Two lab partners, Mary and Paul, are both farsighted. Mary has a near point of 6

Question

Two lab partners, Mary and Paul, are both farsighted. Mary has a near point of 64.4 cm from her eyes and Paul has a near point of 110 cm from his eyes. Both students wear glasses that correct their vision to a normal near point of 25.0 cm from their eyes, and both wear glasses 1.80 cm from their eyes. In the process of wrapping up their lab work and leaving for their next class, they exchange glasses (Mary leaves with Paul's glasses and Paul leaves with Mary's glasses). When they get to their next class, find the following.

(b) Determine the distance to the closest object that Paul can see clearly (relative to his eyes) while wearing Mary's glasses.

I know part a which was the distance to the closest object that Mary can see clearly (relative to her eyes) while wearing Paul's glasses : 21.9 cm

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Explanation / Answer

We need to find the focal lengths of each set of glasses

Apply 1/f = 1/p + 1/q

For Mary

1/f = 1/23.2 + 1/-62.6

f = 36.9 cm

For Paul

1/f = 1/23.2 + 1/-108.2

f = 29.5 cm

Then for Paul wearing Mary's glasses

1/f = 1/p + 1/q

1/36.9 = 1/p + 1/-108.2

p = 27.5 cm from the lens

27.5 + 1.8 = 29.3 cm

For Mary wearing Paul's glasses

1/29.5 = 1/p + 1/-62.6

p = 20.1 cm from the lens

20.1 + 1.8 = 21.9 cm

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