Medical Without glasses, a certain person needs to have his eyes 15.0 cm from a book to read com

step 1 For this problem on the topic of geometrical optics, we are told that a person without glasses n

Medical Without glasses, a certain person needs to have his...

Medical Without glasses, a certain person needs to have his eyes $15.0$ $\mathrm{cm}$ from a book to read comfortably and can focus clearly only on distant objects up to $2.75 \mathrm{~m}$ away, but no farther. A typical normal eye should be able to focus on objects that are between $25.0 \mathrm{~cm}$ (the near point) and infinity (the far point) from the eye. (a) What type of correcting lenses does the person need: single focal length or bifocals? Why? (b) What should an optometrist specify as the focal length(s) of the correcting contact lens or lenses? (c) What is the power (in diopters) of the correcting lens or lenses? SSM $\underline{\text { Example } 24-6}$

Key Concepts

Near and Far Points

The near point is the closest distance at which the eye can focus clearly, and the far point is the furthest distance over which the eye can maintain a clear image. In normal vision, the human eye comfortably focuses on objects roughly between 25.0 cm and infinity. Abnormalities in these limits indicate that the eye’s accommodation is not functioning normally, necessitating optical correction.

Corrective Lenses

Corrective lenses are used to adjust the effective optical power of the eye so that images of objects at desired distances are properly focused on the retina. By introducing an appropriate lens into the optical path, the apparent location of objects (either near or far) can be shifted to lie within the focal range of the eye, compensating for conditions such as myopia or presbyopia.

Bifocals vs Single Vision Lenses

In cases where the eye has two distinct ranges for clear vision—for instance, when near tasks (like reading) require a different adjustment than distance viewing—a single lens correction may not be sufficient. Bifocal lenses provide two different focal lengths in one lens, allowing simultaneous correction for both near and distance vision, which is why they are considered when conflicting requirements exist.

Lens Power (Diopters) and Focal Length

The optical power of a lens, measured in diopters (D), is defined as the inverse of its focal length in meters (P = 1/f). This relationship is central to determining the specifications needed for corrective lenses. Accurately calculating the required diopter strength and corresponding focal length enables an optometrist to prescribe a lens that shifts the effective near or far point to desired distances.

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