How to Determine Focal Length and Power of Lenses for Farsightedness

In summary, the problem involves finding the focal length and power of spectacle lenses for a farsighted woman who cannot see objects closer than 60.0 cm. The equation used is 1/p + 1/q = 1/f for focal length and 1/f = P for power. The solution involves setting p to infinity and solving for q, with the additional information that the book is at a distance of 25.0 cm. It is assumed that the eye and lens are at the same place.
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Homework Statement


A farsighted woman cannot see objects clearly that are closer to her eye than 60.0 cm. Determine the focal length and power of the spectacle lenses that will enable her to read a book at a distance of 25.0 cm.


Homework Equations


The equation I have been using to find the focal length is: 1/p + 1/q = 1/f

For the magnifying power, I believe that equation is 1/f = P


The Attempt at a Solution



I've been getting stuck after setting p to infinity which my instructor said to do, then I'm left with 1/q = 1/f ... I don't see how that helps me narrow down my attempt in solving the problem. I understand that the woman needs a min of 60 cm length for the image to be perfectly seen in her eye but I'm not seeing how to incorporate the other information presented in the problem.
 
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  • #2
The book is at 25 cm distance from the eye, but the women can see something not closer than 60 cm. If the image of the book is at 60 cm, would she see it? What are the object distance and image distance then? And you can assume that the eye and the lens are at the same place. distance from the eye is the same as the distance from the lens.

ehild
 
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1. How do lenses work?

Lenses work by bending and refracting light, causing it to converge or diverge. This allows the eye to focus light onto the retina for clear vision.

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. Concave lenses are thinner in the middle and thicker at the edges, causing light to diverge.

3. How do glasses correct vision?

Glasses use lenses to correct vision by changing the way light enters and is focused by the eye. For nearsightedness, concave lenses are used to diverge light before it enters the eye. For farsightedness, convex lenses are used to converge light before it enters the eye.

4. Can lenses be used for more than just vision correction?

Yes, lenses have many other applications such as in cameras, telescopes, and microscopes. They can also be used in laser technology, fiber optics, and other scientific and industrial fields.

5. How do we see objects at different distances?

The lens of the eye can change its shape to adjust the focal length and focus light from objects at different distances. This process is called accommodation and is controlled by the ciliary muscles in the eye.

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