Farsightedness (Hypermetropia)

Hypermetropia (farsightedness, or hyperopia) occurs when the eye lens has too long a focal length, from a thinned lens or an eyeball shorter than normal, so rays from a near object are brought to a focus behind the retina, blurring near vision; the person's own near point $y$ is pushed appreciably beyond the normal 25 cm, forcing them to hold reading material inconveniently far away. Age-related loss of accommodation producing this same effect is specifically called presbyopia. The correcting lens must make the virtual image of an object at the normal near point (25 cm) form instead at the person's own near point $y$; using the lens equation with $u=-y$, $v=-25$ cm gives $\boxed{f=\dfrac{25y}{y-25}}$ (in cm) -- always positive since $y>25$, a converging (convex) lens, which slightly converges the incoming rays so they appear (to the eye) to originate from the person's own near point $y$, and are then focused correctly on the retina. A person developing both myopia and hype …