What Is the Closest Object That Can Be Seen Clearly with Swapped Glasses?

[RicXeoR]

hello all,

i've been working on this whole day, still can't figure out, any help would be appreciated! thanks a bunch!

Problem as follows:
Bill is farsighted and has a near point located 140 cm from his eyes. Anne is also farsighted, but her near point is 75.6 cm from her eyes. Both have glasses that correct their vision to a normal near point (25.0 cm) from their eyes, and both wear glasses 2.0 cm from the eyes. Relative to the eyes, what is the closest object that can be seen clearly (a) by Anne when she wars Bill’s glasses and (b) by Bill when he wears Anne’s glasses.

This is what I have interpreted: I have S(near point) as 140-2 and 75.6-2, d of object as 25 cm, and d of image as -138 and -73.6 because it's on the same side as the object. With these numbers i plug into the thin lens equation to get 1/f or power of the lens. Then I switched the powers around, used d of image as 140 and 75.6, and solved for each d of object.

Those answers turn out as wrong. What I'm doing wrong here, any help is much appreciated...Thanks!

 

[HallsofIvy]

I presume that you used 140-2= 138 and 75.6-2= 73.6 to get the distance relative to the lens but I don't see why you then used 25 as d rather than 25-2= 23 for the same reason.

 

[M98Ranger]

Hi there! It sounds like you are on the right track with your calculations. However, there may be a few things that you are missing or not taking into account. Here are some suggestions that may help you solve this problem:

1. Make sure you are using the correct formula for the thin lens equation. The formula is 1/f = 1/di + 1/do, where f is the focal length of the lens, di is the distance of the image from the lens, and do is the distance of the object from the lens.

2. When plugging in values for di and do, make sure you are using the correct signs (+ or -) depending on whether the image is on the same side or opposite side as the object.

3. Double check your calculations and make sure you are using the correct units (cm or m). This can sometimes cause errors in your final answer.

4. It may also be helpful to draw a diagram to visualize the problem and make sure you are using the correct distances and signs.

If you are still having trouble, it may be helpful to reach out to your teacher or a classmate for assistance. Good luck!