Calculating Lens Power for New Eyeglasses

  • Thread starter matt72lsu
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In summary, a middle-aged man starts wearing eyeglasses with 2.0 D lenses that allow him to read a book 25 cm away. After several years, he needs to hold the book at least 35 cm away to read it clearly. By using the thin lens equation, it can be determined that the new lenses have a power of approximately 3.1 D.
  • #1
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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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  • #2
By your reasoning the original pair of glasses should have been 4 D (P = 1/0.25 = 4.0). Think about it some more.
 
  • #3
So the only thing I can come up with is .5/.35 = 1.4 (based on what you said)
 
  • #4
I'm still not sure what I'm doing wrong here. Help?
 
  • #5
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
 
  • #6
ok i still don't completely understand, but I come up with 3.1 ?
 
  • #7
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.
 
  • #8
Ok cool. Thanks everybody!
 

What is lens power?

Lens power, also known as diopters, is a measurement of the refractive power of a lens. It tells us how much a lens can bend light to focus it on the retina of the eye.

How is lens power measured?

Lens power is measured in diopters, which is the reciprocal of the focal length of the lens in meters. For example, a lens with a focal length of 0.5 meters has a power of 2 diopters.

What does a positive lens power indicate?

A positive lens power indicates that the lens is convex, meaning it is thicker in the middle and thinner at the edges. This type of lens is used to correct for farsightedness (hyperopia).

What does a negative lens power indicate?

A negative lens power indicates that the lens is concave, meaning it is thinner in the middle and thicker at the edges. This type of lens is used to correct for nearsightedness (myopia).

How does lens power affect vision?

The lens power of eyeglasses or contact lenses helps to bend light in a way that compensates for any refractive errors in the eye. This allows for clear vision by focusing light on the retina. The higher the lens power, the more correction is needed for vision problems.

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