Why is the image distance equal to the focal length when the object is a very great distance from a simple thin converging lens?
IT is that because all light converges on the focus. THe incoming rays are all parallel with the optic axis.
When an object is at a very great distance from a simple thin converging lens, all the incoming rays from the object are nearly parallel to each other and to the optic axis. In this case, the lens is said to be focusing "at infinity".
Since all the incoming rays are parallel, they converge at a single point on the other side of the lens called the focus. The distance from the lens to this focus is known as the focal length (f) of the lens.
Now, coming back to your question, when the object is at a very great distance, the rays coming from the object are essentially parallel to each other. These parallel rays pass through the lens and converge at the focus on the other side of the lens.
As a result, the image distance (di) of the object is equal to the focal length (f) of the lens. In other words, the distance between the lens and the point where the image is formed is equivalent to the focal length of the lens.