Alice is farsighted and cannot see objects clearly that are closer to her eye than 80.0 cm.What is the refractive power of the contact lenses that will enable her to comfortably see objects at a distance of 25.0 cm from her eyes?
A)+2.75 diopters
B)-2.75 diopters
C)-4.72 diopters
D)+4.72 diopters
E)+7.00 diopters

Question

Quizplus · Accepted Answer

To correct farsightedness and allow Alice to see objects at 25.0 cm, we need to calculate the lens power required to change her near point to 25.0 cm. The formula for lens power (P) in diopters is P = 1/f, where f is the focal length in meters. The lens should change the image location from 25.0 cm (0.25 m) to her comfortable viewing distance of 80.0 cm (0.80 m). Using the lens formula 1/f = 1/v - 1/u, where v is the image distance (0.80 m) and u is the object distance (-0.25 m, negative because it's on the same side of the lens as the light is coming from), we find 1/f = 1/0.80 - 1/(-0.25) = 1.25 + 4 = 5.25. Therefore, P = 5.25 diopters. Since we're dealing with a lens that corrects farsightedness, it's a converging lens, which has a positive diopter value, making the correct answer +5.25 diopters. However, given the options, it seems there might have been a calculation or typographical error in the question or answer choices. Based on the provided choices, the closest correct answer by the logic of calculation would be +4.72 diopters, but this does not match the calculation. The correct calculation approach would ideally yield a result that matches one of the given options exactly, suggesting a need to reevaluate the calculation or the provided options for accuracy.

Alice Is Farsighted and Cannot See Objects Clearly That Are