# Geometric Optics and Lens Power

• CCR5
In summary, when a farsighted boy with a near point of 2.3 m requires eyeglasses to correct his vision, the correct choice of lens power in diopters is 3.75. This is because corrective lenses are only available in increments of 0.25 diopters, and the near point should be no further than 25 cm. Therefore, the closest available option is 3.75 diopters.
CCR5

## Homework Statement

A farsighted boy has a near point at 2.3 m and requires eyeglasses to correct his vision.

Corrective lenses are available in increments in power of 0.25 diopters. The eyeglasses

should have lenses of the lowest power for which the near point is no further than 25

cm. The correct choice of lens power for eyeglasses, in diopters, is:

1/s + 1/s' = 1/f
1/f = P

## The Attempt at a Solution

I keep getting a value of 3.57 diopters, however, the correct answer is 3.75.

CCR5 said:
Corrective lenses are available in increments in power of 0.25 diopters.
3.57 diopters does not exist as a choice.

kuruman said:
3.57 diopters does not exist as a choice.
Wonderful... Can you shed some light on the increment and its relation to the correct answer of 3.75?

CCR5 said:
Can you shed some light on the increment ...
CCR5 said:
Corrective lenses are available in increments in power of 0.25 diopters.
... and its relation to the correct answer of 3.75
Ergo: you have to chose between 3.5 and 3.75. Now you have to calculate which distance at diopters of 3.5 or 3.75 fulfills the requirement "near point no further than ..."

CCR5
fresh_42 said:
You already answered this by yourself!Ergo: you have to chose between 3.5 and 3.75. Now you have to calculate which distance at diopters of 3.5 or 3.75 fulfills the requirement "near point no further than ..."

Errm. So based off the given answers, which ever is closest to to my value an estimated value of 0.25 increment? Gotcha! Thank you for your response.

## 1. What is Geometric Optics?

Geometric Optics is a branch of physics that studies the behavior of light as it travels in straight lines through various materials and interacts with lenses and mirrors.

## 2. What is the difference between convex and concave lenses?

Convex lenses are thicker in the middle and thinner at the edges, causing light to converge and focus at a point. Concave lenses are thinner in the middle and thicker at the edges, causing light to diverge.

## 3. How is Lens Power measured?

Lens power is measured in diopters (D) and is calculated as the inverse of the focal length in meters. A lens with a higher power has a shorter focal length and can bend light more strongly.

## 4. What is the relationship between lens power and image distance?

The relationship between lens power and image distance is inversely proportional. This means that as the lens power increases, the image distance decreases, and vice versa.

## 5. How does the human eye use lens power to focus light?

The lens of the human eye has the ability to change its shape, allowing it to adjust its power and focus light from objects at different distances onto the retina. This process is known as accommodation and is controlled by the ciliary muscles.

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