Question

Carol is farsighted ( presbyopia) and cannot see objects clearly that are closer to her eyes than about meter. She sees objects clearly with a relaxed eye when they are distant. What is the refractive power of reading glasses that would allow her to read a book 50 cm away with a relaxed eye

Answer 1

Answer:

1.0 dioptres

Explanation:

Farsightedness is an eye defect in which a person can see far objects clearly but not near objects. That implies that the patients' near point is farther than 25cm which is the normal least distance of distinct vision.

Farsightedness results from the eyeball being too long or the crystalline lens not being sufficiently converging.

Carol is farsighted with a near point of about a meter (100cm). We desire to make a lens to enable her near point be reduced to about 50cm. The focal length and power of this lens is calculated in the image attached.

The power of a lens is the inverse of its focal length in meters hence the 100 in the formula for power of the lens.

Answer 2

Answer:

+1.00 diopter

Explanation:

The power of a lens can be described simply as the reciprocal of the focal length of the lens measured in meters.

But f is unknown, hence we look for the focal length with the formula

1/f = 1/u + 1/v

where u is former near point = 100cm

v is the new intended near point = 50cm

1/f = 1/50 - 1/100

1/f = 1/100

f = 100 cm

Hence we get Power (D) = 1/f

where f = focal length of the lens in meter

From the question, the focal length of the lens = 100cm = 1m

Hence D = 1/1

D = +1.00

Hence the refractive power of the reading glasses that would allow Carol to read a book 50cm away from the relaxed eye will be +1.00 diopters.