Glasses to fix near points and far points

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In summary: For the new far point you have that 1/f = - 0.51 mThe image needs to form at a distance of 0.23 m in front of the lens in order for him to see it. That is i = -0.23 m. The object distance that you get will then be his new far point. That is it is the new farthest point (- 2 cm) that he can hold something in front of him and still see it in focus with his glasses on.
  • #1
vu10758
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Homework Statement



a)A person has a near point of .6m and far point of 2m . What power of glasses would be needed for the person to see infinitely far away. Assume that glasses are 2cm from the person's eyes. If the person used those glasses, what would his new near point be?

b) What power of glasses would be needed to bring the person's near point to .25m. If the person used those glasses, what would their new far point be?



Homework Equations



1/f = 1/o + 1/i
P=1/f

The Attempt at a Solution



This is what I have so far.

I know that
1/f = 1/o + 1/i

I want an image at infinity so 1/f = 1/o
The object is 2m from the eyes so it is 1.98 m from the glasses. The direction of the light is toward the glasses while the image is in the opposite direction. so o is negative.

1/-1.98 = -.505


And this is the correct answer according to the answer key.

I have problem solving for the new near point though.

1/f = 1/o + 1/i
-.505 = 1/o + 1/i

I want to create a new image for a distance of .6 m from the eyes or .58 from the glasses

-.505 = 1/.58 + 1/-i
-1/1.98 - 1/.58 = -1/i
I get i = .44 meters

but the correct answer is .82 meters. What did i do wrong?

I am having a similar problem for part b so I think I can get it if I find out what I did wrong here in part a.
 
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  • #2
a) The object is at infinity (what the person wants to look at). The image needs to form at -1.98 meters (his far point, in front of the glasses).
 
  • #3
Thanks for your help.

I just realized that I need help for part b as well.

b)

1/f = 1/o + 1/i

The person's far point is .6 or .58 from the glasses. I want him to see at .25 m or .23 m from the glasses.

1/-f = 1/.58 + 1/-.23
1/-f = -2.62
1/f = 2.62

that is the power. I am getting the wrong answer when I have to calculate the new near point though.

-2.62 = 1/1.98 + 1/-i

I get i = .32 m but the correct answer is .34m. Is there anything wrong with the 1/f and 1/1.98? I know that i/f =2.62 according to the answer key so I think I either rounded something wrong or have 1/1.98 wrong. However, I don't know what the object distance would be if it is not 1.98.

Thanks in advance for your help.
 
  • #4
If -2.62 is 1/f and the answer is indeed .34 for as in the answer key then o must be greater than 3 meters away. How is that possible? Do I somehow combine that 1.98 m with the other part a, which is .82 meters?
 
  • #5
a) For the new near point you have that 1/f = - 0.51 m
The image needs to form at a distance of 0.58 m in front of the lens in order for him to see it. That is i = - 0.58 m. The object distance that you get will then be his new near point. That is it is the new closest point (+ 2 cm) that he can hold something in front of him and still see it in focus with his glasses on.
 
Last edited:

1. How do glasses fix near and far points?

Glasses are able to fix near and far points by using lenses to bend light and adjust the focal point of the eye. Near-sightedness is corrected by using concave lenses, which diverge the light and move the focal point back to the retina. Far-sightedness is corrected by using convex lenses, which converge the light and move the focal point forward to the retina.

2. How do I know if I need glasses for near and far points?

If you have difficulty seeing objects up close or far away, you may need glasses to correct your near and far points. Other signs that you may need glasses include headaches, eye strain, and squinting to see clearly. It is important to have regular eye exams to determine if you need glasses and to ensure your prescription is up to date.

3. Can glasses fix both near and far points at the same time?

Yes, glasses can correct both near and far points at the same time. Bifocal or multifocal lenses have different areas for near and far vision, allowing you to see clearly at all distances without needing to switch glasses. Progressive lenses are also available, which gradually change in prescription from top to bottom to provide clear vision at all distances.

4. Will glasses for near and far points improve my vision permanently?

Glasses for near and far points can improve your vision while you are wearing them, but they will not permanently fix your vision. These glasses are a corrective tool and do not change the structure or function of your eyes. However, wearing glasses can help prevent further eye strain and fatigue, which can improve your overall vision over time.

5. Can I use glasses for near and far points for activities like reading and driving?

Yes, glasses for near and far points can be used for various activities, including reading and driving. The prescription of the lenses can be adjusted to meet your specific needs for different tasks. However, it is important to consult with your eye doctor to determine the best type of glasses for your particular activities and to ensure your prescription is accurate.

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