# Thin Lens Equation: Nearsighted

• blue_lilly
In summary, the lens of the eye can adjust its focal length to form a clear image on the retina for both distant and close objects. However, some people may need corrective lenses if their eye cannot adjust well enough, resulting in a near- or far-sightedness. To find the focal length of a lens needed for a near-sighted person with a far point of 71.5 cm, the formula (1/od)+(1/id)=(1/f) can be used, where od is the object distance (71.5 cm in this case) and id is the image distance (which is the distance of the retina from the lens). The refractive power of the lens can also be calculated using the formula Power=1/f
blue_lilly

## Homework Statement

For those fortunate souls who do not need glasses, the lens of the eye adjusts its focal length in order to form a proper image on the retina. This typically means that very distant objects as well as objects as close as 25 cm can be seen clearly.
Many of us need corrective lenses since the lens in our eye cannot adjust sufficiently to produce a clear image over the full range object distances. This may be because the lens itself does not adjust well or because the eye is either longer or shorter than ‘normal’.
In the case of someone who is nearsighted (can see up close) the eye may only be able to see clearly items up to 50cm or 1m away (this would be the far point). In order to see something further away, a lens (either glasses or contacts) is used to produce a virtual image of a distant object at the person’s far point. Their eye can then accommodate the rest of the way and produce a clear image.
1) Suppose a person who has a far point of 71.5 cm is trying to view a distant object. What is the focal length (with correct sign) of a lens that would take a distant object and make an image on the same side of the lens as the object a distance 71.5 cm from the lens?​
2) Lenses are prescribed in terms of their refractive power, which is expressed in terms of diopters (see the text or your favorite search engine for the definition of a diopter). What is the refractive power of this lens in terms of diopters? (do not enter units.)​

## Homework Equations

(1/od)+(1/id)=(1/f)

Power=1/f

## The Attempt at a Solution

I know that the object distance is 71.5cm. I think the image distance is -50cm because the object is on the same side as the object which would make it a virtual image and virtual images have a neg number.
(1/od)+(1/id)=(1/f)
(1/71.5cm)+(-1/50)=(1/f)
-.006013986=(1/f)
(1/f)=-.006013986
f=(1/-.006013986)
f=-166.2790
So the focal length I got was -166.2790cm. However the answer is wrong and I'm not sure what I am doing that is incorrect.

Any help would be greatly appreciated!

blue_lilly said:

## The Attempt at a Solution

I know that the object distance is 71.5cm. I think the image distance is -50cm because the object is on the same side as the object which would make it a virtual image and virtual images have a neg number.
(1/od)+(1/id)=(1/f)
(1/71.5cm)+(-1/50)=(1/f)
-.006013986=(1/f)
(1/f)=-.006013986
f=(1/-.006013986)
f=-166.2790
So the focal length I got was -166.2790cm. However the answer is wrong and I'm not sure what I am doing that is incorrect.

Any help would be greatly appreciated!
No, the image distance is not -50 cm. 50-100 cm are the far points of near-sighted persons.

In the problem, the far point is at 71.5 cm from the eye. The image falls on the retina if the object is at 71.5 cm distance. So the image distance is the distance of the retina from the lens.
The near-sighted person needs glasses to bring in infinity to his/her far point which is 71.5 cm in the problem.

ehild

## 1. What is the Thin Lens Equation?

The Thin Lens Equation is a formula used to calculate the distance between an object and its image formed by a thin lens. It takes into account the focal length of the lens, the distance of the object from the lens, and the distance of the image from the lens.

## 2. How does the Thin Lens Equation work for nearsighted individuals?

Nearsightedness, or myopia, is a condition where an individual has trouble seeing distant objects clearly. In this case, the Thin Lens Equation can be used to determine the position and size of the image formed by a lens for nearsighted individuals. The equation takes into account the focal length, object distance, and image distance, which can be used to calculate the corrective lens prescription needed for the individual.

## 3. What causes nearsightedness?

Nearsightedness is caused by a refractive error in the eye, where the light entering the eye is focused in front of the retina instead of directly on it. This can be due to a longer-than-normal eyeball or a steeply curved cornea. This causes distant objects to appear blurry, but near objects can still be seen clearly.

## 4. How is the Thin Lens Equation related to corrective lenses for nearsightedness?

The Thin Lens Equation is used to calculate the prescription for corrective lenses for nearsighted individuals. The lens prescription is determined by the focal length of the lens needed to bring the image of a distant object into focus on the retina. This is based on the individual's degree of nearsightedness and the distance at which they can see clearly.

## 5. Can the Thin Lens Equation be used for all types of lenses?

Yes, the Thin Lens Equation can be used for all types of lenses, including concave, convex, and even non-spherical lenses. However, it is important to note that the equation assumes thin lenses and small angles, so it may not be as accurate for thicker lenses or for objects that are too far from the lens.

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