Calculating Lens Power for New Eyeglasses

[matt72lsu]

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)

 

[skeptic2]

By your reasoning the original pair of glasses should have been 4 D (P = 1/0.25 = 4.0). Think about it some more.

 

[matt72lsu]

So the only thing I can come up with is .5/.35 = 1.4 (based on what you said)

 

[matt72lsu]

I'm still not sure what I'm doing wrong here. Help?

 

[mgb_phys]

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

 

[matt72lsu]

ok i still don't completely understand, but I come up with 3.1 ?

 

[AtticusFinch]

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.

 

[matt72lsu]

Ok cool. Thanks everybody!