at what image distance is it difficult, but not impossible to locate a clearly focused image? i think that would be far from object.
If you have access to an image, you can always locate it. If the image is formed in outer space, you'd have to go there to find it.
You can also insert an intervening optical lens or mirror to compute where the image (without the inserted element) would be.
When it comes to locating a clearly focused image, the distance at which it becomes difficult but not impossible depends on various factors such as the optical properties of the lens or the human eye, the size and distinctness of the object, and the observer's visual acuity.
To understand this concept better, let's consider a standard camera lens. Generally, the lens can focus on objects that are far away, providing clear and sharp images. However, as the distance between the lens and the object decreases, the difficulty of locating a clearly focused image increases.
The lens has a limited depth of field, which refers to the range of distances where objects appear acceptably sharp in an image. When focusing on objects that are very close to the lens, the depth of field becomes shallow, and the margin for error in focusing decreases. Thus, it becomes more challenging to locate the exact focus point, resulting in a less clear image.
If the object is far away, such as several meters or more, the depth of field tends to be larger, making it relatively easier to locate a clearly focused image. However, it is important to note that this can still vary depending on factors like the specific lens, aperture settings, and the observer's visual acuity.
In summary, while it is generally true that locating a clearly focused image becomes more difficult as the distance from the object increases, the exact distance at which it becomes challenging but not impossible can vary based on several factors.