As a treatment for cataracts (a cloudiness of the lens of the eye), the natural

Question

As a treatment for cataracts (a cloudiness of the lens of the eye), the natural lens is removed and a plastic lens is implanted. After this is done a person can see distant objects clearly, but he cannot accommodate to focus on nearby objects. If for example such a person wanted to read a book at a distance of 25 cm, he would have to wear eyeglasses whose diopter power was approximately
a) -1.78 diopters
b) -4.00 diopters
c) +2.78 diopters
d) +3.33 diopters
e) +4.00 diopters
Please show all work.

Explanation / Answer

Since the person can't focus on the near object we need to shift the near point to far point by using appropirate lens.This gives us Image distance = v = Object distance= u = -25 Focal length lens = -f We know the formula is 1/f =1/u+1/v =>1/-f = 1/-0.25 +1/' =>1/-f = -4+0 =>1/f =4 Now power of lens = 1/f = 4 Diaopters So e)         

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