What are the types of lenses? Four types. Which four types? Concave, Convex, Bi-concave, Bi-convex.
Which are these? Concave, Convex, Convex. They are not the same. Concave, Convex.
Depending on their shapes, we can say there are five different kinds of lenses, depending on their shapes. Its surface is convex, its both are concave, one is plane and one is convex. So five different types of lenses. Numerical can be seen on all. This is called double convex, biconvex is called double convex, this is double concave and this is plano convex and that is plano concave and this is concavo concave.
or we can also call it Convex or concave. So, their names are given according to the shape of their surfaces. So, their names are given according to the shape of their surfaces. Obviously, the effect of this will be like a concave lens. Obviously, the effect of this will be like a concave lens.
This is like a convex lens. This is concave and that is convex. This depends on the radius of the surface of both these surfaces.
This depends on the radius of the surface of both these surfaces. Whether it will behave as a concave lens or a convex lens. Which is used the most in these? Which lens is used in the glasses? Concave How long have you been using it?
4 years 4 years From which lens is it used? Plano concave Plano concave, this one Since when have you been using the glasses? Concave concave Yes, this one Check the surface. It is on the inside and one is on the outside. So that's a concave or convex or convex or concave.
Make a diagram quickly. Okay. We have to make some of these diagrams and derive some formulas.
So let's start. Starting with the double convex lengths. Lenses, don't make thick lenses. Focus will be on both the sides. Rays parallel to the principal axis will pass through focus.
If they diverge, then this convex lens will be... Converging lens we call it. Converging lens. It is also called positive lens. Will someone tell us why we call it positive lens?
We take the focal length to be positive. The rays parallel to the principal axis will pass through focus. And if there is any rays coming from focus, then they will go parallel. And raise through optical centre. See, undivided.
All the 10th syllabus is being taught in 12th. Make it fast. Fast.
Done? Okay. That's focus 2F, same way. Focus will be on both the sides.
That's why rays are coming from here, so they will meet here. And if they are coming from here, then they will meet here. So focus will be on both sides. And we have an object somewhere here. Where will the image be made?
Anybody? between f and 2f and if the object is here on 2f then add 2f and between f and 2f then beyond 2f dash will be bigger. Earlier it was small now it is of same size now it gets magnified.
So, if the object moves towards the convex lens, the image moves away from it and gets bigger in size. What happens to the image when object is moved towards the convex lens? What happens to the image when object is moved towards the convex lens?
Answer likho. The image moves away from the lens, the image moves away from the lens and gets bigger in size. Image moves away from the lens and gets bigger in size. Where to get the image? This is the mantra of the chapter.
We should remember the images. Where will they be made? You should know beforehand, if you want to prepare the chapter properly, beforehand you must have a knowledge that where the image is going to be made.
On the same side or virtual and direct or magnified. Exactly. Make it. Yes, make it.
You should know the image characteristics beforehand in every question. The ray parallel to the principal axis will pass through focus. Focus is made on this side.
Another through O will go undeviated. Produce both of them. Wherever they meet, that gives you the point of formation of image.
So, image characteristics, it's on the same side of the object, virtual and erect and magnified. Right, next is lens formula. Whenever we draw lenses, we assume that the lenses should be thin.
The formula itself is called thin lens formula. This means that the lens will be thin. That's f to f.
The object is kept here. Where will the image be made? Beyond 2f dash. So a ray parallel to the principal axis will pass through focus, another through O goes undeviated and we get a magnified real inverted magnified image beyond 2x.
Make sure to mark the directions. Take this point as M. AB is the object. A dash B dash is the image. O is the optical centre.
Same method which we used in mirrors. Two similar triangles. Can you find them? Can you see them?
Two similar triangles. Which ones are they? Triangle AOB is similar to triangle A dash OB dash.
Okay. This angle will be equal to this. And this will be equal to this.
So, triangle is similar. Sides ratio AB by A dash B dash equal to OA by OA dash. This by this will be equal to this by this.
So, AB by A dash P dash equal to OA by OA dash. Next triangle. M OF'is similar to triangle A'B'F'. Same procedure, two similar triangles, first found, then found two more.
Sides ratio is taken, hypotenuse will not be considered. It is not necessary. So, OM by A'B'equal to OM.
f dash by a dash f dash. We are not using any special physics. Check the left hand sides. Are they equal? Denominators are the same.
And numerator OM and AB. Check from the diagram. Both are equal.
OM and AB. The left hand sides are equal. Therefore, the right hand sides are also equal. So, we can say that OA by OA dash will be equal to OF dash by A dash F dash.
Any question till now? Go and ask anything. Jaskirat, ok? Ok, now first convention OA by OA dash all distances to be taken from optical center or pole. A dash F dash how can we write?
We can write it as OA dash minus OF dash. Okay. Object distance OA represented by U. Image distance OA dash represented by V. So, OA minus U, OA dash V, the distance from O is negative and the distance from this side is positive.
OA dash F, OA dash V, check it. Everyone should understand this step. Okay?
Right, cross multiply karenge minus uv plus uf equal to vf and dividing by uvf kya jayega minus 1 by f plus 1 by v equal to 1 by u or 1 by f equal to 1 by v minus 1 by u that is length formula. Next is magnification. What is magnification?
Height of the image by height of the object. We are using this diagram and we will derive result for magnification as well. Magnification, it is HI by HO. Let's pay attention. Triangle A dash OB dash is similar to triangle AOB.
Check it. We have taken this earlier also. Earlier we had written it here and here.
So, we have changed the sides. a dash b dash by ab equal to oa dash by oa. Is it clear?
Right. a dash b dash height of the image a b height of the object o a dash image distance o a that's object distance ok ok Is there any problem in this? Yes.
Both of these will be negative. HI will also be negative. HI below the principal axis will be negative.
Now see, if the convention is not used and is used, Both the cases have same results. It is not always the case. It is not always the case.
Sometimes it happens, sometimes it does not. So, always use conventions. Examiner will definitely check this step.
That whether you have used conventions or not. M equals to what? V. What was the formula? Lens formula. 1 by f equal to 1 by v minus 1 by.
What was in mirrors? In mirrors, this was plus and here was minus. In lenses, here is minus and here is plus. Note it. We are using the same diagram.
So, write the derivation steps. We will be going through more important topics from the next class. This is all very easy. In the next class, we will study refraction. Okay.
Next, let us make a diagram of concave lens. Image formation in concave lens. We have made it in convex.
So, let us do it for concave as well. That is f, f dash place the object anywhere but ray parallel to the principal axis diverging lens is called as rays diverge and another through o goes undivided. A dash, B dash, images on the same side, virtual erect and diminished. In convex lens, virtual images are magnified. Erect images are magnified.
And in concave, images are erect but diminished. On the same side, virtual and erect, smaller in size. Power of a lens, reciprocal of focal length, note the definition.
It is the reciprocal of focal length of a lens, reciprocal of focal length of a lens taken in meter. Focal length meter is 1 by F and F must be in meters. P equal to 1 by F.
Unit is diopter, capital D. How much power is there? Minus 5 equal to 1 by F. So, F equal to minus 1 by 5 meter. Multiply by 100. So, 20 centimeter.
Minus sign means? It's a concave lens. Be careful. Negative sign means it's a concave lens.
They ask in exams. Find nature and focal length. Focal length and nature of the lens. Since it's negative, power or focal length, we will say it's a concave lens. Okay, then we have combination of lenses Combination say a matlur.
Nia cap. Okay. Just remember say the lens combination. No no no lenses in contact Lenses in contact So, there are two lenses in contact, both convex, both concave, one convex, one concave, anything can happen, more than two can also happen.
So, we have to use some of their formulas, power P1 plus P2 focal length 1 by F equal to obviously focal length is 1 by F, so we will write it 1 by F1 and what will we write 1 by F2, we will derive the magnification product, multiply it, so we will get the magnification you will get magnification of combination. Note it down. The topic is very easy.
There will be some difficulty in questions. You will have to keep some things in mind. Write the question. Find focal length of a lens which is in contact with a concave lens of focal length 20 centimeter focal length, 20 centimeter and power of the combination is and power of the combination is 2 diopter, 2 diopter curve.
Question is clear. There are two lenses. What are they given?
Power is given as a combination of two diopters and one focal length is given. How much? Minus 20. Concave lens is minus 20. So how much will be the other? We have to calculate this.
Try it. Simple question. Power questions are very common.
They come in exams. MCQs me me lega question Its power is given as 1 by F2. F equals 1 by 2, i.e. 50 cm. Okay?
So, 1 by 50 equals 1 by F1 plus 1 by F2. So, 1 by F2 equals 1 by 50 plus 1 by 20. This is what we get. Yes, what a great job!
So, how much is F2? 100 by 7 cm. Okay?