Question

With unaided vision, a librarian can focus only on objects that lie at distances between 4.8 m and 0.45 m.

Find the refractive power needed for each part of the bifocal eyeglass lenses that will give the librarian normal visual acuity from 25 cm out to infinity. (Include the sign.) (Assume the lenses rest 2.0 cm from his eyes.)
diverging:_______ diopters
converging: _______ diopters

Answer 1

For distance vision, we need to take objects at infinity and focus them at 4.8 m from the eye (That image will be on the same side of the lenses as the objects, so the image is virtual, and 4.78 m away from the lenses since the lenses are 2 cm from the eyes

Apply 1/f = 1/p + 1/q

1/f = 1/-4.78

f = -4.78

D = 1/f = 1/-4.78 = -.209 Diopters

For near distance, we need to take images 25 cm from the eyes and focus them at 45 cm from the eyes (dont forget about the 2 cm lens to eye distance)

1/f = 1/.23 + 1/-.43

f = .4945

D = 1/f =1/.4945 = 2.02 Diopters