Q.What is presbyopia?

In a normal healthy eye, the eye lens's focal length can be varied (accommodation) between a maximum value $f_{\max}=2.5$ cm (fully relaxed, viewing a distant object at infinity) and a minimum value $f_{\min}\approx2.27$ cm (maximally strained, viewing an object at the near point, 25 cm), since the retina-to-lens image distance is fixed at about 2.5 cm; this small variation, only about 0.23 cm of focal-length change, is enough to bring everything from infinity down to the near point into sharp focus. Myopia (nearsightedness) occurs when the eye lens has too short a focal length (from a thickened lens or an elongated eyeball), so that parallel rays from a distant object focus in front of the retina rather than on it, blurring distant vision while nearby objects (within the person's own reduced far point $x$) remain clear; using the lens equation with the correcting lens required to image an object at infinity onto the person's far point ($u=-\infty$, $v=-x$) gives a required focal length $f=-x$, i.e. a diverging (concave) spectacle lens, whose negative power spreads the parallel rays out slightly before they enter the eye so they now focus correctly at the retina. Hypermetropia (farsightedness or hyperopia -- age-related loss of accommodation of this kind is specifically called presbyopia) occurs when the eye lens has too long a focal length (from a thinned lens or a shortened eyeball), so near objects focus behind the retina and the person's near point $y$ is pushed out well beyond the normal 25 cm; using the lens equation for a correcting lens that images an object at $y$ onto the standard near point ($u=-y$, $v=-25\,\text{cm}$) gives a required focal length $f=\dfrac{25y}{y-25}$ (in cm), always positive since $y>25$, i …