Defects of Vision: Myopia and Hypermetropia

A normal eye can accommodate comfortably over the full range from its near point (about $25\ \text{cm}$) out to infinity. Two very common defects of vision arise when this range shifts away from normal, in each case simply because the eyeball's own length or the eye lens's converging power no longer matches each other correctly, and each is corrected, non-surgically, by placing an external spectacle (or contact) lens of an appropriate power in front of the eye, purely to shift the effective range of object distances the eye is asked to focus on back to what its natural accommodation range can actually manage. In myopia (near-sightedness or short-sightedness), the eyeball is slightly too long (or the eye lens's converging power is slightly too great), so that rays from a very distant object are brought to a focus in front of the retina rather than exactly on it, leaving distant objects permanently blurred even though near objects can still be seen clearly; the far point has moved in from infinity to some finite distance. Myopia is corrected with a concave (diverging, negative-power) lens, chosen so that it first diverges the parallel rays from a truly distant object just enough that the eye's own lens, following its normal accommodation, can then bring these now-diverging rays to a sharp focus exactly on the retina -- in other words, the corrective lens is chosen to form a virtual image of every distant object exactly at the person's own (now-too-close) far point, so the eye is never actually asked to focus on anything beyond its own far point at all. In hypermetropia (far-sightedness or long-sightedness), by contrast, the eyeball is slightly too short (or the eye lens's converging power is slightly too weak), so that rays from a nearby object are brought to a focus behind the retina, leaving near objects blurred while distant objects can still be seen clearly; the near point has moved out from $25\ \text{cm}$ to some larger distance. Hypermetropia is corrected with a convex (converging, positive-power) lens, chosen so that it forms a virtual image, of any object actually held at the normal $25\ \text{cm}$ near point, out at the person's own (now-too-far) actual near point, wh …