 Alright friends, so today we are going to discuss a question which was asked by one of our students and since I think that we are going to learn many things from this particular question. I'm creating a video out of it. Okay. So the question goes like this. You can see there is this spherical thing which has a radius of r. There's nothing but a bubble. Alright, so let us say a refractive index of the bubble is one. Okay. And outside outside of this bubble is a refractive index of let's say four by three. Basically, it's a bubble that is trapped inside the water. Okay. Now the question is that a parallel rays are coming which are parallel to this dotted line. Okay. And we need to find out the final image. Okay. So first of all, since the rays are coming parallel, so definitely we can say that the object is at infinity. Right. So the ray diagram would look something like this. This ray which will be along the dotted line will straight away go because it is along the normal. Right. Another rate we have to take because we have to find intersection. Right. Now this rate when it when it hits the first interface which is between the water and the bubble, what will happen to it. It will bend away from the normal. Right. Because it is traveling from a denser medium to a rarer medium. So this is what will happen. Let us say. Right. Now if you try to find out the image, forget about the fact that there is one more refraction that has to happen. Okay. If we ignore that fact, then suppose only these two rays are there, this one and this one, then the final image would be formed somewhere behind. Right. Because this ray and this one, they are diverging. So image will be somewhere here. Right. So the ray diagram, if I have to draw it properly would look something like this. So this is my image. Right. Now the thing will not stop here because there is one more refraction that has to happen on the other interface. Right. Now when refraction is happening on the other interface, the rays are coming along this ray. Right. Along this line, the rays are coming. Now, if let us say hypothetically speaking, if this interface would not have been there. Okay. And instead, the object was kept here where the image was getting formed. Let's say object is kept here only. Then will there be any difference felt by the second interface. Think over it. This ray will go as it is. And another ray, if I can send from here, will go straight till it meets the second interface. Yes or no. If the first interface is not present. So what I'm trying to tell you, what I'm trying to tell you is that the image of the first interface, which you can call it as Ivan over here, is acting like an object for the second interface, because second interface will feel as if the rays are coming from this point. Isn't it. So we need to draw the further path of this ray. So when you do that, you can see now the ray will bend towards the normal. So it will be something like this. Okay. And you can see still this ray and this ray, they are diverging. So we need to do some construction to find out the final image. So this is the location of the final image. This is the final image. Now why we are calling it as a final image because my observer is sitting here outside. Okay. Observer will get these two rays. Observer will not get to see the image formed by this ray and that ray. But this interface, the second interface will feel as if object is kept over here. Isn't it. So that is the reason why we can say that the object of the second interface is the image of the first interface. All right. So once we understand the ray diagram like this, it becomes very easy to solve problem. Okay. And just one more thing, when you solve a question like this, you need to be very careful with respect to from where you're measuring the distances. Okay. So when you're talking about refraction from this interface, you measure all the distance from this optical center, this one. Okay. O1, let us say. And when you're talking about this interface, okay, you're talking about this one, this is spherical interface, right. For that, the second refraction, you have to measure the distances from here. Okay. So I hope you got to learn something new today. Thanks for watching.