 A bacteria is being studied under a compound microscope, having focal length of objective which is 4 cm and focal length of the eyepiece is 5 cm. The length of the tube of the microscope L is 30 cm. The question is how far from the objective should the bacteria be kept to view them in normal adjustment? And there is a note which says the final image is formed at infinity in normal adjustment. Alright, we need to figure out U0, U0 or this distance right here. Now let's see what all is provided. We know the focal length of the objective lens, we know the focal length of the eyepiece lens. We also know that the final image is being formed at the infinity, right? So we have the object in the first place, there is an image, this image acts as the object for the eyepiece lens. And the final image is formed at the infinity. We also know the distance between the tube of the microscope, the length of the tube, this L, this is 30 cm, right, this is 30 and the final image is at infinity. Now the question that we can ask ourselves is where should the object be placed in front of a convex lens so that the image is formed at the infinity. And the answer really is the object should be at the focal length. So this image which is acting as the object for the eyepiece lens, it should be formed, this image should be formed at the focal length of the eyepiece lens. So the object distance for the eyepiece lens really becomes the focal length. This object distance of the eyepiece lens is really is the focal length, right? And which is equal to 5 cm. So if we know this, we can figure out the image distance V0. That comes out to be equal to L minus the object distance, Ue. So this is 25, sorry, this is 30, 30 minus, 30 minus 5 cm. This comes out to be 25 cm. Now we know the focal length and we know the image distance. We can figure out the object distance Ue. And we can use a thin lens equation to do that, right? Which is 1 by V0 minus 1 by U0. This equals to 1 by F, the focal length. So focal length of the objective lens. Now we can take this, we can keep this on one side and take everything on the left side. We need to figure out the object distance. So this will be 1 by U0. This is equal to 1 by V0 minus 1 by F0. Now this is plus 25 cm. The image is formed to the right of the lens. And focal length is 4 cm, which is given in the question. So let's plug in the values to figure out the object distance or where the bacteria is placed. So this is 1 by U0 equals to 1 by 25 minus 1 by 4. We can take the LCM as 100. So this is 4 minus 25 or minus 21 by 100. So the object distance is minus 100 by 21 cm. It's negative, which makes sense because it's to the left of the objective lens. And this is approximately minus 4.8 cm. So this distance right here is 4.8 cm to the left of the objective lens. And over here we need to write the magnitude. So we will just remove the negative sign. This just becomes 4.8 cm.