# Glasses to fix near points and far points

## Homework Statement

a)A person has a near point of .6m and far point of 2m . What power of glasses would be needed for the person to see infinitely far away. Assume that glasses are 2cm from the person's eyes. If the person used those glasses, what would his new near point be?

b) What power of glasses would be needed to bring the person's near point to .25m. If the person used those glasses, what would their new far point be?

1/f = 1/o + 1/i
P=1/f

## The Attempt at a Solution

This is what I have so far.

I know that
1/f = 1/o + 1/i

I want an image at infinity so 1/f = 1/o
The object is 2m from the eyes so it is 1.98 m from the glasses. The direction of the light is toward the glasses while the image is in the opposite direction. so o is negative.

1/-1.98 = -.505

I have problem solving for the new near point though.

1/f = 1/o + 1/i
-.505 = 1/o + 1/i

I want to create a new image for a distance of .6 m from the eyes or .58 from the glasses

-.505 = 1/.58 + 1/-i
-1/1.98 - 1/.58 = -1/i
I get i = .44 meters

but the correct answer is .82 meters. What did i do wrong?

I am having a similar problem for part b so I think I can get it if I find out what I did wrong here in part a.

Last edited:

andrevdh
Homework Helper
a) The object is at infinity (what the person wants to look at). The image needs to form at -1.98 meters (his far point, in front of the glasses).

I just realized that I need help for part b as well.

b)

1/f = 1/o + 1/i

The person's far point is .6 or .58 from the glasses. I want him to see at .25 m or .23 m from the glasses.

1/-f = 1/.58 + 1/-.23
1/-f = -2.62
1/f = 2.62

that is the power. I am getting the wrong answer when I have to calculate the new near point though.

-2.62 = 1/1.98 + 1/-i

I get i = .32 m but the correct answer is .34m. Is there anything wrong with the 1/f and 1/1.98? I know that i/f =2.62 according to the answer key so I think I either rounded something wrong or have 1/1.98 wrong. However, I don't know what the object distance would be if it is not 1.98.