Final answer:
When an object is placed 6-mm from a convex lens with a 3-mm focal length, the image is formed at a distance of 6-mm from the lens according to the lens formula. Due to the nature of convex lenses, this implies the creation of a virtual image.
Step-by-step explanation:
To find the distance at which an image is formed by a convex lens when an object is placed at a certain distance from it, we use the lens formula 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance.
Given that the focal length (f) of the convex lens is 3 mm and the object distance (do) is 6 mm, we can rearrange the formula to solve for the image distance (di):
1/di = 1/f - 1/do
1/di = 1/3 mm - 1/6 mm
1/di = 2/6 mm - 1/6 mm
1/di = 1/6 mm
di = 6 mm
Therefore, the image is formed at a distance of 6 mm from the lens. However, it is important to note that this value results in a virtual image since the object is placed within the focal length of the lens, which is not possible for a real image with a convex lens. In reality, an object placed at 6 mm from a 3 mm focal length convex lens would result in a virtual image located on the same side as the object.