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 52.9 cm from your eyes will appear blurry unless you use glasses. The purpose of glasses would be to make objects that are close to you appear to be at your near point. 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 24.00 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

Part A)

Apply the lens equation

1/f = 1/p + 1/q

We need to take objects at 24 cm and form images at 52.9 cm away from the lens. Since the image is in the same side of the lens as the object, it is vitrual (thus needs a negative sign by convention.)

1/f = 1/24 + 1/-52.9

f = 43.9 cm

The dioptic power is the inverse of the focal length (in meters)

D = 1/(.439)

D = 2.28 Diopters

Part B)

1/f = 1/p + 1/q

When q becomes infinite, the image is impossible to see...

1/43.9 = 1/p + 1/(infinity)   (1/infinity = 0)

Thus p = 43.9 cm

So anything further than 43.9 cm will not be focused clearly

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