What is the term for a refractive error that causes difficulty focusing on near objects due to a short eyeball?

The term that refers to a refractive error causing difficulty in focusing on near objects due to a shorter than average eyeball is indeed farsightedness, also known as hyperopia. In this condition, light entering the eye is focused behind the retina rather than directly on it, making nearby objects appear blurry while distant objects can be seen more clearly. This occurs because the eye is shorter than normal, resulting in the light being improperly focused.

In contrast, other conditions such as nearsightedness (myopia) arise when the eyeball is too long, causing difficulty seeing distant objects. Cataracts involve clouding of the lens in the eye, affecting vision but not specifically tied to the shape of the eyeball or to near vision. Astigmatism results from an irregularly shaped cornea or lens, which can lead to blurred vision at any distance but doesn’t specifically relate to the eyeball's length affecting near vision. Thus, the characteristic of a short eyeball directly correlating with the inability to focus on near objects uniquely identifies farsightedness as the correct term.