How to Determine Focal Length and Power of Lenses for Farsightedness

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SUMMARY

The discussion focuses on determining the focal length and power of spectacle lenses for a farsighted woman who cannot see objects closer than 60.0 cm. Using the lens formula 1/p + 1/q = 1/f, where p is the object distance and q is the image distance, the user attempts to solve for the focal length needed to read a book at 25.0 cm. The key insight is that the image of the book must be formed at 60.0 cm for the woman to see it clearly, leading to the conclusion that the appropriate calculations must incorporate both the object distance of 25.0 cm and the required image distance of 60.0 cm.

PREREQUISITES
  • Understanding of the lens formula: 1/p + 1/q = 1/f
  • Knowledge of focal length and power of lenses
  • Basic concepts of optics, specifically related to farsightedness
  • Ability to manipulate equations involving object and image distances
NEXT STEPS
  • Calculate the focal length of lenses using the lens formula with given distances.
  • Learn about the power of lenses and how it relates to focal length using P = 1/f.
  • Explore practical applications of corrective lenses for different types of vision impairments.
  • Study the effects of lens curvature on focal length and image formation.
USEFUL FOR

Optometry students, physics students studying optics, and individuals interested in understanding corrective lenses for farsightedness.

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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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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
 
Last edited:

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