Question

Using the data you obtained from measurements, determine the focal length of your corrective lenses and then use that focal length to determine where your new near point will be. Compare (% error) with the actual near point you found with your glasses/lenses on. Account for distance between your prescription lens and your eye if any.

I know I am near sighted. An the lense measurements account for the 2cm from my lenses to my eye already. I can't figure out how to do this as it wasn't covered yet.

naked eye	Left eye Near point cm	Left eye Far Point cm	Right eye Near Point cm	Right eye Far Point cm
trial1	8cm	15.2cm	11.5cm	18.8cm
2	8.2	15.4	11.7	19
3	8.4	14.8	10.8	19.2
4	8.1	15	11.6	18.9
Avg	8.2	15.1	11.4	18.7
n/a	n/a	n/a	n/a	n/a

With glasses	Left Eye Near Point cm	Left Eye Far Point cm	Right Eye Near Point cm	Right Eye Far Point cm
1	13.5cm	262.9cm	14cm	372.1cm
2	13.7	255.1	13.5	360.4
3	14	265.7	13.8	366.2
4	14	268.1	14.1	370.7
Avg	13.8	263	13.9	367.4

Answer 1

As you are near sighted the far point needs to be corrected. Now far points with the glasses on have to be subtracted by 2cm, because x cm from your eye = x-2cm from the lens, as the lens is 2cm away from your eye.

Now we'll use the lens equation :

, f is focal length.

For the Left eye far point with and without glasses:

o = object distance = -(15.1cm - 2cm) = -13.1cm = -0.131m (applying Cartesian sign convention)

i = image distance = -(263cm-2cm) = -261cm = -2.61m

So,

,

-ve sign indicates it is a concave lens, D is diopter, unit of lens power.

So applying this for the near point data,

o = -(8.2-2) = -6.2cm = -0.062m

f = -0.124m

so,

the actual near point with the glasses on is 13.8cm = 0.138m, so the error :

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For right eye:

Applying this value of f for near point:

The actual near point for right eye = 13.9cm = 0.139m, the calculated value has a difference.

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Note: This error shows that the same focal point is not suitable to treat near and far sightedness at the same time, that's why in the severe cases of far sightedness we need bifocal lenses. But that's a thing for aged eyes.