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Chapter 2: Problem 21

It has become common to replace the cataract-clouded lens of the eye with an internal lens. This intraocular lens can be chosen so that the person has perfect distant vision. Will the person be able to read without glasses? If the person was nearsighted, is the power of the intraocular lens greater or less than the removed lens?

Short Answer

Expert verified
The person with an intraocular lens will not be able to read without glasses, as the lens is designed to correct distant vision, which requires a convex lens. Reading requires focusing on nearby objects and would likely be more challenging with an additional convex lens. For a nearsighted person, the power of the intraocular lens is greater than the power of the removed lens, as it must compensate for their nearsightedness with a positive (convex) power.

Step by step solution

01

Understand the problem

A person has undergone cataract surgery, and an intraocular lens is placed to correct their distant vision. We need to determine whether: - The person will be able to read without glasses after the surgery - For a nearsighted person, if the power of the intraocular lens is greater or less than the removed lens.
02

Optics concepts

To solve this problem, we must understand the following concepts from optics: 1. Lens power (P): It is the inverse of focal length (f), measured in diopters (D). Formula: P = 1/f, f in meters. 2. Nearsightedness (myopia): A condition where the person can see nearby objects clearly, but distant objects are blurry. In this case, the eye focuses the light in front of the retina. This is typically corrected with a negative (concave) lens. 3. Farsightedness (hyperopia): A condition where the person can see distant objects clearly, but nearby objects are blurry. In this case, the eye focuses the light behind the retinal plane. This is typically corrected with a positive (convex) lens.
03

Determine if the person can read without glasses

Since the intraocular lens corrects the person's distant vision, it is acting like a convex lens (used to correct farsightedness). However, reading requires the eye to focus on nearby objects, so an additional convex lens could make the reading even more challenging for the person as it would cause the eye to focus even further behind the retina. Therefore, the person will not be able to read without glasses after the surgery.
04

Compare the power of the intraocular lens and the removed lens

As the person was nearsighted, their removed natural lens would effectively function as a negative (concave) lens. To correct their distant vision, the intraocular lens must have a positive (convex) power to compensate for the person's nearsightedness. So, the power of the intraocular lens is greater than the power of the removed lens for a nearsighted person.

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