Suppose you have hyperopia (you are farsighted). You can clearly focus on very d

Question

Suppose you have hyperopia (you are farsighted). You can clearly focus on very distant objects, but any object which is closer than 64.1 cm from your eyes will appear blurry unless you use glasses. What would be the refractive power (in diopters - do not enter units) for your prescription if you want to be able to clearly read by holding the paper 24.30 cm from your eyes?

If your glasses make close objects appear farther away, it will make objects that are farther appear to be even more distant. If the object gets too far away, the image will become real and be located such that you can no longer focus on the image. What is the farthest distance that an object can be and still be able to see it clearly with your reading glasses on?

Explanation / Answer

apply focal length 1/f = 1/u +1/v

where u is object distance = 64.1 cm

v is image distance = 24.3 cm

so

f = uv/u+v

f = (64.1 * 24.3)/(64.1+ 24.3)

f = 17.62 cm

so power of the lens P = 1/f in meters

P = 1/0.1762

P = +5.67 Diopters

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