Answer:
Moving screen for focusing.
Roshan Mandal
Suppose you want to use a converging lens to project the image of two trees onto a screen. One tree is a distance x from the lens; the other is a distance of 2x, as in the figure below. You adjust the screen so that the near tree is in focus. If you now want the far tree to be in focus, do you move the screen toward or away from the lens?.
To bring the near tree in focus, the lens must be placed at a distance from the tree equal to its focal length. Let's call this distance "f".
Now, for the far tree to be in focus, the light rays coming from the tree must converge at the same point on the screen as the rays from the near tree. This means that the screen must be moved closer to the lens.
To calculate how much closer, we can use the thin lens formula:
1/f = 1/do + 1/di
where "do" is the object distance (distance of the far tree from the lens) and "di" is the image distance (distance of the screen from the lens).
We know that do = 2x (distance of the far tree) and f (focal length of the lens) is the same as before. We can rearrange the formula to solve for di:
1/di = 1/f - 1/do
1/di = 1/f - 1/2x
di = 2fx/(2f-x)
So the screen should be placed at a distance di from the lens given by this formula. As x is less than 2f, this value will be positive and greater than f, meaning the screen should be moved closer to the lens than its initial position to bring the far tree in focus.