Question Detail
Question
A man wears glasses of power +3 diopters and can clearly see a newspaper at 25 cm. If he takes off his glasses, how far away would the newspaper have to be for him to see it clearly (i.e., what is his uncorrected near point)?
Correct Answer
Option A is the correct answer.
Detailed Explanation
The glasses have a power of +3 D, so their focal length (f) is 1/3 m, or approximately +33.33 cm. When he wears the glasses, he can read at an object distance (u) of 25 cm. The glasses form a virtual image (v) at his uncorrected near point. Using the lens formula 1/v = 1/f - 1/u = 1/33.33 - 1/25 = 0.03 - 0.04 = -0.01 cm-1. Therefore, v = -100 cm. His uncorrected near point is 100 cm.
Hint
Use the lens formula. The image formed by the glasses at the desired object distance (25 cm) will be at the man's uncorrected near point. Remember to use consistent units and the correct sign convention for virtual images.