Power Range of the Eye

For clear vision, the image must be on the retina, and so $d_{\text{i}}=\mathrm{2.00\; cm}$ here. For distant vision, $d_{\mathrm{o}}\approx \mathrm{\infty }$, and for close vision, $d_{\mathrm{o}}=\mathrm{25.0\; cm}$, as discussed earlier. The equation $P=\frac{1}{d_{\text{o}}}+\frac{1}{d_{\text{i}}}$ as written just above, can be used directly to solve for $P$ in both cases, since we know $d_{\text{i}}$ and $d_{\mathrm{o}}$. Power has units of diopters, where $\text{1 D}=\text{1/m}$, and so we should express all distances in meters.

For distant vision,

Since $1/\infty =0$, this gives

Now, for close vision,

For an eye with this typical 2.00 cm lens-to-retina distance, the power of the eye ranges from 50.0 D (for distant totally relaxed vision) to 54.0 D (for close fully accommodated vision), which is an 8% increase. This increase in power for close vision is consistent with the preceding discussion and the ray tracing in Figure 26.4. An 8% ability to accommodate is considered normal but is typical for people who are about 40 years old. Younger people have greater accommodation ability, whereas older people gradually lose the ability to accommodate. When an optometrist identifies accommodation as a problem in elder people, it is most likely due to stiffening of the lens. The lens of the eye changes with age in ways that tend to preserve the ability to see distant objects clearly but do not allow the eye to accommodate for close vision, a condition called presbyopia (literally, elder eye). To correct this vision defect, we place a converging, positive power lens in front of the eye, such as found in reading glasses. Commonly available reading glasses are rated by their power in diopters, typically ranging from 1.0 to 3.5 D.