Calculating Lens Power for New Eyeglasses

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Homework Help Overview

The discussion revolves around calculating the power of new eyeglass lenses for a middle-aged man who experiences a change in his near vision. Initially, he used lenses with a power of 2.0 D, allowing him to read at 25 cm, but later found he could only read at a distance of 35 cm, prompting the need for new glasses.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between lens power and focal length, questioning the calculations made for the original and new lenses. Some participants suggest re-evaluating the initial assumptions regarding the focal lengths and the resulting powers.

Discussion Status

The discussion is ongoing, with various participants sharing their calculations and reasoning. Some have arrived at similar values for the new lens power, while others express uncertainty and seek clarification on their approaches. There is a collaborative effort to understand the underlying principles of lens power and focal length.

Contextual Notes

Participants are working under the constraints of the problem statement and the need to derive the new lens power based on changing reading distances. There is an emphasis on understanding the relationship between the eye's focal length and the corrective lenses.

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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