/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 97 In one form of cataract surgery ... [FREE SOLUTION] | 91Ó°ÊÓ

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In one form of cataract surgery the person's natural lens, which has become cloudy, is replaced by an artificial lens. The refracting properties of the replacement lens can be chosen so that the person's eye focuses on distant objects. But there is no accommodation, and glasses or contact lenses are needed for close vision. What is the power, in diopters, of the corrective contact lenses that will enable a person who has had such surgery to focus on the page of a book at a distance of 24 cm?

Short Answer

Expert verified
The power of the corrective lenses needed is approximately 4.17 diopters.

Step by step solution

01

Understand the Problem

The question asks for the power in diopters of corrective lenses needed for post-surgery close vision. In this case, the eye is set for distant vision, meaning it lacks the ability to focus on nearby objects.
02

Identify Lens Formula

The formula for lens power, measured in diopters, is given by:\[ P = \frac{1}{f} \]where \( f \) is the focal length in meters.
03

Determine Desire Viewing Distance

Since the person wants to read at a distance of 24 cm, this distance is the desired focal length for the corrective lens to provide clear vision at this range.
04

Convert Viewing Distance to Meters

Convert the distance from centimeters to meters.\[ 24\, \text{cm} = 0.24\, \text{m} \]
05

Calculate the Power of Lens

Use the lens power formula with \( f = 0.24 \) m:\[ P = \frac{1}{0.24} \approx 4.17 \text{ diopters} \]
06

Conclusion

The calculated power of the corrective lenses is approximately \( 4.17 \) diopters.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Lens Power
Lens power is a crucial factor in determining how well a lens can focus light onto the retina to create clear images. It is measured in diopters (D), which quantify the lens's ability to bend light. Calculating lens power involves the formula:
  • \( P = \frac{1}{f} \)
where \( P \) represents the power in diopters and \( f \) is the focal length in meters.
For example, a lens with a short focal length will have a higher power, enabling it to bend light more strongly. This concept is particularly important when creating lenses for corrective purposes in eyewear. Understanding lens power is essential when determining the strength needed in glasses or contact lenses to correct vision deficiencies.
Cataract Surgery
Cataract surgery is a common procedure aimed at correcting the vision problems caused by cataracts. Cataracts occur when the natural lens of the eye becomes cloudy, affecting vision quality and clarity. During surgery, the cloudy lens is removed and typically replaced with a clear, artificial lens, known as an intraocular lens (IOL).
The primary goal of cataract surgery is to restore focusing ability for distant vision; however, accommodation, or the ability to focus on close objects, is often limited or lost. That's why many patients require additional corrective lenses (glasses or contacts) to see objects up close clearly. Understanding the impact of cataract surgery on lens power and accommodation can help optimize visual outcomes for patients.
Corrective Lenses
Corrective lenses are designed to change the focal point of light entering the eye to improve visual clarity. These lenses compensate for refractive errors, such as myopia and hyperopia. These problems are due to the eye's inability to focus light directly onto the retina.
In the context of post-cataract surgery, corrective lenses are often necessary for reading or close work, as the artificial lens typically focuses on distant objects. This captures the need for glasses or contacts with a specific power to allow the eye to focus appropriately at a desired distance – like reading at 24 cm, for example.
When calculating the necessary power for these lenses, it’s important to rely on accurate measurements and calculations to ensure the best visual outcome.
Focal Length Conversion
Converting focal lengths is an important step in determining the power of a lens. Focal length is the distance over which parallel rays of light are brought to focus and it's typically measured in meters for lens power calculations.
When you're given a focal length in centimeters, as often happens in practical scenarios, you'll first need to convert it to meters. This is done by dividing the measurement in centimeters by 100.
  • For instance, 24 cm is converted to 0.24 m by dividing 24 by 100.
This conversion ensures accurate calculations when you're using the lens power formula, as diopters depend on using the focal length in meters. Proper conversion is key to effectively calculating and understanding lens power.

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Most popular questions from this chapter

A frog can see an insect clearly at a distance of 10 cm. At that point the effective distance from the lens to the retina is 8 mm. If the insect moves 5 cm farther from the frog, by how much and in which direction does the lens of the frog's eye have to move to keep the insect in focus? (a) 0.02 cm, toward the retina; (b) 0.02 cm, away from the retina; (c) 0.06 cm, toward the retina; (d) 0.06 cm, away from the retina.

A coin is placed next to the convex side of a thin spherical glass shell having a radius of curvature of 18.0 cm. Reflection from the surface of the shell forms an image of the 1.5-cm-tall coin that is 6.00 cm behind the glass shell. Where is the coin located? Determine the size, orientation, and nature (real or virtual) of the image.

The cornea of the eye has a radius of curvature of approximately 0.50 cm, and the aqueous humor behind it has an index of refraction of 1.35. The thickness of the cornea itself is small enough that we shall neglect it. The depth of a typical human eye is around 25 mm. (a) What would have to be the radius of curvature of the cornea so that it alone would focus the image of a distant mountain on the retina, which is at the back of the eye opposite the cornea? (b) If the cornea focused the mountain correctly on the retina as described in part (a), would it also focus the text from a computer screen on the retina if that screen were 25 cm in front of the eye? If not, where would it focus that text: in front of or behind the retina? (c) Given that the cornea has a radius of curvature of about 5.0 mm, where does it actually focus the mountain? Is this in front of or behind the retina? Does this help you see why the eye needs help from a lens to complete the task of focusing?

The diameter of Mars is 6794 km, and its minimum distance from the earth is 5.58 \(\times\) 10\(^7\)km. When Mars is at this distance, find the diameter of the image of Mars formed by a spherical, concave telescope mirror with a focal length of 1.75 m.

A person can see clearly up close but cannot focus on objects beyond 75.0 cm. She opts for contact lenses to correct her vision. (a) Is she nearsighted or farsighted? (b) What type of lens (converging or diverging) is needed to correct her vision? (c) What focal length contact lens is needed, and what is its power in diopters?

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