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) $- 4.72$ diopters
B) $+ 7.00$ diopters
C) $- 2.75$ diopters
D) $+ 4.72$ diopters
E) $+ 2.75$ diopters

Question

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) $- 4.72$ diopters
B) $+ 7.00$ diopters
C) $- 2.75$ diopters
D) $+ 4.72$ diopters
E) $+ 2.75$ diopters

Quizplus · Accepted Answer

The refractive power $P$ of the lens is given by $P = \frac{1}{f}$, where $f$ is the focal length in meters. Alice needs to see objects clearly at 25 cm (0.25 m), but her near point is 80 cm (0.8 m). The lens should form an image at her near point for objects at 25 cm. Using the lens formula $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$, where $v = -0.8$ m (image distance) and $u = -0.25$ m (object distance), we find $f = 0.3636$ m. Thus, $P = \frac{1}{0.3636} \approx +2.75$ diopters.

Alice Is Farsighted and Cannot See Objects Clearly That Are −4.72- 4.72−4.72

Alice Is Farsighted and Cannot See Objects Clearly That Are $- 4.72$