Question Detail
Question
How far would a person whose near point is 90 cm have to hold a book to be able to read it while wearing reading glasses with a power of 2 diopters? Assume the near point for a normal eye is 25 cm.
Correct Answer
Option A is the correct answer.
Detailed Explanation
The person's near point without glasses is 90 cm (virtual image distance, so v = -90 cm). The power of the glasses is P = 2 D, so f = 1/P = 0.5 m = 50 cm. The lens formula: 1/f = 1/v - 1/u. 1/50 = 1/(-90) - 1/u => 1/u = -1/90 - 1/50 = (-5 - 9)/450 = -14/450. u = -450/14 = -32.14 cm. The negative sign indicates the object is on the same side as the light entering, so the book should be held 32.1 cm from the eye.
Hint
The lens forms a virtual image at the person's near point. Use the lens formula with v = -90 cm.