Please show work so I can follow along and understand how to figure it out. Two

Question

Please show work so I can follow along and understand how to figure it out.

Two lab partners, Mary and Paul are both farsighted. Mary has a near point of 6.2 cm from her eyes and Paul has a near point of 116 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 get their glasses exchanged (Mary leaves with Paul's glasses and Paul leaves with Mary's glasses). When they get to their next class, find the following. Determine the closest object that Mary can see clearly (relative to her eyes) while wearing Paul's glasses. Determine the closest object that Paul can see clearly (relative to his eyes) while wearing Mary's glasses.

Explanation / Answer

Here both Mary and Paul are effectviely using a combination of lenses(eye + spectacles) seperated by a small distance(1.80cm here). For such an arrangement, the effective focal length f is given by 1/f = 1/f1 + 1/f2 - d/f1f2

a) let focal length of Paul's glasses be fP. so 25-1 = 116-1 + fP-1 - 1.8/116fP. Solving for fP, we get fP = 31.37cm

So near point of Mary wearing Paul's glasses = (6.2-1 + 31.37-1 - 1.8/(6.2*31.37))-1 = 5.4cm

b) let focal length of Mary's glasses be fM. so 25-1 = 6.2-1 + fM-1 - 1.8/6.2fM. Solving, we get fM = 5.85 cm

So near point of Paul while wearing Mary's glasses = (116-1 + 5.85-1 - 1.8/(116*5.85))-1 = 5.65 cm

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