Normal human eyes can focus on objects that are from about 25 cm away from the eye (Dmin = 25 cm, the near point of a normal human eye) up to infinitely far away (Dmax = ¥ (infinity), the far point for a normal human eye). A hyperopic eye has trouble focusing the light from things that are close up. It can only see clearly to a near point that is farther away than 25 cm, so that Dmin > 25 cm for a hyperopic eye. To correct such vision defects, opticians prescribe corrective lenses.
What a corrective lens does in the case of hyperopia is the following. Consider an object that is a distance Do = 25 cm from the eye (the near point for a normal eye). The hyperopic eye cannot focus on this object since it is closer than the eye’s near point, which is at a distance Dmin> 25 cm from the eye. The proper corrective lens is placed (of course) between the object and the eye. The lens takes the object at 25 cm and forms a virtual image that is at the distance of the eye’s actual near point at Dmin. (When doing this, we neglect the small distance between the eye’s surface and the corrective lens, so that we say that an object that is 25 cm from the eye is also 25 cm from the corrective lens.) Thus, we require that Di = Dmin, and di = –Dmin. The eye can then focus on the image of the object as seen through the corrective lens. (Do you see why the image must be virtual?)
Most adults with normal eyes eventually become hyperopic since the eye’s lens tends to become less flexible as it ages. This decrease in flexibility means that it will be more difficult for the ciliary muscle to accommodate the eye’s lens to see objects as they move in from infinity.