 So, we are going to see now various cases in case of concave mirror and find out where the image will be. Write down case number 1, object at infinity, this is the mirror, this is the principal axis, focus r, object is at infinity. So, where the image will be? Focus. So, draw the ray diagram for that. Done. So, this is one ray. What will happen to this ray? Come to focus. You need at least two rays to form the image. Draw another parallel ray. What will happen to this ray? Again focus. So, they intersect here. So, if a person is here watching it. So, one ray will go like this, other ray will go like this. So, these two rays will appear to meet at the focus. So, image will be at the focus. Now, object is at infinity does not mean that object is at like million kilometers away. Like for example, if the focal length is 10 centimeter and object is like 100 meters away that is also infinity. Object beyond r as in I want to say object between infinity and r. So, draw a ray diagram. This is focus. This is r. This is p and here is this object. Draw a ray diagram. When you show focus, radius should be equidistant. Focus should be between r and p. So, that your ray diagrams are proper. Done. One ray goes like this. What will happen to this ray? Passes through focus. Then what? Which other ray you can draw? Through the focus. Draw this ray. It will parallel. So, you got the intersection point. Can you draw any other ray? Which one? Through the pole you can draw. Like this and it will come and meet here. What else you can do? You can pass a ray through radius like this. What will happen to this ray? It will come back. So, again image will be here only. But you just need only two rays. So, this is the image of what? Image of this point. Let us say this is point p. So, this p becomes p dash comes here. Are you getting it? So, this is the entire image. So, this is object beyond r. So, wherever you keep, wherever you keep the object between infinity and r, the image will be always between r and f. So, the object is travelling from infinity to r, but image is only travelling from f to r. So, the speed of image is very slow. Are you getting it? If you put the object at r image will be on r only. Write down characteristic of this image, characteristics. What do you think the characteristics are? Real, inverted, diminished, real, inverted, diminished and between r and f between r and f. Can you put this image on screen? You can because lights are actually intersecting. So, you can have a screen here and observe it. Have you ever used ray opt in your lab in a school? You do not? So, you have a screen that there is a bench onto which lens can move for optical bench and there will be a screen also. So, that screen if you were asked to look at the far away object may be like beyond the window, some object and adjust the screen. So, the far away object becomes object at infinity. So, wherever the sharp image falls, that is the distance of the focus. That is a focus. Same thing. Case number 3, object between r and f. This is f, this is r. You have an object like this. Of course, you will draw a line that is parallel and it will pass through the focus. Go like this. Which other ray will you draw? Through the focus or draw a line which passes through the r. So, here will be the image. You can immediately identify. Otherwise do this. This is not to the scale. So, slightly this is the image. So, what kind of image you get? Beyond r. The image is beyond r now and it will be enlarged also and inverted. Write down characteristic. Inverted enlarged real and beyond r. Now, if you put the object at focus, where the image will be? Any guesses? Let us do that at infinity. If you put the object at the focus, the image will be infinity. So, now see here. You have moved the object from r to f. The image has moved from r to infinity. So, now speed of image is more. Object is between p and f. This is p, this is f and this is r. Here is the object. Find out its location. This parallel ray will go from focus and what you will do now? Can you draw a line passing through focus? If something line passes through focus, it will never hit the, but if there is a ray along the direction of r like this, it is hitting in the direction of radius only. So, will this ray, these two ray, ever meet? Whatever reflects off and this one, they ever meet or not? They will not ever meet. They will just keep on going away from each other, but they will appear to meet behind. So, it looks like a plane mirror scenario. So, there will be a virtual image, but erect this time. Write down characteristics. So, the image will be erect, enlarged and virtual. So, just imagine that when it was at focus, the image was at plus infinity and as soon as you slightly go towards the mirror, the image came all the way from infinity and appeared here. So, these are the four cases that we have discussed.