A farsighted person cannot see clearly objects that are closer to her eyes than 60.0 cm.Which one of the following combinations represents the correct focal length and the refractive power of the contact lenses that will enable her to comfortably see the objects at a distance of 25.0 cm from her eyes?
A)-42.9 cm,+2.33 diopters
B)-42.9 cm,-2.33 diopters
C)+42.9 cm,+2.33 diopters
D)+42.9 cm,-2.33 diopters
E)+60 cm,+42.9 diopters

Question

Quizplus · Accepted Answer

Since the person is farsighted, the contact lenses have to provide diverging rays of light. The lens formula is given by:

1/f = 1/di + 1/do

where f is the focal length, di is the distance of the object from the lens, and do is the distance of the image from the lens.

Given that the person cannot see objects at a distance closer than 60.0 cm, the distance from the lens (do) to the image has to be (-25.0 cm) to bring the image closer to her eyes.

Using the lens formula and substituting the values, we get:

1/f = 1/di + 1/do
= 1/(-25.0 cm) + 1/(-42.9 cm)

Solving for f, we get:

f = +42.9 cm

Since the focal length is positive, the contact lenses have to be convex, and since the person wants to comfortably see objects at a distance of 25.0 cm, the refractive power has to be positive (to provide diverging rays of light).

The refractive power of the lenses is given by:

P = 1/f

Substituting the value of f, we get:

P = 1/(+42.9 cm)
= +2.33 diopters.

Therefore, the correct choice is (C).

A Farsighted Person Cannot See Clearly Objects That Are Closer