If the lens of a person's eye is removed because of cataracts (as has been done since ancient times), why would you expect an eyeglass lens of about 16 D to be prescribed?

The human eye typically has a focal length of about 17mm when focusing on distant objects and 22mm when focusing on near objects. If the lens of a person's eye is removed due to cataracts, the eye loses its ability to change its focal length and focus on objects at different distances. In other words, the eye becomes ametropic.

In order to determine the type and power of an eyeglass lens that would best compensate for the lost focusing ability of a person with a removed eye lens, we need to use the Lens formula: \(\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}\) Here, \(f\) represents the lens's focal length, \(d_o\) represents the object distance (relative to the lens), and \(d_i\) represents the image distance (relative to the lens).

Diopter (D) is a unit used to measure the refractive power of a lens. It is defined as the inverse of the focal length of the lens (in meters). So, if we need to find the power of a lens needed, we can use the following equation: Lens power (D) = \(\frac{1}{f}\) (in meters)

We know that a normal human eye has a focal length of about 17mm when focused on distant objects, which is approximately equal to the distance between the retina and the cornea. So, we can assume that the required eyeglass lens should focus light similarly to a normal eye, around the same focal length. First, we need to convert the focal length from millimeters to meters: \(f = 17mm = 0.017m\) Using the equation for lens power, we get: Lens power (D) = \(\frac{1}{0.017m}\) ≈ 58.82D However, we must take into account that the removed human eye lens has a power of approximately 43D when focused on distant objects. To find the correct eyeglass lens power, we subtract the power of the removed eye lens from the calculated lens power: Eyeglass Lens Power (D) = 58.82D - 43D ≈ 15.82D ≈ 16D

An eyeglass lens with around 16 diopters would be prescribed for a person with a removed eye lens due to cataracts because it compensates for the lost focusing ability of the human eye and provides the necessary additional refractive power to focus on distant objects similarly to a normal eye.