Calculating Lens Power for New Eyeglasses

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SUMMARY

The discussion centers on calculating the power of new eyeglass lenses for a middle-aged man who initially used 2.0 D lenses to read at 25 cm but later required a distance of 35 cm for clear vision. The correct power of the new lenses was determined to be approximately 3.1 D. Participants utilized the thin lens equation, P = 1/f, to derive the necessary calculations, clarifying the relationship between the focal lengths of the eye and the glasses. The final consensus emphasized the importance of understanding how the focal lengths interact to achieve the desired vision correction.

PREREQUISITES
  • Understanding of lens power calculations using the formula P = 1/f
  • Knowledge of focal length in meters
  • Familiarity with the thin lens equation
  • Basic concepts of vision correction and diopters
NEXT STEPS
  • Study the thin lens equation in detail to understand its applications in optics
  • Learn about the relationship between focal length and lens power in diopters
  • Research common vision correction methods and their optical principles
  • Explore advanced topics in optics, such as aberrations and lens design
USEFUL FOR

Optometrists, optical technicians, students studying optics, and anyone involved in vision correction and eyeglass lens design will benefit from this discussion.

matt72lsu
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Homework Statement


A middle-aged man starts to wear eyeglasses with lenses of 2.0 D that allow him to read a book held as close as 25 cm. Several years later, he finds that he must hold a book no closer than 35 cm to read it clearly with the same glasses, so he gets new glasses.

What is the power of the new lenses?

Homework Equations


P = 1/f (f in meters)


The Attempt at a Solution


P = 1/.35 = 2.9 (it was wrong)
 
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By your reasoning the original pair of glasses should have been 4 D (P = 1/0.25 = 4.0). Think about it some more.
 
So the only thing I can come up with is .5/.35 = 1.4 (based on what you said)
 
I'm still not sure what I'm doing wrong here. Help?
 
In diptres the focal length of the eye and the glasses add.

Currently, eyeD + 2D = 1/0.35
Wants, eyeD + xD = 1/0.25
You are trying to find x
 
ok i still don't completely understand, but I come up with 3.1 ?
 
That's what I get as well but here's how I did it.

Several years later an object placed 35 cm away from the lens focuses on his retina. Using the thin lens equation I found the retina's distance from the lens. Then I said that a new lens will focus an object at 25 cm at the retina's distance and just used the thin lens equation again.
 
Ok cool. Thanks everybody!
 

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