A nearsighted person cannot read a sign that is more than 7.8 m from his eyes. To deal with this problem, he wears contact lenses that do not correct his vision completely, but do allow him to read signs located up to distances of 15.8 m from his eyes. What is the focal length of the contacts?

Focal length of contacts required = 15.41 m

Explanation:

To obtain the focal length of the contacts, we use the relation,

(1/f) = (1/v) - (1/u)

v = image distance = - 7.8 m (negative because of convention)

u = object distance = - 15.8 m

(1/f) = (-1/7.8) + (1/15.8) = - 0.1282 + 0.0633 = - 0.0649

f = -1/0.0649 = - 15.41 m

Focal length of contacts required = 15.41 m

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