Question

A woman can read the large print in a newspaper only when it is at a distance of 62 cm or more from her eyes. (a) Is she nearsighted (myopic) or farsighted (hyperopic), and what kind of lens is used in her glasses to correct her eyesight? (b) What should be the refractive power (in diopters) of her glasses (worn 2.9 cm from the eyes), so she can read the newspaper at a distance of 29 cm from the eyes?

A: I know she's farsighted

B: I did (1/ 29-2.9 + 1/(62-2.9) = .05523 x 100 = 5.52 cm, which was wrong. How do I solve this part of the equation?

Answer 1

A) Without a given age, we can assume she is hyperopic since the near point is 25 cm from the retina in someone in their early 20s. Since her near point is further than that, she is unable to see objects closer than that clearly, and is farsighted.

This I'm uncertain about (though fairly confident it's correct, but I give no 100% guarantees), but I did the same equations on a similar problem and it resulted in the right answer:
B) Because the eyeglasses are a distance away from her eyes, you have to factor them into both the image and object distance in the equation 1/f (focal point) = 1/di (image distance) + 1/do (object distance). The reason each of them are factored in is because the equation accounts for the lens of the glasses, not that of the eye. This causes the object distance (where she wants to read the paper at, 29cm) to be 2.9cm closer to the glasses' lens than her eyes, and her near point (the distance she can read the paper at without glasses) to similarly be 2.9cm closer to the glasses' lens than her eyes.

In this case:
1/f = 1/di + 1/do
1/f = 1/-(62-2.9) + 1/(29-2.9)
f = 46.74
When the inverse is taken, the focal point is shown to be 46.74 cm. Note that the distance of the object is negative because it's to the left of the lens of the eyeglass. Now to get the answer in diopters, you have to use the equation R(refractive power) = 1/f (in meters), which is 1/0.4674, or 2.13 diopters (which should be rounded to an even 2).

I hope it was helpful.. please rate me positive..