Question

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

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

Step-by-step solution

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.

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.

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.

Convert Viewing Distance to Meters

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

Calculate the Power of Lens

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

Conclusion

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

Key concepts

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.