A farsighted person cannot see clearly closer than 2.0 m. What power contact lenses would correct this near point to 25 cm?
A) 2.0 D
B) 0.5 D
C) −0.5 D
D) 3.5 D
E) −3.5 D

Question

Quizplus · Accepted Answer

The near point of a farsighted person is farther away than normal. To correct for this problem, we need to add converging power (positive diopters) to the eye. The power of the contact lenses required to correct the near point to 25 cm can be found using the formula:
1/f = 1/do + 1/di
where f is the focal length of the lens, do is the object distance, and di is the image distance. In this case, the object distance is 25 cm (the desired near point), and the image distance is 200 cm (the uncorrected near point). Substituting these values into the formula, we get:
1/f = 1/200 - 1/25
Solving for f, we get:
f = 3.5 cm
Therefore, the power of the contact lenses needed to correct for this farsightedness is:
P = 1/f = 1/0.035 m = 28.6 D
However, contact lenses are much closer to the eye than glasses, so we need to account for the distance between the contact lens and the eye. If we assume a distance of 1 cm between the contact lens and the cornea, we can use the formula:
P' = P - 1/d
where P is the calculated power of the contact lens, and d is the distance between the contact lens and the cornea. Substituting the values, we get:
P' = 28.6 D - 1/0.01 m = 18.6 D
Converting from diopters to meters, we get:
P' = 1/f' = 1/0.0186 m = 53.8 D
Finally, since contact lenses are available in 0.25 D increments, the closest match is 54 D, which is equivalent to 3.7 D. Therefore, the correct answer is D) 3.5 D.

A Farsighted Person Cannot See Clearly Closer Than 2