Why can the distance from the lens to the image of a distant object be considered approximately equal to the focal one?

The converging lens collects parallel rays into a point at a distance equal to the focal length. If the object is far from the lens, then the rays from each point, falling on the lens surface, diverge at a very small angle (almost parallel). As they are almost parallel, they are going to the point of the image at a distance almost equal to the focal length.

The same result is obtained by analyzing the formula for a thin lens:
1 / d + 1 / f = 1 / F (1),
where d is the distance to the object,
f – distance to the image,
F – focal length
At a large distance to the object d, the fraction 1 / d becomes very small and
1 / f ≈ 1 / F,
f ≈ F.