With unaided vision, a librarian can focus only on objects that lie at distances

Question

With unaided vision, a librarian can focus only on objects that lie at distances between 5.5 m and 0.40 m .

A) Explain why nearsightedness needs a converging lens and why farsightedness needs a diverging lens.

B) 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. (Assume the lenses rest 2.0 cm from his eyes.)

Express your answer using two significant figures. Enter your answers numerically separated by a comma.

Explanation / Answer

A) first of all

nearsightedness needs a diverging lens and farsightedness needs a converging lens.

this is because in nearsightedness the image of distant objects get formed before the retina and diverging lens helps to focus that on ratina by diverging the rays coming from object. basically it decreases the overall power of lens to increase focal length.

in farsightedness the image of nearby objects get formed after crossing the retina and converging lens helps to focus that on ratina by converging the rays coming from object. basically it increases the overall power of lens to decrease focal length.

B) upper part power =

1/f = 1/o + 1/i
distance of obj = 5.5; negative since image form on the same side as the object with respect to lens
distance of image = infinity;
1/f = -1/5.5 = -0.1818 dp

lower part

1/f = 1/o + 1/i
distance of obj = 40; negative since image form on the same side as the object with respect to lens
distance of image = 25;
1/f = 0.015
Answer is 1.5 dp

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