Ray optics class 12 | Reflection of light |

Added: 2026-05-06

[00:00:01]my dear students we shall discuss about the basic concept of reflection and deviation because of single mirror you have taken a single mirror light Ray is incident and reflected back okay so this is called as this is called as incident Ray this is called as reflected ray okay angle made by the incident Ray with the glass with the mirror is taken as angle of glancing or glancing angle so G and G are said to be glancing angles here okay this angle of incidence angle of reflection now let us see here what is going to happen so now here uh let us discuss some of the concepts which we are going to learn today so here this is angle of incidence this is angle of glancing angle of incidence plus angle of glancing is always equal to angle of reflection plus angle of glancing and this these two are combined together always 90° some of these because this is normal these two are 90 these two are going to be 90 same okay now so here what are the properties of reflection first thing is always angle of incidence angle of reflection both are same okay that means if both are same then incident glancing angle and reflected glancing angle are also going to be be same these two are going to be same now let me discuss about deviation because of a single mirror what do you mean by deviation because of a single mirror this is called as deviation light R has to travel like this but it is reflecting in this way and that's why this is called as a deviation now we shall discuss about what is this deviation to understand the deviation first thing is this angle plus this angle plus deviation I + r + Delta = 180° okay I + r + Delta is equal to 180 and you all know angle of incidence is equal to angle of reflection so we can take I + I + Delta is = 180 so Delta this I + I is nothing but 2 I so therefore we can write this as 180 we can write this as 180 - 2 I okay Delta is equal to 180 - 2 y this is going to be the deviation okay my dear students we shall discuss about deviation because of two mirrors let me discuss there are two mirrors this is mirror M and M dash one light Ray enters in this direction okay this is set to be P Q R and S it enters like PQ QR and rs it exits now he's asking us to find out what is the deviation what do you mean by deviation it is entering it is entering from here and exiting from here it is entering like this and exit is in this direction and that's why that is going to be the deviation here so we need to find out the deviation let us consider this angle is going to be exterior angle external angle no let us imagine this is alpha alpha Dash and Alpha this is beta beta Das and beta already I told you one thing what is that a light Ray incident and it reflects okay now this is going to be the normal I said this is said to be glancing angle this is said to be glancing angle and this is a mirror and angle of incidence and angle of reflection are going to be same here glancing incidence and glancing Reflections are going to be same here so these two angles always same you just remember that one okay so let us see what is going to happen now so in this case here you can take Alpha + Alpha Das + Alpha is = 180° so these three angles are 180° because this is a straight line so can I write Alpha Das is = 180 - 2 Alpha because Alpha plus Alpha is nothing but 2 Alpha here okay so Alpha Das we got it as 180 - 2 Alpha similarly we can write beta + beta Das + beta is equal 180° because this is going to be the straight line here then we can write beta Das is = 180 - 2 Beta okay you just remember these two things here you have to remember these two things you have to take into consideration these two things here now one more thing here we have to understand is you can just see exterior angle is equal to this exterior angle is equal to sum of interior opposite angles that is Alpha Dash plus beta Das exterior angle is equal to sum of interior opposite angles therefore you take ex angle Alpha Dash can be taken as 180 - 2 Alpha okay plus beta Das can be taken as 180° - 2 bet so what are going to consider now exteror angle so exterior angle become 180 + 180 is nothing but 360° here common out two here you'll be getting how much if you common out two here you'll be getting Alpha + beta okay now if you consider here in this case we all know alpha alpha + bet + Theta these three angles is going to be 180° so can I write Alpha + beta is equal 180- Theta this is equation number one this is going to be two I'll substitute 2 in 1 let me see what I'm going to get now two I'll substitute in one let us see what is going to give me this is here so exterior angle is equal to 360 I will write minus okay 360 I will write here 2 into Alpha + beta means it is going to be how much 180- Theta here I'll be writing 2 it is 180- Theta so therefore xra angle is equal to 360 2 into 180 is again 360 - 2 Theta I'm getting 2 Theta I'm getting 2 into th 2 Theta 360 360 gets cancell so exterior angle how much I'm getting now this exterior angle I'm getting it as 2 th but my aim is to find out the deviation how I'm going get how I'm going to get the deviation now so therefore deviation Delta is equal to total is 360 total is 360 I'm substracting E from 360 if i substract e I'll be getting Delta so 360 minus extra angle so therefore deviation is equal to 360 minus E is nothing but double always exterior angle is double to that of angle between the two mirrors isn't it if Theta is 60 exterior angle is going to be 120 there is one previous year question regarding this also so this final step you have to remember now this is our final step which you have to remember here so deviation is equal to 360 minus to here thank you very much my dear students this is a previous year question regarding reflection you can just see these two mirrors are there om and op light Ray enters from here PQ it strikes the first mirror then reflects strikes the second mirror then reflects and comes out it comes out along the direction of RS so PQ RS is the direction of light and and now when the light Ray incident on the first mirror this is the second mirror it incidents with an angle Theta it takes double Reflections and comes out and it is said in the question that what it is said the reflected ray is parall to the first mirror this mean this is the first and this is second after taking two Reflections the light R which is coming out which is set to be RS it is going to be the parallel to om this is going to parallel to om that is the question here if these two are parallel then what happens let us see here now when these two are parallel this is said to be 70° why it is 70 these two are corresponding angles if this is 70 this is also 70 these are called as glancing angles and they are going to be same let me discuss what is the meaning of glancing angle for example this is a normal this is a mirror here a light R strikes in this direction and reflects back angle of incidence is there angle of reflection is there this is said to be glancing angle this is also said to be the glancing angle these two angles are same always you just remember that concept that means these two are going to be glancing this is taken as normal here okay so therefore these two are glancing they are going to be same and he's asking us to find out Theta here let us see here now this is 70 70 it is going to be 140 and what is this remaining angle we should find out now this remaining angle is nothing but 180 - 140 because angle sum property the sum of an angles of a triangle are going to be 180° 70 70 plus some other angle here this is question mark these three combined together should be 180 that is said to be ASP angle some property let us see what is going to Happ if you want to find out this one substract 180 with 70 + 70 is 140 getting 40 here that means what is this going to be we got this as 40 we got this as 40 that means If This is 40 this is also 40 because of glancing angles glancing angles are same now let us see 40 and 40 and this is the normal that means as this is normal Theta + 40 should be equal to 90 this plus this should be equal to 90 that means Theta will be 90 - 40 that is taken as 50° so therefore that is going to be your correct answer your correct answer is going to be 50 that is this one hope you enjoyed this lecture regarding previous year for full lectures download the app which is given in the description thank you my dear students this is a previous year question of a mirror shifting now this is an object and this is a original position of a mirror the distance is 12 CM that means from an object to the mirror and the mirror to the image the distance is going to be same that means this is 12 means that is also 12 if the mirror is shifted 4 cm how much distance the image is shifted that is the question Here My Dear from here if it is shifted 4 cm now the new distance from the mirror to the object is reducing by 12 - 4 that is going to be 8 cm okay that means from the mirror to the image also it is going to be 8 cm that means now the image will be here image is shifted from I to I Dash okay that means how much is image shifted means actually the total distance is 24 cm now the new distance from the object and the new image is going to be 16 cm that means 12 - 16 12 - 16 sorry 24 - 16 gives you 8 cm that means the image is also shifted how much 8 cm from here to here thank you my dear friends how to find out the time in the image of a clock when in the object the time is going to be 9:27 a.m.

[00:13:08]then what is the time shown by the image of a clock because of the mirror this is a case of lateral inversion the watch appears to be laterally inverted then what is the time in the image of a clock for that the simple method which will eliminate all the confusions is 12 hours can be written as 11 hours 60 minutes because the 60 minutes if you add here it becomes 12 hours again so what you have to do this time you have to subtract from here that means 9 hours 27 minutes if you subtract from instead of writing 12 you write 1160 then what happens let us here now so it is going to be three so here it is five again three so therefore from here if you subtract you'll be getting how much two okay so therefore the clock is showing 233 okay it is showing 233 that's it my dear friends this is a case of deviation how to find out the deviation when the light Ray when the incident Ray makes angle 30° with the normal if this is 30 this is going to be 30° he's asking us to find out the deviation okay what is the meaning of deviation actual path of the light Ray is this one but the reflector is moving in this direction so how much it is deviated from the actual path this is an actual part it is deviated in this direction how much is going to be the deviation so for that you should know one thing here so 30 + 30 + deviation is equal to 180 so therefore deviation is 180 - 60 which is nothing but 120° this is one question then let us go for the next question so in this question uh a light R strikes the mirror at an angle of 30° is with the mirror previously it was making with the normal 30° but it is making with the mirror because this is going to be the mirror okay so this is going to be the mirror with the mirror it is making 60° means with the normal it is going to make 60° this is 30 means this is 60 because Normal means some will be 90° normal is nothing but 90° so this is 60 means this is also 60 okay so here the total if you consider 60 + 60 plus deviation is 180° because this is a straight line which is making 180° therefore deviation is equal to 180 - 60 + 60 is nothing but 12 our answer is going to be 60° so this is going to be your answer hope you have enjoyed my dear students let us discuss this problem which is given in the previous year questions he is giving the two mirrors M1 and M2 and the angle between them is Theta and we have to find out that angle Theta it is said in the problem that one light Ray PQ enters in this direction in such a way that PQ is parallel to om2 here PQ is parall to it enters like this it takes single reflection again it takes double reflection it comes up like this and while coming out these two are parall that means this mirror M om1 and rs are going to be parallel here in such situation he's asking us to find out this angle Theta how should we find out this angle Theta here for that as these two are parallel okay if this is Theta this is also going to be Theta here this is said to be corresponding angles if this is Theta this is also Theta because these two are called as glancing angles or angle of glancing and similarly these two are parallel according to the problem if this is Theta this is also going to be Theta because of corresponding angles if this is Theta this is also going to be Theta because these two are called as glancing angles and we have discussed about glancing angles already if this is the normal a light Ray enters strikes and reflects back like this and this is going to be the mirror here this is going to be the mirror so this is angle of incident this is angle of reflection these two are called as glancing angles and they are going to be always same in a concept of reflection so therefore these two are same these two are same because these are just like glancing angles here now these three angles are Theta + Theta + Theta they are going to be same and they are going to be 180° this is set to be angle sum property that means sum of angles in a triangle is going to be 180° therefore 3 Theta is = 180° and therefore Theta is = 180° by 3 which is nothing but 60° so this unknown angle the angle between the two mirrors is going to be 60° that you have to remember now let us go for the next problem here in this next problem it is said that the angle between the two mirrors is going to be 75° and the light is incident in this direction that is p q and R and in this direction it is coming out okay and it is given that it is 30° in the problem itself and what is's going to ask he's asking us to find out what is the total deviation okay so how are you going to find out the total deviation for example uh this is the light Ray which is this is the light Ray which is going to enter like this and this is the light which is coming outside like this okay entering in this direction exit so this total angle is set to be angle of deviation and we have already given the derivation for angle of deviation for two mirrors at certain angle the angle of deviation is going to be Theta isal to 360 I mean Delta is equal 360 - 2 Theta Delta is said to be deviation which is 360 - 2 Theta where Theta is the angle between the two mirrors therefore Delta is = 360 - 2 into 75 it is nothing but 360 minus 2 into 75 is nothing but 150° so therefore which is going to be 210° C hence we got the solution for this type of reflection problems thank you my dear students let me discuss a super simple shortcut for this type of problems which are regarding concave mirror this is a concave mirror object is placed at 15 cm whereas he has given us the radius of curvature he has given us the radius of curvature and what is going to be the radius of curvature radius of curvature is 40 cm if the radius of curvature is 40 cm then focal length is going to be half of the radius of curvature that is 20 cm and now object is placed at 15 cm first and then it is placed at 25 cm okay so if object is placed at 15 cm you may get the image somewhere here and if an object is placed at at 25 cm you may get image somewhere here okay so let us see what is going to happen you have to find out the distances between the two images you find out the distance between two images according to this problem yeah so let us see what is going to happen so for this I'll tell you a simple concept you all know 1 by f is = 1 by V + 1 by U this is a mirror formula I know concave mirror means this is minus and this is also minus that means 1X V is equal to 1 by u - 1X F so 1 by V IS = F into U by Fus U that means V is going to become F U by Fus U you can use this shortcut formula you can use this shortcut formula to find find out the solution okay now let us see what is going to happen first of all he has given you one as 15 cm substitute in this formula that is V is equal to FU by f- U this is U1 so f f U1 by f - U1 f is 20 20 into 15 by 20 - 15 that is 5 okay so you'll be getting answer at 60 M this is called as object distance V1 second object distance you to find out V2 and how much it is going to be F U2 by f- U2 okay so if you sub you'll be getting how much 20 into 25 by 20 - 25 okay so this is 20 into 25 / - 5 so we getting how much - 100 cm you are to subtract these two V1 minus V2 how much it is going to be it is 60 minus of - 100 you'll be getting as 160 as an answer 160 cm is going to be your answer that's it so what is the shortcut formula shortcut formula is this one F U by Fus U if you remember in two stages you'll get the answers you just substract them final answer is going to be 160 cm hope you enjoyed this shortcut formula thank you very much my dear friends this is a neat previous year question asked in 2020 what is the detailed explanation about this problem here so there is a con mirror whose principle of focus and center of curvature here it is said that object is placed at a distance of 1.5 F that means this is F this is a focal length and this is going to be 1 5 F object distance is 1.5 F and he's asking us to find out what is an image distance if this is an object placed between principal of focus and center of curvature image is beyond C if object is between F and C image is beyond C that means it is greater than object distance how are you going to find out an image distance with a simple shortcut formula let us first create what is a shortcut formula here so that is 1 by f is = to 1x V + 1 by U this is called as a mirror formula now as focal length is going to be left side it is considered to be negative here object distance is left side it is also considered to be negative whatever you are going to find out that is image distance you should not consider any sign conventions because answer will tell you the sign convention answer will tell you the sign convention only at if you have to say convention you have to take sign conventions at U that is object distance but image distance you do not take any sign convention because answer will tell you that it is at left side sign convention is given by the answer now let us see so here 1 by minus F here you need not so this is minus sign you have to consider because left side so now 1 by V is equal to this comes to left side becomes positive 1 by F so 1X V is equal to LCM UF which is nothing but Fus U therefore image distance can be taken as F U by Fus U this is going to be your structed formula whenever you want to find out the problems of this type you can just remember this formula need not write all the process and sign conventions can just write F U by F minus U you'll be getting the answer directly in a super simple way so what is f f is f what is u u is 1 1.5 F / f- u f - u u is 1.5 F so this is 1.5 F ² divided by - 0.5 because f - 1.5 is going to be 0.5 that's it so here are we getting now see this is one time it is going to be three times here already one f is there f f Square gets cancelled so therefore V is going to be how much this minus comes to left side I mean upwards that is your answer is minus 3F is going to be your correct answer hope you have enjoyed this problem thank you very much my dear studs this is a rotation of a mirror what happens in the rotation of a mirror concept let us see this is a mirror it has been rotated through an angle Theta if it is rotated through an angle Theta how much angle the reflected ray is rotated that means when the mirror is in this horizontal Direction then this is incident Ray this is reflected ray this is normal but when the mirror has been tilted through an angle Theta then instead of this light Ray coming outside you'll get this light Ray and normal is not n now the normal has been changed to N Dash when the mirror is tilted normal also gets tilted through an angle Theta here and he is asking us to find out what is r what is r q r not he's asking us to find out this angle so how are you going to find out this angle R QR Das very simple what you have to do here is you have to find out for example you have to find out this R QR Dash then you have to take pqr Dash this pqr Dash and subtract in this pqr Dash you have to substract pqr this angle pqr then what happens let us see here so angle pqr Dash is nothing but from here to here if this is angle of incidence this is angle of incidence and this is angle of reflection both are going to be same this is I means this is also I when this is called as pqr incident R is I and reflected ray is I but when the angle is tiled by the mirror to angle Theta then normal gets shifted then now the new incident Ray will become I + Theta here from here to here I + Theta from here to here I + Theta so I + Theta I + Theta is going to be how much I + Theta and I + Theta because he has ask us to find out pqr D so pqr D is nothing but I + Theta and I + Theta which is nothing but 2 I + 2 Theta and you have to substract pqr P QR this is I + I which is nothing but - 2 I so 2 I 2 I gets cancel what is left 2 Theta is left that means this angle is taken as this unknown angle is taken as 2 Theta okay based on this concept there is a previous year question let us see here so this is a question here when an angle of the mirror is rotated through angle Theta then the light which is coming and falling on the mirror it gets reflected through an angle 2 Theta 2 Theta then he's asking us to find out what is this angle Theta given by so let us take this diagram as a sector let us imagine to be a small part of a circle sector then in this this is 2 Theta is written like this and this is X and Y and you know according to mensuration and geometry AR of a sector is nothing but radius into angle what is the arc here AR is nothing but Y and what is radius which is nothing but X and what is an angle here which is nothing but 2 Theta here okay so this implies that Theta can be taken as y by 2x y by 2x your option is going to be D hope you have enjoyed my dear students this is a previous year question asked in me 2018 okay there is a simple shortcut to solve this problem which is very amazing here let us see what is the shortcut here first of all try to understand here this is a concave mirror and the object is placed at a distance of 40 cm from the pole of a mirror this is going to be the pole of a mirror and here focal length of a mirror is going to be just 15 cm now if this is an object distance which is taken as U1 which is 40 cm here 40 cm and slowly it is say the problem that object has been shifted towards the mirror then what happens to the image you should know that when object is shifted towards the mirror image is moving away from the mirror that means it should be away from the mirror that we know already but what is the value that we have to find out for that there is a simple concept which should have to remember here let us see what is that concept here you all know there is a mirror Formula 1 by V + 1 by U for a concave mirror focal length is left side you know for a concave mirror focal length is left side that's why it is taken as negative and object is also placed left side that's why it is also taken as negative so let us see what is going to happen now we can write this as minus f 1 by V this is also taken as minus U is minus f is minus focal I mean image distance which you are going to find out you should not take s conventions because for image distance you should not take any sign convention because answer is going to tell you the sign convention you need not take from your side answer will tell you what is the sign convention let us see what is going to happen now from this it is understood that 1 by V is equal to you take to this left side 1 by u- 1 by F or 1 by U this is f u and this is f minus U so therefore V is nothing but F U by Fus U this is a shortcut formula to find out the image distance [Music] now let us solve the problem so this shortcut formula we can use to solve this problem in a super simple way what is that let us see here now by using this shortcut here by using this shortcut here we can write now F U1 by Fus U1 that is previously it was at 40 cm now it will be moved now it will be move a little bit aside which is now it is taken as U2 is equal to 20 cm because when you shift it towards 20 the remaining part is going to be 20 cm so previously when the object distance is taken as 40 cm you substitute in this formul getting how much F U1 by Fus U1 if you substitute that is focal length is 15 and object distance is 40 now when has been shifted new object distance is going to be 20 so this formula U by Fus U you have to apply two times first when the object is at 40 cm next when the object has been shifted to 20 cm then this is going to the formula so now we'll be getting 50 into 40 by 50 - 40 is going to be - 24 cm now in the second it has been shifted you'll be getting 15 into 20 by 15 - 20 which is going to be - 60 cm now you have to find out the difference - 60- of -4 gives you the net displacement that is Delta V how much the image has been shifted it is going to be - 60- ofus that is 24 okay so 24 is going how much - 36 CM minus indicates that it has been shifted away from the mirror okay it is been shifted away from the mirror your option is B option hope you have enjoyed this problem thank you very much my dear studs let me make you understand the previous year problem we first asked in neat here that is 2016 this is a conceptual question and I'll tell you a simple logic to understand this conceptual question what is the logic behind this he's asking us to find out the magnifications and compare with the concave lenses concave mirror or concave convex mirrors so magnifications and mirrors you have to compare here a simple and smart logic which you have to understand here is you have to remember just one thing that magnification is nothing but height of the image by height of the object and there is one simple logic that this is taken as the origin what is this this is considered to be the origin of a mirror according to sign conventions so whatever is coming upwards it is positive and what is going to be inwards that means inward that is going to be negative that's it so this is positive inverted is negative a simple logic is enough to understand almost all the problems of this type so what is going to happen here here in this case this is a virtual image whenever an image is formed behind the mirror it is going to be definitely virtual image it cannot be caught on the screen so what happens here now as you know that this is the formula magnification is equal to height of the image by height of the object object here in the case of virtual image whenever the image is form behind the mirror you should remember that both are going to be positives okay so both are going to be positives here this is positive this is positive both are erected images both are erected images both are positive so magnification is going to be positive for virtual images you have to remember that virtual images so here that means how many are positive cases here m = + 2 m is = +2 so here in the case of a concave mirror you should remember that definitely definitely definitely image is going to be larger larger than the object whereas in a convex mirror image is definitely going to be smaller than the object when the image is smaller than the object magnification will be less than one when the image is greater than the object magnification is greater than one because when the numerator is larger than the denominator you'll be getting greater than one when the numerator is lesser image is lesser than the object you'll be getting magnification less than one that means it is understood that this is a case of a con cave mirror and this is a case of a convex mirror Vex xam convex okay that you have differentiated so negative signs indicates that these are real images these are virtual cases these are virtual cases whenever magnifications becomes positive these are said to be virtual cases why in Virtual case only you'll be getting erected images a very beautiful application I'm going to tell you now okay so in Virtual cases only images are erected so magnification is going be positive and these two cases are taken as real cases because you are getting negative sign why negative sign because when an object is placed here you'll be getting image here in the case of inverted image you'll be getting magnification is equal to height of the image height of the image by height of the object object is inverted object is erected so positive image is inverted so negative here so in these cases of real images you will be getting magnification as negative so here both are taken as real cases here both are taken as real cases now just it's very simple when you understand these two Logics it is very simple to match the following here no you just here it's very easy if you understand these two Logics that what is going to be the correct option here correct option is going to be the a option how can you say a option here let us see see p means M isal -2 -2 indicates it's a real image so when it is a real image and that two magnified image because it is greater than one real and magnified so B and C what is B here concave mirror this type of magnifications comes to concave mirror and what else is B and C C is going to be the real image it's correct now so Q is -1 by2 - 1x2 means here - 1x2 real images will get for only concave mirror not a convex mirror convex mirror goes gives you only the virtual image it is not going to give you any real image so therefore plus two means q q means what I'm going to get now b b means concave mirror c means it's going to be a real image but the image size is lesser than the object size so when the image size is lesser than the object size you'll be getting less than one I said these two Logics is very useful to understand now M = to +2 what does it mean here M = +2 means it's a case of a it's a it's a case of a virtual image now so here what is going to be B and B so b means what is a case of a concave mirror concave mirror plus two yeah so concave mirror and also what else is giving r isal b and d d means virtual image yes it's a case of virtual image because you're getting positive signs here now let us take what is plus half M = to+ half means what is the meaning here now let us see so plus half means what are what is going to give you s s equal to a and d a is what convex mirror because it is a virtual image and the image size is smaller than the object if it is a virtual image an image size is smaller than the object definitely it is a case of a convex mirror so like this you might be understanding each and every point which I have discussed in a super simple way thank you very much have a nice day two mirrors are kept at certain angle Theta that is 60° to the other and the body is placed at the middle then total number of images formed are how much okay so this was a question here so to understand this question you should have certain Basics here let us take the two mirrors which are kept like this two mirrors which are kept this making certain angle I have taken one mirror I have taken the other mirror okay so here also one mirror is the other mirror now let us see this one so this is exactly bisecting exactly bisecting and let us take the second case where it is not bisecting okay so let us take this making now just here I told you that this total angle is Theta that means this is Theta by 2 and this is Theta by2 object is placed here this is an object so this is the case where object is at symmetry symmetry means exactly the bis sector now in the second case the object is placed here object is at asymmetry asymmetry is nothing but it is not symmetry so even though the angle between the two mirrors is Theta this is Alpha and this is beta Alpha is not equal to Beta Alpha is going to be not equal to Beta here so as Alpha is not equal to Beta let us see what is going to happen understood so these two cases you are going to see here now if 360 by Theta is uh yeah even and second is odd okay so what is going to happen if it is even n is = 360 by Theta - 1 if it is odd n = 360 by Theta okay so if it is even then you have to subtract minus1 if it is odd you have to take 360 by Theta understood this is the main condition then what is the sub condition here here the sub condition let us discuss here now what is going to be the sub condition if 360 by Theta is odd then again what happens you know symmetry asymmetry two cases will come now if it is a symmetry if it is symmetry what happens if it is asymmetry what happens if it is a symmetry n is = 360 by Theta - 1 and if it is a symmetry n = 360 by so for OD there are again subconditions for odd there are again subconditions so what is the meaning of this you didn't understand I know but I have got on shortcut to make you understand this okay so let me discuss what is that shortcut method to understand all these cases let us draw one table here okay so what is that table you know here we take Theta first the next thing is we will write we will find out what is 360 by th okay then after that we will find out what is the value of n okay so after that we will find out we will find out what is symmetry and what is asymmetry so where n is said to be number of images is it so n is set to be number of images now let us see what is going to happen the first thing is uh let us consider Theta as 30° 45° 60° ° 72° 75° 90° [Music] 120° 180° okay so this many cases we are dealing with you just see here first thing is according to this condition whatever the angle is given we have to just divide the angle 360 then what is this row we shall fill this row now 360 by Theta means 360 by 30 means you get 12 okay the next thing is okay 360 45 is how much you get is it 8 okay huh so 8 5 40 8 4 are 32 32 + 4 36 is it right so 60 means 6 72 means 5 75° means 4.8 90 means 4 120 means 3 and 180 means two okay so let us do one thing here let us Mark let us Mark the odd conditions this is an odd this is an odd condition is it is it clear yes these two are odd so you are doing 36 by Theta so this is the case we are getting even for even there is no sub condition there is no sub for even just what you doing 360 thus you do whatever the value is givenus you right no symmetry as symmetry for even for even no symmetry or symmetry then you just go for OD so if it is odd what is getting now eight so what is your answer seven and seven that's it six five and five no sub conditions for even odd first odd case so you're getting five then go for sub conditions if it is symmetry four and this is five so 4.4 means just four fifth image is not forming there it's a special case special case again you're getting even three and three so again you're getting a special case so what are going write now 2 and three so 180° means just actually the two mirrors will be like this they're going to open open open they'll become flat flat means 180 flat means just a plain mirror in flame how many mes are seeing only one so here two you are getting that is an even case so one and one no subcases for even no subcases for even is it clear yes so this is a TBL column which is used to solve how many problems 1 2 3 4 5 6 7 8 82 are 16 problems Symmetry and asymmetry 16 problems this shortcut table will help you to solve 16 problems and this shortcut table will make you a better understanding of these conditions condition is it okay so let us solve this problem so how are you going to solve this problem now let us see two Mir are kept at 60° to each other and the body is placed at the middle means it's a case of symmetry middle it's a case of symmetry there are two mirrors and the body is object is kept here okay so what is an angle Theta here 60° okay so what is the answer now n is equal to 360 by Theta that is 360 by Theta is how much 60 60 is nothing but 6 so 6 is even number so minus one which is answer is five so second option b option is going to be answer is it for example uh 60° there is no chance of giv even giving even there is no chance of giving asymmetry case there's no use of giving asymmetry because for for even there is no sub case like asymmetry isn't it is it clear now okay you just see here this is a problem where this is a mirror understand this is a mirror and a person is standing before the mirror this is his I so what should be the size of the mirror so that a person can see his full image yes what should be it size see height of the man let us imagine y okay height of the man let us say height of the bo okay and this is height of the mirror so height of the mirror should be height of the boy by exactly half if this mirror is exactly half of your size generally Dressing Table mirrors will be 3 FTS 3.5 FTS and 3 FTS because a six ft person can see maximum six feets in Indians average so for better better it's given 3.5 even 6t person can see easily total total picture of his body before the mirror his dressing his legs his shoe everything can be seen and that's why a mirror should be for girls 6t 3 ft is enough for boys the chance that he may be Crossing 6 FTS like 6.1 like that so better the mirror size will be 3.5 FTS so that a 6 ft or 6.5 ft person can see easily is it clear what I'm telling so why why is it like that what is the reason for that you know reason see this is I let us imagine this is head H okay so what is going to happen he see know he sees this Edge it gets reflected like this he sees the down part of the mirror it gets reflected like this okay getting reflected this is going to be the bis sector Theta let us take this as beta and Beta And if you draw a bis sector here it is Alpha and Al okay so what is the meaning here both angles are same means this is also same what is happening here let us take this is X and this is X same this lens these two lens are same these two are X means is it not X this is y from here to here means is it not again y huh this is y this is y and this is y means this is also y from here to here here and this is going to be X from here to here so height of the Vol is considered as 2x+ 2 2X and 2 is it feet head is there some so his feet is here and his head is here so he is seeing here reflects and see is seeing the bottom of the mirror he sees the feet also easily isn't it this is because of reflection so what are going to understand height of the boy common out 2 x + y height of the boy is equal to 2 into height of the mirror isn't it so what is this X+ Y is nothing but so height of the mirror is nothing but x + y so height of the boy is nothing but 2x + 2 y so two common out X+ y height of the mirror so therefore how much should be the height of the mirror it should be height of the is it understood is it clear so this is the concept so a person is 6t tall how tall must be the mirror if he is able to see the entire length his length 3 ft is going to be your correct answer is it clear so let us go for the next case here so next case is the case of concave mirror okay so in a con miror so this is a Conor so what is this this is going to be the focal point this is Center of curvature okay an object is placed on the principal axis of a concave mirror at a distance of 1.5 times of the focal l so this is a principle of focus means the this this length is going to be F so 1.5 means object object distance is here object is in between f and c means image is going to be Beyond C it is in this it is there in your 10th class isn't it 10th class knowledge is enough to solve this problem just see it's very simple Tech so here this is a focal length and what is this going to from here to here it is said to be object distance and what is this from here to here it is image distance object distance is given by U image distance is given by V and focal length is given by F so object according to the problem U is taken as 1.5 * of f isn't it and he's asking us to find out what is V what is V isn't it so generally what shall we do we shall write 1 by f is = 1 by V plus 1 by U mirror formula plus lens last minus so L minus mirror plus understood so this is a mirror formula now what are you going to do it's a lengthy method you'll follow 1 by F you'll do you'll take 1 by V you will take U as how much 1.5 F the easy method is you can take it as 3x2 3 F by less what can you write this one can you write this as 3x2 F yes okay so 1.5 can be WR as 3x2 F so I have taken 3x2 f is it so what are you going to do now so 1X V equal this will come the sides okay okay so focal length of the mirror is negative because it is left side see in a mirror one thing you should remember this is going to be the origin this is going to be an origin and this is set to be the pole of a mirror so this pole of a mirror is taken as An Origin whatever comes left side is negative whatever comes right side is going to be positive is it understood so object distance is U I'm taking as negative so minus L minus isn't it left side is there it's minus so one thing you should remember whatever the value going to find out V that we should not take any sign conventions so that is minus that the one he asking is not taken as plus or minus the answer will tell that isn't it so what I going to do here so 1 by B you have to find out this you will send here that is 2x 3 Fus 1 by so 1 by is nothing but 3 of is going to be LCM so 2 minus 3 so V is equal how much - 3F okay so- 3F means your image distance this one is going to be this is a general method this is a general method but I have created one shortcut whenever you get this type of problems I have created one shortcut what is the shortcut one byal 1 by V + 1 by U isn't it so 1 by V is equal to this is actually minus huh object distance is minus so this also minus so actually you will take this as 1 by U left side minus 1 by fuh so 1 by V is equal to how much LCM is UF okay and is going to be Fus so V is nothing but UF F okay so this is going to be whenever this type of problem comes Finly can just write FU by Fus U so you'll get an answer what is the answer here f is nothing but F only U is how much 3x2 F okay Fus 3x2 isn't it the answer directly so this is taken as here minus these two are minus F problem so directly you get the answer here 3² how much 3 2 Fus get two how much we getting here 2 f - 3 f isus f getting cancel FF gets cancel so this minus com numor minus got the answer directly so you can use this Formula F by Fus is going to be your answer okay now here you can just see this problem okay so a beam of lighter a beam of light from the source L is incident normally on the plain mirror okay you have taken one source this is a mirror actually is it this is a mirror okay and what is going to happen mirror normally and mirror is so light light falls like this actually is it and what you have done you have just okay then what happens okay so what is this angle double when mirror is rotated through angle Theta reflected R rotates through an angle 2 Theta is it clear okay so what is going to happen let us see okay so Source this is a source L it is again and just see here the beam is reflected back as the spot on the scale is placed just above the source I okay Source I when the mirror is rotated through angle Theta the spot of the light is found to move through a distance y on the scale the angle Theta is given by what is this angle Theta so okay so what is the distance from the source and here is going to be how much is going to be X here okay so source is placed at distance of X so what I going to do here T 2 Theta is equal to Y by X okay for small angles tan Theta is going to be equal to Theta okay I can just write this as 2 Theta equal y by X Theta = y by okay so what is going to be option option the okay so you want the concept here when mirror is rotated through angle Theta reflected rotes to let us rotate the mirror okay actually this is the normal [Music] okay so light R is incident from that place it falls like this and it is getting reflected like this is getting reflected it's a say this is mirror M and this is M Dash it is rotated when you like what is going toen to the reflected okay so previously it was P QR now it is going to be PQ and R Dash Okay so he's asking us to find out what is this angle if angle of the mirror is rotated through Theta what is the reflected ray rotated mean reflected R ch so one thing you should remember here what is that this is I this is is it mirror nor isn't it so n has been changed to so is rated also so here if this is I then what is this going to be I because angle of incidence angle of reflection is same first case may be same second case normal angle of incident incident R to normal is y+ Theta reflected R to normal reflected R to normal is also I plus Theta is it clear so what is that we have to find out now you have to find out rqr D sir rqr D that you to find out so rqr D angle rqr D is nothing but angle pqr R D minus angle pqr so if you want to find out this angle only this question mark angle which is given to find total total angle minus this much angle should be removed no so total angle is pqr Das the angle which should be removed is pqr so pqr D is nothing but the question mark which we have to find out here is but I I + Theta yes sir I + theta plus I + Theta minus pqr pqr is nothing but I + I isn't it so this is 2 I + 2 Theta - 2 I so - 2 I + 2 I cancels angle is Theta so the question mark So if a mirror is rotated through angle Theta reflected R is rotated through an angle that is the conly goes strikes the mirror reflects back in the same direction now once the mirror has been rotated through angle Theta [Music] normal actually previously reflected incident are coinciding with each other they are retracing when you reflected is also 2 opposite y a so y by a so [Music] [Music] so angle very very small if it is less than 5° if it is less than 5° it is said to be small [Music] Ang so here so of this isite you can use uration formula isal radius yes okay so can imagine like that so that is aaal AR means opposite side is nothing this so for small yes sir for small angles R radius radius everywhere is say is it understood not now just see here two mirrors are inclined at 60° to each other and a body is placed at the middle okay now just see here match the corresponding entries of column one and column two where m is set to be the magnification produced by the mirror okay so what is that we are going to get now convex mirror concave real image virtual image if you understand this you you can do that one you can solve this problem so let us take first concave miror okay let us take the first concave mirror next we shall discuss about convex mirror also is it okay F and this is C so just to explain by using Beyond C object is beyond C object is beyond C Is it okay so where will be the image between F and C is it when object is beyond C image is between F and C when object is at C image is also at C okay okay when object is at C image is also at C when object is between F and C image is beyond C [Applause] and and that is said to be the virtual image virtual case when you're going get the virtual case see you getting a virtual case when you are taking an object here you're getting a virtual case okay so you are taking an object here you're getting an inverted face so in all these cases when do you say that magnification is positive when do you say that magnification is negative a simple thing is this is a height of an object this is said to be height of an image isn't it magnification height of the image by height of the object this two things will decide whether the magnification is positive or negative see I told you this is going to be considered as an orig is [Music] it so here if it is a real ined only there is one virtual case where object is placed between F and optic Center I mean po of the mirror image is erected object see image see only for virtual and all the in Virtual when it is called when the image cannot be caught on the screen you just see your plain mirror your face in a plain mirror you can see your face on the other side of the mirror it cannot be caught on the screen it said to be the virtual image it's not a real one any image which cannot be caught on the screen is said to be the virtual image any image which can be caught on the screen to be the real image you can just take one spoon how is it shape concave this side is concave and back part is Con is it not going to fall on the wall so when it is going to fall on the wall it's a real image going to be real and that can be caught on the screen when object is here it's a concave mirror and this concave mirror is used in makeup makeup mirr but generally in cities they go TOA parl they will be Prov it is showing a magnified image so that is said to be the is it is it understood so why is it so because it is showing a magnified image generally after doing makeup some waxing will be done they will take some wax and put on the skin so that your skin is totally covered [Music] what is going to happen now so I think you understood of the image is also positive when height of the object is also positive magnification magnification is virtual okay that means virtual magnification is always positive posi okay so when it is a real case height of the image and height of the object image is inverted object is so this is the only formula which will explain you which is going to be the virtual which is going to be the real okay so it is understood that virtual means negative so okay let us go for thex Mirror you have seen this concave mirror in the case of rare mirrors of your vehicles so small you see that object appears to be closer than they are so there is a concave mirror so this is a concave mirror where you are going to see where you are going to see this is the height of an object and this is going to be the height of the image so magnification is nothing but height of the image by height of the object so height of the image is positive height of the object is also positive magnification posi less than us imagine is only 1 m and that two it's a virtual image and that it's a virtual image virtual it is also behind the mirror any image forms behind the mirror is a virtual image any image forms on the same side of an object it's a real image so p m isalus it is a magnified magnification two two means greater than one what is the meaning of that two means greater than one greater it's a real ined very good B and C so p p b and c so m is equal to- 1 by 2- 1 by2 means it's a case of a minus [Applause] is beyond C 0.5 and that to negative negative means inverted it's a real and it's a concave means Q is equal BC Q it is said to be a virtual image and it's a con B and D andal convex convex and virtual so a b so a is going to okay so let us go for the next okay so here light travels at a distance of thank you okay so light travels at a distance X in time T1 in a and distance 10x in time T2 in the another denser medium okay denser medium what is the critical see here it is a case of so this is a denser medium this is going to be the rer medium it is going to be normal a light Ray false an angle of incidence is going to reflected back which is to be angle of reflection angle of incidence angle of refraction understand angle of incidence angle of refraction so what is going to happen here let us see how many things we have to remember how many things we have to understand here let us see so this is a case of it is a case of refraction isn't it it is a case of refraction what are things we need to understand one by one discuss velocity of light in is taken as V1 velocity of light in medium is V1 denser medium is taken as V2 so refractive index of R medium is taken as mu1 refractive index of denser medium is taken as mu2 so here what is the snail law let us see here refractive index of second medium with respect to First medium okay medium 1 medium 2 when ENT from Medi to Medi what is going to happen it bends towards the normal suddenly velocity decreases Whenever there is a sudden decrease in the velocity what happens it bends towards the normal okay H velocity suddenly decreases here dens Med or one more thing here is refractive index of this is to be one and two is one subt second medium there and now so here this can be taken as mu2 by mu1 refractive index of second medium with respect first medium is taken as mu2 by mu1 which is taken as V1 by V velocity of light in the First Med medium velocity of FL in the second medium because always refractive index is inversely proportional to Velocity just okay ref IND me it isser medium people going your speed will be more speed is more huh today traffic is very less so can go very so inversely related isn't it mu is invers related to Velocity so mu2 by mu1 is equal to V1 by V2 velocity is nothing but displacement by time and displacement by so it is tring X1 dist in1 time it is tring x2 in [Music] is it okay so X1 by X is it clear so you should understand you should remember all points [Music] so it is mu2 1 = mu2 by mu1 which is = V1 by V2 which isal X1 by because time is same for example of in reflection okay 1 sin 1 sin actually R is it clear so mu2 by mu1 V1 by V2 X1 by X2 sin Theta 1 by sin Theta is it clear so these are all formulas for refractive index okay of incidence this is normal and this is angle of refraction this is to be deviation because these areally opposite so what is how much is going to be deviated that be of deviation so what is angle of deviation IUS so okay so this is when it isser to sorry when it is traving from R toser medium is the opposite no I'm taking noral okay okay so this is us imagine so it is bending away [Music] from okay so now this is to of in of refraction reflection no no this is I this is this is taken as r del these are vertically opposite angles that means I = to Rus Rus Dela so Delta is equal r- r r i [Music] just here get Del IUS R means here you get Delta Rus I it is denser to R when it is denser to bends away from the normal is bends towards the normal isn't it so what is aticle just dens mediums Medi just consider this as water and this is a r medium R medium let us imagine to be an so this is an object this is Source here isn't it let's source so normal N1 okay I R2 okay i3 exactly is grazing grazing when graes then this R2 will become R3 which is 90° and then it is called as critical conditional angle with this critical angle when it is called when the refracting angle is just passing through the both surfaces the medium of the surface it is passing it is called astical angle angle is hospitals are Tates to go to hospital this reflection this is called as total internal reflection total internal reflection so this is a RAR medium this is a dener medum so this is a critical that's is called okay so what is this now medium is always superscript second medium is which is always subscript and you should take this as first medium is sin I3 by sin R3 so refractive index of a with respect to Omega sin I3 i c and r990 so you when you want to change superscript as subscript and subscript aspt you to take reciprocal 1 by of water with respect be always always subsp then only it is said to be absolute refractive index absolute [Music] hute sorry so this is not called as absolute marks this is called as relative abute is on J so this is said to be