so that you can get it at one source So the first and the most important part of light is that it's an electromagnetic wave Second is it does not require medium for its propagation and how do you prove it? So when light travels from Sun and it reaches us it travels through so many mediums Which includes vacuum also where there is no atmosphere and it enters our atmosphere With different layers of density it reaches us which shows that light does not require any medium for its propagation now in vacuum the Density of light is Sorry, the speed of light is 3 into 10 to the power 8 meter per second Now this fourth point is very important speed of light is different in different medium So always try to understand any particular wave is Would always have a wavelength and some kind of frequency so light waves so any I mean if I talk about light and why it might would have your Vibyore so V I Be G Y or it is combination of these seven colors so If I talk about these seven colors all seven colors have different Weblance and different frequency So if I go from V to R lambda, which is wavelength increases and Frequency will decrease so what happens in vacuum the speed of all the different seven components of light would be same But as soon as the light enters a different medium Suppose this is medium This is medium one medium one and this is medium two now a white light goes and Goes and penetrates the boundary like this all seven colors will have Will observe a change in The wavelength so what happens I'm writing two three things which are very important and and you should also write it with me First thing is that whenever light changes medium the wavelength of Different components of light the wavelength of different colors of light will change so wavelength lambda changes hence speed of light Changes so what happens is? Speed Will change lambda will change But one thing which remains constant and this is very very important frequency is Constant so in this particular scenario what happens is the color of the light Sorry, the speed of the light is different in different medium Why it happens because as soon as the light will get into a different medium medium The wavelength of the different components of light will change and hence it will observe a change in speed Though frequency never changes with change in medium second color of the light is determined by the wavelength So this is one property light always travels in space Straight line now. I have already explained these two points because it was required over here So I've written here if change in medium light do not change does not change frequency while speed changes and Speed of every color of light is different in different medium except vacuum So all these points I have already explained to you here. So as soon as You see a question based on characteristics of light in your question paper You write first point that you should write is that light is electromagnetic wave Second point if you have to write three points, I'll tell you This should be the first point that it's an electromagnetic wave second point should be it does not need any medium for propagation and third point You can choose any one of them so if you want to write a Simple one you can write it travels in a straight line because and if you have time a 4.5 points have been asked You can include all these points. So in this order only you should write These things now, let me move ahead Now what happens is there are few other terminologies which are important. So We need to understand What is beam of light and what is light rays and all these things so First I define optical medium. So any medium through which light passes through which light passes is It only is only this definition sufficient that any medium through which light passes. No, there is one more condition that light Should not lose much of its intensity. So any particular optical medium is defined by its Capacity to pass the light or let the light waves navigate without much loss in its Intensity so any medium through which light passes without much loss in intensity is Known at so if if somebody asks you to to Define optical medium. You can define optical medium by this Okay, one second guys. There is okay now What is type of beam? So type of beam you can these are small things type of beam is Parallel convergent divergent I'll come to you can you can I'll define parallel convergent and divergent beams for you parallel beam means which is parallel to the Axis so let me define it for you parallel beam is so if if any particular beam is is is like this moving like this after Eliminating from emanating from point source that would be parallel beam Second one is convergent or divergent beam so Divergent beam like Sun rays so they diverge in all the direction after they get emanated from the Sun convergent beam means All the beams converts together from all the direction on on One place. So this is what is quite convergent beam now let's move to the important topic which is law of reflections So law of reflections can be defined by there are two three laws which I have written So let me make some space for you so that I can So law of reflection. So what is law of reflection? So try to understand there are two three things that we can understand here in law of reflection before going to the The two laws which I have written over here So first thing that I want to tell you that light has two Properties or light is studied studied on two different basis. One is particle theory of light and Second is wave theory of light So what is a particle theory suppose a cricket ball? So what happens if this is a ball and this is cricket ball it goes and strikes this particular Wall what happens the wall reflects its back the same mechanism can be understood in the case of light wave light particles also, so What happens in this particular case is that? suppose This is a plain surface at which has been polished on the other side. So what will happen is that? If I draw a normal to this particular surface and suppose this is the incident ray and Suppose the incident angle is I so light will get reflected from here So the first law of reflection says that this incident ray Reflected ray. This is IR incident ray. This is reflected ray, which is our and Normal to the plane of incident. So this is the normal. So suppose this is my Surface AB the light strikes at point O and O M is the normal. So I are RR and O M these three Line segment or ray segments would be in same plane. The second one is very important which says that Angle of incidence is equal to angle of reflection. So whatever angle this Incident ray with make with this normal So what mistake generally student make in in examinations? And I have seen it many times that they take incident angle with respect to this mirror So this mistake you should not make whenever you are taking incident angle You should take the incident ray and normal to the mirror not the mirror. This is not I This is not I this is I the angle between the incident ray and the mirror I have seen many a times people making this mistake please be aware of this fact and similarly the angle of reflect reflection is also measured from the normal To the reflected ray so angle between the normal to the incidence and the reflected ray is known as angle of reflection so please have these Things in mind before let me define to you the different kind of mirrors so One thing which was very important in case of angle of reflection is that suppose the angle of reflection is This is the incident ray. What happens when the incident ray is in the same direction of Normal to the ins and normal to the mirror So it means that this angle of incidence is making zero degree with this normal So if I is zero and I is equal to R Then R will also be zero degrees in that particular scenario What happens is that the reflected ray retraces the path it means that whichever direction it comes from it Reflects itself back to the same direction. So this is called condition of no reflection I have seen one or two question where either you are asked condition of no reflection or no Refraction so if condition of no reflection is asked to you in the examination What you should do is you should make this diagram at least without this diagram your marks would be deducted and after that you should write that if incident ray is normal to the Mirror which means that I is equal to zero degree That also means that R is equal to zero degree in that case The light would not or the light would Get reflected in the same direction. So this diagram is important and then one or two line Which is specified or which throws a light on what is happening in this particular figure Will give you a accurate marks while attempting this question now Let me go to the other other parts of it So what happens is spherical mirror? I am taking two kinds of mirror, which is concave mirror and convex mirror so always remember one thing that This concave and convex lens comes from the ability of reflection What do I mean by this statement is that? that a mirror when the part of mirror which is reflecting the Light is concave. Then it will be called concave mirror. So this is the cave You can see that this cave portion of of of the mirror is Reflecting the light and it had been polished on the other side. So polishing is done on the convex side So this side is called suppose this left side is called concave side and the other side is called convex side So always remember that the size which is reflecting the light The name is given by that. So if concave side is reflecting the light It is called concave mirror if the convict side is Reflecting the light so suppose I mirror the concave side and convict side is reflecting the light like this So this will be called convex mirror Now I am taking the example of concave mirror to explain you what happens and what I mean, I will discuss the important terms Related to mirror so suppose I take a concave mirror So first thing is pole. So concave mirror Any mirror would be cut from some solid glass and it would be a portion of solid glass So if I take that solid glass And and cut suppose this is circular in nature something like this Circular in nature. I have taken only part of that as as mirror and the other part I have just Polished it so the center of this particular periphery from A to B Whatever periphery is this the center of this periphery is known as pole The second thing is center of curvature. So from whichever Sphere I am I am cutting this out center of that particular sphere Would be known as center of curvature of this particular spherical mirror So suppose this is the center of a sphere from where it has been cut down. This would be known as Center of the sphere now distance between any point on the mirror From the center of curvature is known as radius of curvature So distance between this pole P pole is denoted by P center of curvature is denoted by C So CP length CP is equal to radius of curvature If I take any other point Like I take point here and if and what happens is Suppose this point is in so this for this line Cm will also be radius of curvature Because any point on on on on the periphery of it will have equal distance from the center of curvature That would be equal to radius of curvature now. What is principle axis line joining center of curvature? So this line which is joining center of curvature to the pole is known as principle axis now There are two other important terms which are focus and focal length. So what is focus any? Light way which passes parallel to this principle axis Passes through a point Whichever point is it passes through that point is known as focus So what is focus line parallel to principle axis? After reflection from the mirror passes through a point whichever point on the principle axis The reflected light passes through is known as focus point and distance between this focus point F and pole distance between F and P is known as focal length and Focal length is denoted by F now There are other different Terminologies, so first one is linear aperture. What is linear aperture? Let me draw this diagram once more so that you understand Properly, so there are three four more terminologies, which are less common in nature, but maybe asked in the examination So linear aperture what is linear aperture? so suppose this is my spherical mirror concave mirror I am taking and Whatever between two ends of the periphery Whatever distance this linear distance is this linear distance AB is known as linear aperture So what is linear aperture the linear distance between the two ends of the periphery of the spherical mirror is known as linear aperture now what is angular aperture so Angular aperture would be try to understand Draw a line, which is principle axis. What is principle axis any line between the center of curvature and the Pole so the angle Substended by the two ends of the of the spherical mirror The angle Substended by the two ends A and B here in this case on the center of the curvature is known as Angular aperture so whatever angle this theta so angle ACB here, which is equal to theta I'm assuming is known as angular aperture now next one is Paraxial axis so what is Sorry paraxial rage so what is paraxial rage paraxial rage is Any ray which is nearer to principal axis so what happens? Let me categorize the rays which fall on the spherical mirror So suppose this is my concave mirror Raise which are very very closer to principal axis Are known as paraxial Raise so what about raise which are farther from this Principal axis so raise which are farther from the Principal axis are known as marginal rays or Peripheral So this is how it is Now what do you mean by convergence and divergence of rage so try to understand to understand Convergence and divergence of rays. We need to understand how convergence and divergence happens So you see here. I'll explain this What I'm writing concave mirror is also called Converging mirror convex mirror is also known as Diverging mirror now why it is it is like this so try to understand it applies the Basic formula of reflection the second law of reflection that I is equal to our so I'll explain this phenomenon here So that you can understand it properly Suppose this is concave mirror and I'm drawing a line from here This is my center of curvature now. You should know that in in a circle or in a sphere any point on The mirror or on the point any point on the circle or a sphere If I Draw a line from the center so line joining the center and any point on the circle or a sphere So let's let's say here mirror here would be perpendicular to this particular Surface so this line CP is perpendicular to this spherical surface over here. So any ray Which is coming and striking this point suppose. This is I now Our would be on the other side of this normal or reflected light would be on the other side of this normal So this reflected light goes from Here so what happens? This is your art. So what it is doing it is bringing everything So what let me let me draw a line from this side also. So this is my Normal and this is my reflected light. So see what happens? The light which is coming from here. This is ray 1 this is ray 2 and This is Or let me let me call it I1 and I2 so that you can understand properly so two lights To two different rays I1 and I2 and to reflected rays R1 and R2 What happens with R1 and R2 R1 and R2 converge at one point because of the shape of this particular Spherical mirror it's such that it brings all the reflected light together at this focus So this is why this is called converging mirror in case of convex mirror what happens so this is the center and This is the pole. So I draw a line. So this will be lying parallel to So what happens? Let me extend this. So now this is suppose I So this is I1 And you see here this reflected light goes somewhere. So this is I1. This is R1 So this reflected light is going away from the mirror. So what happens is it is diverging in nature So due to the nature or due to the shape of these two kinds of mirror and the polishing on different side One type of mirror which is concave converts into converging mirror and the other Type which is convex converts into diverging mirror So I hope you understand this concept and and if if if nature of this mirror is asked and how it is Converging and diverging you can draw these kind of diagrams and and easily get marks In your examination now, let me move to the next slide So there are different rules for constructing images. So what are those rules? So there are basically four rules which apply in both the cases both in concave mirror and convex mirror So those rules are First rule is first rule is Let me draw a diagram for you. So Suppose this is my concave mirror. So I'm doing it for concave mirror. I Will explain it for convex mirror also first rule is Any ray suppose this is center of curvature. This is full. This is focus so first rule says that any ray which is Parallel to the principal axis after reflection will pass from the focus So this is the first rule a ray of light incident parallel to the principal axis After reflection passes through principal focus. So this is the first point second point is That if a ray passes through focus So suppose a ray passes through focus after reflection it becomes parallel to the principal axis So it is actually a case of reversibility So if I am making a question paper and I want to ask you that explain me the concept of Reversibility in case of concave mirror, you should make these two diagrams and show it to me You you can say that when when it is parallel to principal axis It is it is passing through focus and what is when it is passing through focus. It is parallel to principal axis so so so It's actually the same case if it is coming from this side It will go this way if it is coming from the other side, it will go this way So this is the principle of reversibility in case of concave mirror third point which is very important is that That suppose this is a concave mirror and this is C. This is F. This is P So any point sorry any rays which which comes Through center of curvature Will retrace this part why it happens because see at this point M What is the normal cm is normal and incident ray this incident ray cm is I Mean overlapping with incident ray is suppose I take a different name Ivan So incident ray Ivan is overlapping with cm It means that I is equal to 0 in this case if I is 0 then R is also 0 Hence it retraces its path. It goes back on the same path So any particular ray passing through center of curvature will retraces its path now fourth one is that if I have a ray of light coming and Striking the pole So whichever angle it is striking with the pole because this is this this particular principle axis at pole also works as Normal to this is spherical surface. So this angle between the incident ray Ivan and this Principal axis CP this angle would be Ivan and it will make the same angle here So suppose this is R. So I I this angle I would be equal to R So what I am saying is that if a ray comes and strikes the principal axis it goes on the other side on Making the same angle with the principal axis. So these are the four Loss which are important or which are called rules for constructing images So if somebody is asking you in the question paper that write down rules for Constructing images formed by spherical mirrors. You can write it In this way, you can make these four diagrams and that should be sufficient enough for you to get full marks now What happens in case of convex mirror, so that is very important why because I have not discussed till now Real image and imaginary image. So now I discuss real image and imaginary image with you with the help of few figures So now try to understand What happens in case of concave mirror as it is converging in nature and suppose there is any light passing through something like this Suppose there is any light passing through it and and and getting reflected like this and And there is one light passing through this suppose. This is focus and and passing through this and this Matches here. So what happens here is the image would be formed something like this So now these both the reflected rays are can be captured on a screen here So what is a real image? real image means if Reflected lights can actually be captured on a screen that Image would be known as if I put a screen. I'll find out image of the object here Suppose object is here somewhere and I am finding the image here This image can be captured on the screen here in case of convex lens. So what happens as It is diverging in nature. So what happens is that? so suppose any particular Ray go from this side to here and after reflection goes here from this side it goes here After reflection this goes here. So none of the lights would you will be able to? Show it on a screen. It is diverging in nature. So this this reflected light is going this way This reflected light is going this way none of this them are none of the Reflected lights are merging at one point or on a finite plane So what happens is if it is not merging on a finite plane or on a point You cannot capture it on a screen and if you cannot capture it on a screen What happens is you don't find a real image all these will get masked on a point somewhere here but these This point where they are merging no actual light is coming here If you put a screen over here as the light is reflected from this surface only Actual not isn't light is not falling back on this screen. So this kind of image is known as virtual image made by Extension of reflected lights. So this is what it is called vertical image So always vertical image in case of real image We talk about a language that image is formed and in case of virtual image We use a particular language which is called images appeared to be formed So you should understand the difference between images formed and images appeared to be found images formed is used With the real image scenario and appeared to be formed is used with virtual image scenario. So in case of if I talk about rule of constructing images with Once again for convicts mirror, it's it's the same thing But in all the cases I'll be using language that image is appeared to be found So here also if a line parallel to principal axis is there after reflection It appears to to fall or pass through the focus the second thing is if If any particular line appears to be or any particular way appears to be passing through focus So suppose this is focus so passing through focus after reflection becomes parallel to the principal axis third thing is same that if any particular light If it passes through center of curvature or if it appears in case of convex lens if it appears to Pass through center of curvature. Suppose. This is center of curvature and suppose a light Appears to pass through center of curvature. It retraces its path back and suppose something hits the pole at angle I reflection would Also will happen on angle I so everything is same just the language is different in case of convex lens We'll use the language of appear to be in case of concave lens We will directly write that the image can be found now what is what is Cartesian sign convention for reflection? I'm telling it for concave mirror. It is true for convex mirror also So first thing is any distance measured any distance measured in direction of art of Ray that is supposed to be positive So suppose I I there is an object here and a ray travels Through this direction all the distance in this direction will be considered to be positive and all the distance Taken opposite to the direction of path of ray would be supposed to be Negative so this is positive. This is negative now second point is From where do you measure the distance? So we measure all the distances from the pole So there are three points that I talked about this was full This was focus and this was center of the curvature from where do you measure the distance? So suppose object is here Is this the? Distance that I need to take or is this is the distance that I need to take so suppose this is I? Sorry, this is oh object. So all the distances are measured from pole. So second point is all Distances are measured from As simple as that The third point is object is always taken on the left-hand side of the mirror so When I place the object I suppose mirror to be like this So object will always be considered on The left-hand side of the mirror. So this is the third point fourth point is So how many points we have discussed Positive when it travels through when the distance is in direction of the race Second point is negative when opposite to the direction of the rain third point is All the distance from the pole Distance has to be measured from the pole Fourth point that I discussed that object has to be on the left-hand side fifth point is Anything above the principal axis? so above the principal axis it would be considered to be positive So you can understand that anything below the principal axis would be considered to be negative So height above the principal axis is positive height taken below the principal axis is negative And all the angles which are measured in anti-clockwise direction so angle in Anti-clockwise Direction is considered to be positive any angle measured in clockwise direction is supposed to be negative so these are the Important points from the point of view of Cartesian sign convention of reflection So I'll repeat it for you that if you measure a distance in the direction of path of the ray So that would be positive opposite side would be negative all distances are measured from the pole object is always placed on the left-hand side of the mirror Any height above the principal axis would be positive any height below the principal axis would be negative Angles measured in the anti-clockwise direction is positive an angle measured in the clockwise direction is negative Now, let's decide a few things about our Concave and convex mirrors. So what about focal length and radius of curvature and all those things about concave and convex mirror So, please understand that suppose this is Concave mirror and object is placed over here. So light ray will Always go in this direction. So this is the direction of flow of light And this is my center of curvature. See this is my focal point F Try to understand if all the distances are measured from pole So this focal distance would be in opposite direction of Travel of light. So concave length for concave length This focal length would be negative for convex lens What it will be so suppose object is here and light ray is traveling in this direction And this is the focal point. So this is the distance I cover. So for convex lens This would be positive Similarly radius of curvature would be negative here because I am measuring in opposite direction The radius of curvature would be positive here in this direction. So This is how you have to understand Cartesian sign convention. Now, let me move to another topic, which is position and nature of image So this particular question is asked in most of the question paper and there are so many possibilities So, let me discuss it For a few possibilities. So if if I talk about concave mirror What happens is that you should understand that let me finish it in two minutes quickly So there are different distances which are considered over here. So Let me make a diagram for you. Suppose this is pole. This is center of curvature and this is focus So what I assume is that suppose any object or any particular Point source is at very large distance. So always understand whenever I use this language in Optics that very large distance by very large distance What I mean is that the rays coming from that source would I am considering it to be parallel to the principal axis now from the Rule of constructing image. I know that if any ray is coming parallel to the principal axis All these rays will converge on the focus. So if Distance of the image and always remember distance of image in optics is denoted by word you Distance of sorry, I'm sorry distance of object is denoted by word you and distance of image is Denoted by letter V. So letter U and letter V. So if U is infinite, which is in this case we would be at focus and This as this is the image is getting formed only at one point. So size of the image would be infinitely small So this is called diminished in Optical Terminology, so next one is suppose I take If U is equal to F second case, I am taking I'm not taking all the cases So if U is equal to F if an object is kept over here at F what happens is So suppose a light rays goes from here so It is trace is path back and it will pass through center of curvature and anything Which passes through this again, it will trace it its path So all these lines would be parallel to each other. So hence they'll if U is equal to F V becomes infinite. So when U was infinite V was equal to F when U became F V became infinite. So these are the cases that you need to understand So try to find out all these things and mug it up properly so that You don't miss any this kind of question one way one trick to solve this kind of question is that you take your You you draw a line and take any point and you draw draw an arc like this and After drawing the arc measure this this this length This would be your radius of Curvature and exactly half the point would be your focus I'll prove that radius of curvature is two times the focal length in next of the slides And what happens is that whatever distance that has been given to you you put your object there And from there you start drawing a parallel line and a line passing through center of curvature and where wherever it meets So I always see that a lot of people make mistake in this kind of question You should never make a mistake Even if you don't know or you don't remember how to draw this diagram. You just do one thing You take your compass and you draw this kind of arc and from midpoint of it you From midpoint of it you draw our lines which which which which passes through center of curvature And and half of the point would be focused and you put your object at the place where it has been given and a Start drawing a line parallel to principal axis and one passing through center of curvature and wherever they meet at that particular Point your image would be formed So if you do this particular exercise It's better to lose one marks than to lose five marks or three marks So do this exercise at least on your copy which it is not difficult It can be found out very easily if you if you draw a correct diagram. Now, let me move to next slide I'm proving this that R is f is equal to r by 2 or r is equal to 2f It means that radius of the curvature is 2 times the focal length. Now, how do you prove it? So suppose Let me draw a diagram for you Suppose there is a light ray coming like this And this is my center of curvature C So from this is parallel to Principal axis. So suppose this is C. This is f. This is P and After Reflection it will pass from this. So suppose this incident light is AB and reflected light is BT and suppose this Conquered mirror I am assuming to be Mn Now what happens is You look at here Let me draw another do a construction. So this is this CB is perpendicular to the surface of Mn at point B Now this is the incident ray I and this is R Now I is equal to R Now what would be this angle? So you try to understand angle ABC Is equal to angle BCP. Why it is so because AB is parallel to CP. So these two would be alternate interior angles So what happens is this both these angles are equal to R. So in triangle BCF Opposite to this side CF is there this angle CF is there and opposite to this Opposite to angle B's line CF is there and opposite to angle C line BF is there now try to understand In a very very small aperture this line BF if if if this Percher is very small this BF Would be equal to FP So what I'm trying to say is that if aperture is very very small if this distance is very small Very small aperture means I am assuming BP to be negligible equal to zero So this line if it becomes to zero this particular line BF will keep on coming down and become FP when BP automate I mean BP becomes almost equal to zero So what I am saying is BF is equal to FP So I am writing here BF is equal to FP now what I have to do is that I know CP is equal to CF plus FP or I can write that So what what I need to do is that I have already written that CF is equal to BF and BF is equal to FP. So I am writing CF is equal to FP. So CP is equal to FP plus FP So let me write here CP is equal to FP plus FP and What is FP? FP is equal to focal length. You see here. What is this? This is your focal length F So CP which is your radius of curvature R is equal to F plus F So R comes out to be equal to 2F or you can write that F is equal to R by 2 So this is how it is. So I hope you understand this this this complete Derivation now, let me move to proving your mirror formula. So your mirror formula is 1 by V plus 1 by U is equal to 1 by F. Now, how do you prove it? So to prove this concepts of similarity are used so I Will I will draw a diagram? Please look at it. This can come as 34 marks question or maybe a So what I do in this case is that I take an Object so suppose first, let me mark over here. Suppose. This is center of curvature C This is focal point F and this is P so let me Have an object. I name the object as AP. This is my Concave lens Now I as I told what I do I'll draw a line parallel to principal axis And this will go from the focus here and I'll draw a Give me a moment. I'll draw a line From the center of the curvature and I know that If a line passes through center of the curvature, it retraces its past So where does this tool to Reflected rays meet the meet at point suppose this I call as a dash and This would be the image formed a dash B dash so now it's all everything now is the Application of concept of similarity, so I'm just removing this so that I can write it So I'm taking triangle triangle ABC I Know that triangle ABC is similar to triangle a dash B dash C. Why because this is 90 degrees So this is 90 degree and these two are opposite angles. So if two angles have same third angle has to be same so the Thing would be that ratio of corresponding sites would be equal So a dash by a dash B dash divided by AB would be equal to B dash C divided by AC Now once again, I have I made other the diagram I need to change the diagram here because I've taken B dash on on the principal axis so V dash by BC so this is the first equation which I am making Now second equation I will take it from this triangle and and I as I already told you this length Fp Let me draw a perpendicular from here So suppose this length I'm calling it as suppose this point is B and this point is n So I am telling that Fn is equal to Fp why because if aperture is very very small this this length and P would be negligible to 0 Hence, I'm assuming that fn is equal to fp now I Try to understand in in triangle. I'm taking the triangle on the other side. I am taking triangle a dash B dash F and triangle B and F So I am taking this triangle this triangle and this triangle again. These two are Opposite angles so that would be equal and this two would be 90 degrees. So they are similar in nature So you try to understand it would be a dash by B dash divided by B dash F That would be equal to DN divided by Fn Now you try to understand if these two lines are parallel ad I'm writing here If ad is parallel to BP then you automatically understand that AB would be equal to DN Because this becomes the height of the object and I have already I already know that Fn is equal to Fp So now what I am doing is that I'm just changing it a little bit a dash B a dash B dash divided by DN is equal to B dash F divided by Fn and I replace DN with what I do is I write a dash B dash I replace DN with AP AB and B dash F divided by Fn I replace with Fp So now this is my second equation now from equation one and two a dash B dash by AB is equal to B dash C divided by BC and B dash F divided by Fp. So I can write here that B dash C divided by BC is equal to B dash F divided by Fp I can easily write that from these two equations now. What is B dash F B dash F is this Pb dash Pb dash minus Pf divided by this complete length this length from here to here would be this complete length from pole to here minus this length divided by BC I can write it as Pb minus PC That is equal to No, once again I've written B dash F. So I will have to write here Fp Fp will remain Fp and B dash C. I'll I'll I'll write that so B dash C would be PC minus B dash P divided by BC I can write as Pb minus PC So what I get over here is I get over here now. What is What is P? So you look at here Pb dash. What is Pb dash? Pb dash is where image is found and it is in the opposite direction of the rate So I am writing here minus V This Pf would be how much Pf is focal length again, this is negative minus F divided by Fp Fp is Again minus F and that is equal to PC So How much is PC PC is equal to 2f because PC is radius of curvature So I'm writing it 2f, but it will come with a negative sign Minus 2f B dash P is again minus V divided by Pb Pb is equal to minus you Minus PC minus PC will again be minus 2f So let me remove this for you Let me remove these things for you if you solve these this equation So this this comes out to be minus V plus F divided by minus F is equal to V minus 2f divided by 2f minus you which becomes F minus V divided by F is Equal to V minus 2f divided by 2f minus you if you do the cross Multiplication and everything you will find that it will come out to be 1 by V plus 1 by U That would be equal to 1 by F. So this is the formula of mirror Please remember it whenever you are putting the values put the values with the sign convention Generally people make mistake. I'll make videos on for the numeric also, but as I am doing the mirror formula here I am revinding you once again that whenever you are doing these these kind of questions Never forget the sign convention The most important thing in the case of Mirror formula is sign convention if you put the sign convention if you Follow the sign convention properly you will never make a mistake Now in this case only You can easily find out the formula of magnification So formula of magnification is I have written here Size of the image h i by h o Is equal to minus V by U. So this is your formula of magnification Anyone you can use magnification is also this size of image divided by size of object for mirror It is minus V by U. So you can prove it through the similarity similarity diagram, which I just made on On on the on the slides now, let me move to another important topic. So Let me go to refraction So I hope you understood the concepts of reflection pretty well Now refraction. What is the refraction? So till till till now we were discussing About the light rays which were coming to the medium Coming back to the same medium after getting thrown away from the Optical medium. So there was a mirror kept over there and it was polished from the other side So what happened is that whenever any particular light rays striked with that mirror It was thrown back again to the same medium. It it is not always the same. What happened? It don't polish the other side. So in that particular case Or normally also in different situations Light passes through different medium and when light passes through different medium I have already explained that there is a change in the wavelength of Of of the light when it goes from one medium to another medium Due to change in the wavelength the speed of the light also changes So optical medium. I have already explained you an optical medium is Any medium through which the light passes through Without its intensity getting affected much now optical medium can be classified into two categories The first category is rarer Optical medium. The second category is denser optical medium. So what is a rarer optical medium? So as I have already told you that the speed of the light changes in in different medium So if light goes from one medium to another medium such that the speed of the light increases So If lights light starts traveling faster than The other media it is called optically rarer medium The second case is denser medium in this particular case The speed of the light reduces from the previous medium from which it is coming So if the light increases it if the speed increases it is a rarer medium If it speed decreases it becomes the denser medium So let me draw a diagram for you and let me explain over here. Suppose This is medium one And this is medium two a light is Coming like this now. This is incidence Angle and suppose it is getting Ref refracted like this. Suppose. This is angle of refraction now if this particular light wave Suppose speed is v and suppose medium one I am assuming to be air and in air The speed of light is denoted by c. So if v is greater than c this is rarer medium And if v is lesser than c that is denser medium Now always remember that optical density Optical density Is different from Normal density that we discuss For an example, let's take kerosene So when you put kerosene in in water Kerosene starts floating on the water. What does it show? It shows that the density of the kerosene is lesser than the normal density of the kerosene is lesser than that of water But in case of light speed of the light reduces more in kerosene than in water Which shows that kerosene is optically more denser than water So always remember that this the density which i'm talking about here is is is not normal density I define it as optical density and optical density is different from normal density anything I mean you cannot compare optical density with normal density. I gave you an example of kerosene For that matter now Let's discuss the direction of bending or how the bending happens And what is the phenomenon of bending? So Please understand here. This is the medium which is separating And this this is another medium. I'm taking I'm making two diagrams. So suppose this is medium one and this In two and there is an incident ray over here So if medium two is rarer than medium one So the light ray Deflects away from the normal So in this case angle of refraction would be more than angle of incidence Here this is m1 and this is m2 if m2 is denser than m1 So light rays Deflects towards the normal here light ray deflects away from the normal here light ray deflects towards the normal So r would be lesser than i So why this phenomenon happens because I have told you that frequency remains the remains the constant when the Medium changes and only wavelength changes. So uh, so there is a band party theorem over here So suppose this is or this is the direction in which the band party is moving. So what happens is suppose This is normal road and I put sand Over here. So sand is more denser or in sand the speed of the human being coming from our road Normal road will reduce so whichever person comes over here will And and suppose there is a person over here over here will take a path which Provides them a path which takes the least time crossing this sandy path So try to understand light always follows in any medium light always follows that path Which provides its least time to cross that particular medium It is not the path which is shortest it is the path which takes the shortest time So light always takes that path Which takes shortest time for it to pass that particular medium and that is why This particular human being which is coming like this will start moving towards Here so that he follows this path and moves away from this sandy path as soon as possible. So This is how the bending of the light happens in this particular direction So always remember that whenever a light goes from denser medium to rare or medium The bending will happen away from the normal whenever the light goes from Rarer to denser medium the band bending will happen towards the normal Now let me go to lodge of refraction So I have already explained you The bending of light. So now let's understand. So so support. This is Incident ray I And this is my media medium M1 and this is M2 before I explain you law of reflection There is one thing that you need to understand. There is something called refractive index of a medium Now refractive index of a medium is defined by a ratio that ratio is Speed of light in vacuum or in air divided by speed of light In That medium So try to understand speed of light in air I told this is c and suppose the speed of light in that medium is vm Now try to understand if it is a denser medium So vm would be less than c if if if the medium is denser than air It means that it is slow down the speed of light Hence vm would be less than c if vm is less than c then this ratio c by vm Would be greater than one. So for a denser medium denser as compared to air Refractive index would be more than one if there is a medium where It is it is it is rarer than air in that particular Scenario vm would be greater than c and refractive index would be less than one So that is how you define the refractive index now. Let me go to this particular place Suppose refractive index is mu 1 here and mu 2 here So The first law tells me that this incident ray Refracted ray and this normal to the point of incidence will be all in same plane So this is similar to reflect reflection. The second one is known as snails law and it is very important So I never explained snails law as mu 1 sin theta 1 and all these things always remember Refractive index of the medium. So I'm writing mu m multiplied by Sign value of the angle in the same medium. So sin theta m Will always remain constant So what happens is what is the refractive index here mu 1 and what is the sign value of the angle is this In this medium i so mu 1 sin i that's if it is equal what is Mu 2 here and what is sign value of angle r here So mu 1 sin i is equal to mu 2 sin r because both of them will remain constant So I am equating the constant here. So mu 1 sin i is equal to mu 2 sin r. So this is this is your Snails law mu 1 sin i is equal to mu 2 sin r. Now, let's discuss snails law in in in a bit of details here So what I will do over here is let me Just make a little bit of a space So mu there was a this was i this was r This was mu 1 this was mu 2 so mu 1 sin i Is equal to mu 2 sin r So try to understand sin i by sin r Is equal to mu 2 by mu 1 So if mu 2 is greater than mu 1 it means that if Try to understand if mu 2 is greater than mu mu 1. So it means that this is denser medium Because mu 2 is greater and mu 1 is rarer medium So what happens is this becomes greater than 1 So it means that sin i is greater than sin r So i is greater than r. It means that the light ray is bending to if r is less than i It means that this displacement From normal of this refracted ray is lesser than this displacement of incident ray So it means that i is greater than r or if r is lesser it means that it is moving towards the normal So that's how we prove that if It is going to the denser medium So r would be lesser than i it means that it is going towards the normal in opposite case It will deflect away from the normal Now let me go to condition of no refraction Condition of no refraction is same as condition of no reflection. So what happens is any light ray Which falls Or overlaps the normal to this refracting surface It would be i equal to 0. So mu 1 sin i Is equal to mu 2 sin r so As mu 1 and mu 2 are not 0 mu 1 Sin 0 is equal to mu 2 sin r now sin 0 is 0. So 0 divided by mu 2 is Sin r r comes out to be 0 r comes out to be 0 It means that the light ray keeps on traveling in the same direction and this is the condition of no refraction So if somebody asks you condition of no refraction, this diagram should be there along with this Particular calculation and write a few lines about that If it falls or overlaps the normal. So there would be No refraction because i is equal to 0 and hence r becomes 0 you get full marks for that Now let me move to Principle of reversibility. So let me move to another Slide so what is principle of reversibility principle of reversibility is like this so suppose This is a medium and from here the incident ray is coming And this is i and suppose This is r So principle of reverse reversibility means By explaining it if it is coming from from this side Suppose medium one and medium two if incident ray is in medium one is this And reflected ray in suppose. Let me put it a b c So incident ray i1 is equal to ab and reflected ray r1 is equal to bc So principle of reversibility says that if incident ray becomes bc Then refracted ray will become ab So if light Goes from this direction it will come out in this direction. So it's this is the principle of reversibility. Now, how do you prove it? so You can you can take mu 1 sign i Is equal to mu 2 sin r And you can assume this to be i this will come out to be r So you can assume this to be i now suppose r is equal to i So this i will come out to be equal This i will come out to be equal to r. So mu 1 sin i is equal to mu 2 sin r And if I make mu 2 sin i So this i will have to Make it from other side or sin i1. So from other side this i will convert to r So this is how you prove this Now let me go to refractive index of two mediums with respect to each other So How do you solve it refractive index of two mediums with respect to each other? So let me make two mediums first of all. So suppose this is air And on the other side, this is also air and this i am assuming to be water And this i am assuming to be glass Now there is a Incident ray which falls here So Let me draw a line perpendicular to this So suppose this is this i am assuming to be r So this falls here And due to alternate angle theorem, this will also be r And if this is r So suppose This is theta So this is theta This is also theta And this is or suppose i am assuming to be theta 1. This is theta So let me write snell's log for you. So suppose this is mu a This is mu w This is mu g And this is mu a again. So let me write it for you mu a sin i Is equal to mu w sin r Now for this surface, this is suppose. This is surface number one. This is surface number two And this is surface number three So for surface one, this is the case for surface two, it will be mu w Sin r is equal to mu g sin theta 1 and For third case, it will be mu g sin theta 1 Is equal to mu a sin theta Now try to understand First of all you you you if you equate these three equations What do you get? So what I get is get over here is that mu a sin i Is equal to mu a sin theta 2. It means that i would be equal to theta 2 Now If you understand by this method also that mu w Or let's take mu a divided by mu w is equal to or let me take water first here So mu w divided by mu a Is equal to Sin i by sin r and the second equation is mu g Divided by mu w Is equal to sin r divided by Sin theta There are and and and the third equation I write here mu a divided by mu g is equal to sin theta 1 divided by Sin theta So I have these three equation if you multiply all of them. So what happens is you see here Let me erase it for you. So I multiply all of them mu w by mu a Multiplied by mu g by mu w Multiplied by mu a by mu g and that is sin i by sin r Multiplied by Sin r divided by sin theta 1 Multiplied by sin theta 1 divided by sin theta 2 So What does it give me it gives me that this is this sin r sin r gone Sin theta 1 sin theta and I prove that i is equal to sin theta 2 So this and this this one so mu w by mu a mu g by mu w and mu a by mu g is equal to 1 Or I can say that This I can write as a mu w this I can write as W mu g this I can write as G mu a is equal to 1 So I know that w mu g is equal to 1 by a mu w Multiplied by g mu a So it comes out to be W mu g and whatever I am writing on this right hand side that goes in the numerator Whatever I am writing on the left hand side that goes in the denominator. So mu g w is mu g by mu w as simple as that or Refractive index of the glass with respect to refract Refractive with respect to water. So here I can write that this will come out to be Mu g by mu w will come out to be Mu g because a a will get cancelled out or let me explain this for you once again This I will write as Let me make space here This I'll write as Mu g is equal to 1 by a mu w Multiplied by g mu a so write it down. This comes out to be 1 by Mu w by mu a Into mu a by mu g. So this and this one this mu g goes in the denominator new meter So this becomes mu g by mu w. So Refractive index of glass with respect to water is Refractive index of glass with respect to air if you don't cancel it out This this will become mu g by mu a so refractive index of glass with respect to air And this is anyway mu w by mu a so refractive index of water with respect to air So this is how you have to prove that How to find so you take an example of glass and water as I took in this example And you prove that refractive index of glass with respect to water is Refractive index of glass with respect to air divided by refractive index of water with respect to air So that's how you prove this this thing now. Let me move to Another uh Topic Which is Refraction through rectangular slam so And measurement of later So How to do it? We'll have to make a rectangular slab. So let's make rectangular slab And then let's Let me make a rectangular slab for you So suppose this is the incident ray. This is the refracted ray Is the normal this goes away. So this is my medium one This is my medium two And I am assuming medium one to be air I am assuming this to be glass So this is i this is r This is r And if this is r by principle of reversibility, this will be i Now, how do you measure this? So what happens is this is how later? This is how refraction happens through a slab now. What is lateral displacement? So this is the actual direction of the incident ray And this is the direction of the reflect reflected ray. So I know that from see what happens with this normal here this Incident ray was making angle i I know that with with principle of reversibility because this is r and this is r this has to be i So what happens is that Here also with the normal the final refracted ray means the made makes the direction or makes the angle i it means that the angle or Both these rays the refracted ray and the incident ray are parallel to each other If they are parallel to each other, but they are not coinciding with each other It means that there is some kind of lateral displacement Which is there so to find out lateral displacement I need to find out perpendicular distance between these Two parallel lines incident ray which has been extended in this direction and final refracted ray. So how to do that? So I know that try to understand So for that suppose this this is t So I am assuming that t is equal to Width of slab Now if t is width of slab So I will measure this lateral displacement with help of slab So what I need to do is that I need to find out this particular length. How will I find this particular length? So this is t So try to understand. Let me mark it a b c x So I have to find out cx cx is my lateral displacement ld So for that I am finding out ac. So I am taking triangle, which is a right angle triangle abc So in right angle triangle abc Cos r is equal to ab divided by ac So ac is equal to ab divided by cos r And what is ab ab is equal to t.  So this is how you can calculate the lateral displacement this In your book or most of the book this cos r is written as second r. So you can also write p sin minus r Cos r as second r. This is also true for you. So this is how you can find out the thickness of your lateral displacement sorry lateral displacement in terms of thickness of the Glass slab now factors On which the lateral displacement depends is thickness t because if t changes lateral displacement will change and Obviously in r because on i and r value This this particular thing will Depend on now. Let me move to another slide. So What happens is actually i'm trying to find out that Generally you you see a phenomenon that if a bucket is full of water and and you throw a coin inside it The coin will not look at the depth It is originally at the depth at which it will appear to be would be less than its actual depth Why does this phenomenon happens? So that is what i'm going to discuss in this particular slide So I have defined it by naming it real and apparent depth Because the depth is the the depth at which it is appearing is not equal to actual depth I I I call it apparent depth and how much is the distance between the apparent depth and Real depth that is known as normal shift. So How do we do it what happens is try to understand the phenomenon here the phenomenon is something like this So suppose there is a light ray here and and my eye is here. I'm I'm looking from this particular point So what happens there would be a parallel line which is going and there would be no refraction. There would be One ray which will be going from here and suppose this is water and this is air So light is moving from denser to rarer medium. So it will move away from the Normal, so this is I and this is your And what happens The object will appear to the person standing here at a point from where Refracted ray appears to come from so let's increase the length of this refracted ray So as refracted ray is Coming from here or appears to be coming from here. This particular object O will appear to be at this point O dash this O dash suppose this point is x So this O dash x is known as apparent depth And O x is equal to Real depth So how do you calculate it? So try to understand Now if this is I this particular thing is I and If this is r So with this if with this normal this line is making r. This is parallel to the normal This angle will also be r. So I am assuming this to be r So what happens is So suppose let me make put this point as m. So Sin r Is equal to in triangle Suppose this is O dash in triangle m x O dash Sin r is equal to this mx Divided by this m O dash And in triangle M x O Sin I is equal to m x Divided by Now try to understand if if if this length is very very small if this length is very very small If I consider x mx to be very very small in that case m O dash would be equal to x O dash and O m Would be equal to O x So what I can do over here is that sin r is equal to m x divided by m O dash can be written as x O dash and Sin I can be written as M x divided by O x So what happens is Sin r by sin or Sin I Is equal to Sin r by sin I would be equal to O x divided by x O dash which is O x is actual height divided by Apparent height. So I'm real and apparent. I am writing now the sin r by sin I is mu of water with respect to air Is equal to h r by h a Now let me make some space for you if I write it in other term h a by h r apparent depth divided by real depth would be equal to 1 by a Mu w So this is what the formula that we generally use that apparent depth divided by real depth Sorry, this this would be opposite Here so apparent depth divided by real depth would be equal to So what I have used water here. So would be equal to mu of water with respect to air So this sin r by sin I would be equal to Mu of air divided by Mu of water I can I can prove it. I can write it that mu a here here. It will be mu a sin I That is equal to by snell's law mu r sin mu w sin r So sin r by sin I Is equal to mu a divided by mu w. So Which becomes uh, so if I write Uh, uh, and sin r by sin I is h r by h a so if I write h a by h r This becomes opposite. So this becomes mu w by mu a so this is how you have to prove that That apparent depth is equal to apparent depth divided by real depth is equal to Uh Refractive index of water or glass whatever you are taking with respect to air So this is what the formula is So now what is the vertical shift try to understand so our apparent depth Divided by real depth is equal to mu water. I'm only writing now. Let me find out the vertical shift for you So vertical shift would be Just look at here the vertical shift would be Vertical shift would be if I draw this once again for you So this is your apparent and this is your h r So vertical shift would be h r minus h a So this is suppose This depth I am assuming to be p. So a real height or real depth h r is equal to t So I am assuming h a by h r, which is t is equal to mu So h a is equal to w a or mu ga. So h a is t Into mu a w now you can Substract it and you can find out the formula. So If you subtract it it will come out to be suppose this vertical shift I'm taking it to be x x will come out to be t One minus one by a mu w this is the formula So I'll remove everything and write down the two formulas that we have just proved We have proved that real depth divided by actual depth, sorry apparent depth divided by real depth is equal to mu w divided by mu a or mu w a And vertical shift x is equal to t one minus one by mu a w it is as simple as that Now let me move to lenses. It's already two hours. So let me move to lenses I'll prove the lenses formula and then I and magnification and then I'll finish the syllabus for you So what is the lens formula? Let me go to the another slide So let me go to the lenses. So I will discuss two kind of lenses for you. That would be your convex lens And concave lens so I have Already discussed terminologies and Cartesian sign formula in case of mirror Whatever is would be difference principal focus optical center is same from wherever it has been cut. So this is called as your optical center This draw a line from here and this midpoint is known as optical center for this concave lens Draw a line. This is your optical center now If a line if if if a line parallel to this is principal axis And somewhere here would be or because a line parallel to principal axis will go from focus So this this particular thing becomes your focal length Here it will appear to be Going from focus. So again virtual image and real image situation Which we already discussed in case of mirrors so Cartesian sign formula important terminologies would be same as it was in mirror if it is different somewhere I will discuss that for you Now let me go to another slide So let me prove lenses formula for you So for lens formula what I'm doing is I'm drawing a convex lens for you So suppose this is my convex lens a double convex lens I'm using And this is my principal axis I put an object over here And a line parallel to principal axis Is coming over here now line parallel to principal axis Will go somewhere from the focus And line which passes from center of the curvature will keep on Going through its own path So this is where I find out suppose this is a b this is n and this is a dash b dash now This this doesn't look like what this is. This is a straight line which I'm trying to follow And this is center of curvature. Oh Now I take triangle a b o And triangle a dash b dash o So here a b by a a dash b dash Would be equal to b o divided by b dash o and in triangle Let's let's take this triangle. So I'm taking triangle One second. I'm taking triangle Second triangle that I'm taking is a dash b dash and suppose There is f here.  So a dash b dash o n is replaced by a b and that is equal to b dash f divided by o f So this is my equation number one. This is my equation number two with equation one and two I can write that d o divided by b dash o So now this is this is opposite.  So I'm just taking Reciprocal of it.   So when you are solving it, please write that these are similar triangles and And and and by writing similar triangle use this sign so that similarity is proved So I'm not written here. I'm I'm I'm ending myself I'm I'm showing that these two are trying similar triangles and when you write here you write that You write a line that for in a similar triangle Ratio of corresponding sides are equal. So this is how it has to be Now let me move to magnification so magnification and and there was one doubt in case of magnification which I read in in in in from Somewhere that whether in magnification. So magnification is height of image So let me remove this and let me write it in terms of Height of image divided by height of object is equal to v by u Now everything in this particular formula has to be written with sign convention Nothing here comes without sign convention So if you find that h i is below principal axis, I will write it minus h i and not h i If h o is positive, I'll write h o if v comes out to be negative I'll write minus v u is negative. I'll write minus u. So nothing is without sign convention You cannot write anything without sign convention. It always comes with sign convention Now what is power of lens so power of lens is 1 by f f is the focal length of the lens and f is always in meters Generally f wherever you have to find power of the lens f is not given in meter. It has been all it It is always given like 25 centimeter 20 centimeter and in hurry. We just write it 1 by 25 centimeter as power of lens Which is absolutely wrong. So when you solve these kind of things in in in examination Don't do this. You should just write 100 by 25 because if you are converting it into centimeter So the other formula is 100 by f into centimeters or 1 by f into meters. So that's how you solve these kind of trickier things. They are not difficult, but they are made trickier By changing the unit Over here. Now what happens if different lenses are kept over here? So power would be added So if five lenses are there and powers are p1 to p5 Power of all the lenses combined would be p1 plus p2 plus p3 plus p4 plus p5 So this is what The formula is Now in case of try to understand guys in case of convex lens The focal length is positive. So p divided by 1 by f. This is positive It is in terms of meter. So p would be positive. Now. What is the unit of power? This is diopter So unit of power is all is is is is known as diopter And It is denoted by word d So for convex lens power is positive for concave lens as f is negative So what happens is p divided by 1 by f, but as this f is negative So power comes out to be negative. So And if if negative power you see somewhere, you should understand that this is a For concave lens and if positive power you see somewhere you should find that this is convex lens So I'll discuss all these things negative power and and and positive power when I'm discussing optical instrument in a different class for together I've kept a different session for optical instruments. So Optical instruments, I'll explain why power positive negative where it is used and all these things So now let's go to next slide. I have already derived magnification and lenses formula for you. So Now let's go to total internal reflection and this is the This is one of the last topics now. What is total internal reflection? So first criteria for total internal reflection is That Light should it is it is first of all a refraction phenomenon and The criteria is light should go from denser to rarer medium so Let me draw a line here. This is a denser medium And this is angle of incident i so light Goes away from the normal Now there would be a value of i for which r becomes 90 degree and that Value of i will be known as critical angle. So what is a critical angle? I see is that value of i for which r becomes 90 degree and the total internal reflection Start coming into picture So what happens is that if i if i is greater than i see then the light rays start coming back to the same medium And that is total internal reflection reflection. So If you have to define total internal reflection It has to be demonstrated like this. So i will use apply snails law for this So suppose this is mu 1 and this is mu 2 So mu 1 sin i is equal to mu 2 sin r So mu 1 sin ic and at value of ic r becomes 90 degree. So this becomes sin 90 So mu 1 sin ic Is equal to mu 2 I can write that mu 1 by mu 2 is 1 by sin ic So it means that What is mu 1 by mu 2? So refractive index of this medium with respect to another medium So i am writing it by mu. So mu is equal to 1 by sin ic This is And what is sin ic critical angle? So refractive index is equal to critical angle So there are different phenomenons or there are different application of refractive So total internal reflection one is optical fiber people are examiner ask why Total internal reflection and not reflection. So because total Internal reflection is a phenomenon Refraction. So what happens? There are two two conditions or there are two things which are very important in case of total internal reflection which makes is makes it better than The actual reflection first is in case of normal reflection A lot of light is absorbed by the surface from where it is getting reflected So intensity of the light gets affected in case of total internal reflection Intensity of the light remains same because the total light is internally reflected There is no absorption over there or minimal absorption over there. The second thing is that in case of Normal surface where it is getting reflected if there is some kind of dust or some kind of impurity Due to that the reflection phenomenon doesn't happen properly And due to that also intensity of the light gets affected The reflection is not proper in case of total internal reflection as the medium is same And and the light doesn't doesn't go out. The problem of dust mist for Any other minot particle can be neglected and due to this The reflection happens very properly. That is why total internal reflection is preferred in in example Optical fiber and not the normal reflection. So if you write these two three points, you should get proper marks So with this I come to the end of this particular Topic optics now optical instruments are left out that would be covered in Next session and If you have any doubt you can post it on our Our website you can post it. You can message it to our numbers center academy number and You will get a specific or you if you have any doubt you send it to our number We'll make videos for that and we will send you solution of all those Problems or doubts that that are there with you. So don't hesitate in sending Your doubts to us. So thank you so much for attending this session


David Navarra drew with Wesley so on the top board in round five of the Gibraltar Masters. Let's find out what happened David you were up against Wesley today. Tell us about the game Okay, I misplayed the opening somehow and the position remained equal, but Black's position was easier to play because I had Vulnerable center points and needed to play carefully in order not to lose one of them Well, I believed to be able to defend my position, but just defend it. I mean I didn't perceive it being equal because I Understood I had to play carefully But I believed I should be able to do in that. Now you were playing with white Could you tell us what was the critical moment where you probably lost a bit of control? I think my F2F4 push was quite optimistic and Afterwards it remained perhaps objectively equal, but somehow I needed to Take care to maintain the balance Right you're on four and a half out of five pleased with the way things have gone so far Okay, I haven't expected such a good start All the more because last year I played just terribly most of the quite many games And okay, I hope to score well in the second half of the tournament. We will see Now tonight is also the big night of the battle of the sexes. Are you looking forward to it? I will go there to get a free dinner I'm sorry. Okay. I'm living in another hotel and Have just a breakfast. So I am looking forward to it But I don't know if I take part if so then just in one game All right. Well, we wish you all the best with the remaining rounds and hope to have you back in our studio. Okay. Thank you


Let's revisit the accounting cycle. Notice that step five relates to adjusting journal entries. So question, why adjust account balances? Why do they need adjustment? Adjusting entries are necessary because the unadjusted trial balance may not contain up-to-date and complete data as you've learned when you studied the unadjusted trial balance. Adjusting entries update asset and liability accounts as well as revenue and expense accounts. Without this adjustment, our financial statements could mislead investors and creditors. Finally, adjusting entries help ensure that the revenue recognition and matching principle are followed. So let's look at an example. A company buys $500 of supplies during the month. At the end of the month, the unadjusted trial balance shows $500 for supplies. Is $500 the correct amount? Isn't it likely that the company has used some of the supplies? Yet no one wants to make a journal entry each time someone takes a pen or staples some papers. That would be a horribly inefficient use of time. Yet pens were used and papers were stapled and those things need to be accounted for. So this is why accountants record adjusting journal entries at the end of the period. Failure to record the adjusting journal entry to adjust the supplies account would result in an overstatement of assets, meaning too much money in assets and an understatement of expense, too little supplies expense at the end of the accounting period. Overstatement and understatement are two concepts students struggle with. They definitely require critical thinking about the transactions to figure it out. So when we make adjusting entries, there are two main types of subcategories. One is deferrals and the other is accruals. One type of deferral is prepaid expenses. This means that cash is paid before expenses incurred. Some common examples of adjusting entries for prepaid expenses are prepaid rent, supplies and depreciation. Another type of deferral is unearned revenue. This means that cash is received before revenue is earned. Some common examples of adjusting entries for unearned revenues are unearned rent revenue, season ticket revenue, airline ticket revenue, like that. An example of an accrual is accrued revenues. This means that cash is received after revenue is earned. Some common examples of adjusting entries for accrued revenues are service revenue and interest revenue. Another type of accrual is accrued expenses. This means that cash is paid after the expenses incurred. Companies tend to have a lot of accrued expenses as this is the most common type of adjusting entry. Some common examples of adjusting entries for accrued expenses are salary expense and interest expense. Finally, let's look at some characteristics of an adjusting entry and how they differ from a regular journal entry made in the ordinary course of business. The first is that there is no underlying business event that causes an adjusting entry to happen. They happen most often because of the passage of time or that information isn't available in the period we need it. They are recorded at the end of the accounting period. So adjusting journal entries will be dated at the end of the month. They will always include one income statement account and one balance sheet account. Again, this requires some critical thinking, but you can usually figure out the accounts affected by an adjusting entry by remembering this. And finally, they will never, ever, never, ever, ever include the cash account. At some point, you are going to be really tempted to use the cash account when doing an adjusting entry. Please don't, it is certainly wrong. Now, I will say that there is an exception to this and that is when we are doing adjusting entries from the bank reconciliation. But that's not what's happening in this context, so don't use cash. They are required every time a company prepares financial statements. Look at the steps here. You can't do step seven, prepare financial statements without first doing step five, journalize and post adjusting entries.


Hi everyone, Joe for jaspyscasewrakes.com coming at you with 2020 Leaf Metal Draft Football College Footballer and their college gear. Five box, serial number break, number five. Pro tip works just like our random number block breaks. Big thanks to these folks right here and there are the numbers right there. Let's roll it and randomize it. Five and a six, eleven times for each list. What? And eleven in the final time. Joe P, last spot mojo star in his name on the pole and Brady in the tenth spot after eleven. Eleven times for the numbers and eleven in the final time after eleven we've got seven down to zero. Zero gets any and all redemptions. Brady including one of one redemptions. The only redemption I know of is Chase Young which is pretty nice if he's in here. Joe you got seven, Ron with five, Nick with six, Max with four, Matthew with three, Stephen with nine, Marlon with one, Matthew with eight, Joe with two and Brady with zero. Let's order these by number. Any trades and like I said before I just grabbed five random boxes off the pile of boxes right there so there you go. I don't think there's going to be any trades. Did that sell out Ryan? All right I don't think there's going to be any trades so let's close up the trade window. Three once in a while we'll see a number block, a number get traded but not this time. Five stars super close, it is super close. All right nice. We might be able to slot that into the time slot after flawless because I think that's probably, we'll probably sell it shortly. All right there you go ladies and gentlemen. Thanks for getting into it. Another five boxes will be posted. We've got JJ Taylor, three out of ten that'll go to Matthew and if there's any non-numbered cards we'll just randomize them individually like so if there's like two non-numbered cards then I'll randomize it to the group. Name on top we'll get the first one I pulled, second name we'll get the second one I pulled. There's Jerry Judy by the way. He's pretty good. Fourteen out of fifty, Max with number four. My college knowledge not super strong with these players but I at least know Jerry Judy. Ten out of twenty-five Ryzen Hopkins that goes to Brady with number zero. Jalen Hertz, I've also heard of him, nine out of fifty that goes to Stephen Cohen, number nine. CD Lam, Jerry Judy and CD Lam in the same box, fifteen out of fifteen Ron Hollins number five. Hi Colleen Wolfe. We are notable invited prospects ladies and gentlemen some of which we'll find in here. Joe Burrow, Jalen Hertz, Chase Young, Jerry Judy, Jonathan Taylor. There's Albert Okuenubam, Okue Bonham, close two out of ten Touchdown Kings that will go to Joe P. We've got Cam Akers, thirty out of thirty-five Brady with that zero. Henry Ruggs, eight out of fifteen that will go to Matthew. We've got T Higgins, twenty-six out of sixty. Another Jerry Judy, Touchdown Kings and that is one out of two. Wow Marlon with number one all aboard the Big Hit Express. Oh not this again Stephen Punk. Stephen Punk thinks that Joe Burrow is going to be the next Ryan Leif. Who agrees? Who is actually on Stephen Punk's side on this one? Maybe they don't want to get shamed. Only Stephen Punk is bold enough to make that hot take. Anyone else on his side? There's James Morgan. That will be five out of fifty. That will be for Ron. We've got Tenacious D, Claiborne Chasen, twenty-two out of forty that will go to Joe P. And the number two. We've got Kendrick Rogers, twelve out of fifteen. Joe P with number two, there you go Joe. Armed and Dangerous. I've got Jacob Eason back there. Stephen Montez, armed and dangerous. That will be three out of forty Matthew with number three. The Jacob Eason is twenty-two out of twenty-five that will be for Joe P and number two. Derek says Tua is going to be the next, the best QB in the class. Riffer thinks Tua is going to be the next Ryan Leif. What does everyone else's thoughts? We've got Colin Johnson, four out of fifteen, Max, number four. State Pride, Troy Dye, one of my favorite inserts, twenty-one out of fifty that goes to Marlon. We've got Cole McDonald, seven out of twenty. Joe P, last by Mojo. Oh right, this guy's another Redemption, Jeff Okuda goes to zero, Brady with the Redemption. And we've got Jake from State Farm and that is two out of seven. That's for Joe P. Number two. What about this guy? Do we like this guy? I hope he gets you after the first round so we can get that State Farm money. Or here's another spicy take, advertising take. What if someone else other than State Farm gets him and then makes fun of State Farm somehow? Start like a little friendly rivalry, insurance rivalry. Stephen Pong saying Joe Burrow is going to be like Mitch Trebisky. Jayvon Kinlaugh, twenty-eight. Stephen Pong also thinks Paris Campbell will have twelve touchdowns this year too. Double digit touchdowns. There's Julien Okwara, three out of sixty, Matthew. Jake Fromm again, Jake Fromm State Farm, fourteen out of fifty, so Max, number four. There's Isaiah Simmonds, Snacious D. He could be yanking the chain a little bit, Joe. Brady with zero. Is that sold out? Yes. Yes. All that. And the last one here is Jalen Hurts. Jalen Hurts going to number six. Six out of ten. That goes to Nick T. With number six. There you have it, ladies and gentlemen. Fun little break right here. This is good. This helps me learn these college players as we're leading into the draft, which is what? A week and a half away, two weeks away, so that should be a lot of fun. Thanks for watching everybody. Go for Jasper's Case Breaks.com. We'll see you next time for the next break. Bye-bye.