Mahmood is farsighted and cannot see objects clearly that are closer to his eye than 80.0 cm. What is the focal length of the contact lenses that will enable him to comfortably see objects at a distance
Of 25.0 cm from his eyes?
A) $+ 36.4 \mathrm {~cm}$
B) $+ 32.5 \mathrm {~cm}$
C) $+ 21.2 \mathrm {~cm}$
D) $- 21.2 \mathrm {~cm}$
E) $- 36.4 \mathrm {~cm}$

Question

Mahmood is farsighted and cannot see objects clearly that are closer to his eye than 80.0 cm. What is the focal length of the contact lenses that will enable him to comfortably see objects at a distance
Of 25.0 cm from his eyes? 
A) $+ 36.4 \mathrm {~cm}$
B) $+ 32.5 \mathrm {~cm}$
C) $+ 21.2 \mathrm {~cm}$
D) $- 21.2 \mathrm {~cm}$
E) $- 36.4 \mathrm {~cm}$

Quizplus · Accepted Answer

To correct farsightedness and allow Mahmood to see objects at 25.0 cm, we use the lens formula: $1/f = 1/v - 1/u$, where $f$ is the focal length of the lens, $v$ is the image distance (which should be the near point of comfortable vision, 80.0 cm in Mahmood's case, but since it's a virtual image formed behind the eye, we take it as +80.0 cm), and $u$ is the object distance (25.0 cm, but since it's in front of the lens, it's -25.0 cm). Plugging in the values, we get $1/f = 1/80 - 1/(-25) = 1/80 + 1/25$, solving this gives $f \approx + 36.4 \mathrm {~cm}$, which means the contact lenses should have a focal length of +36.4 cm to correct Mahmood's vision.

Mahmood Is Farsighted and Cannot See Objects Clearly That Are +36.4 cm+ 36.4 \mathrm {~cm}+36.4 cm

Mahmood Is Farsighted and Cannot See Objects Clearly That Are $+ 36.4 \mathrm {~cm}$