Question

A person is having trouble seeing. Bifocals should be prescribed for him. His far
point is 135 cm. The normal far point is infinity. His near point is 79.0 cm, but he would
like to hold a book 20 cm from his eyes. What two lenses (with power in diopters)
should be prescribed?

Answer 1

For the correction of short sight :
let f is the focal length of the lens needed.
object distance, u = infinite
image distance, v = -135 cm

use, 1/f = 1/u + 1/v

1/f = 1/infinite + 1/(-135)

f = -135

= -1.35 m

Power of the lens, P = 1/f

= 1/(-1.35)

= -0.741 Diopters <<<<<--------------Answer

For the correction of long sight :
let f is the focal length of the lens needed.
object distance, u = 20 cm
image distance, v = -79 cm

use, 1/f = 1/u + 1/v

1/f = 1/20 + 1/(-79)

f = 26.8 cm

= 0.268 m

Power of the lens, P = 1/f

= 1/0.268

= 3.73 Diopters <<<<<--------------Answer