A person with a nearsighted eye has near and far points of14 cm and 32 cm,respec

Question

A person with a nearsighted eye has near and far points of14 cm and 32 cm,respectively. (a) Assuming a lens is placed 2.0 cm from theeye, what power must the lens have to correct this condition?
P = 1 diopters

(b) Suppose contact lenses placed directly on the cornea are usedto correct the person's eye. What is the power of the lens requiredin this case, and what is the new near point? Hint: Thecontact lens and the eyeglass lens require slightly differentpowers because they are at different distances from the eye.
P = 2 diopters
p = 3 cm (a) Assuming a lens is placed 2.0 cm from theeye, what power must the lens have to correct this condition?
P = 1 diopters

(b) Suppose contact lenses placed directly on the cornea are usedto correct the person's eye. What is the power of the lens requiredin this case, and what is the new near point? Hint: Thecontact lens and the eyeglass lens require slightly differentpowers because they are at different distances from the eye.
P = 2 diopters
p = 3 cm

Explanation / Answer

(a)     since this eye can already focus on objectslocated at the near point of a normal eye (32 cm) no correction isneeded         for near objects, tocorrect the distant vision a corrective lens (located 2.0 cm fromthe eye) should form virtual images     of very distant objects at 30 cm in front of thelens     so we must require that     q = - 30 cm when p is infinity     from which we get that     p = 1 / f    = (1 / p) + (1 / q)    = ......... diopters (b)     a corrective lens in contact with the corneashould form virtual images of very distant objects at the far pointof the eye     so we require that     q = - 32 cm when p is infinity     p = 1 / f    = (1 / p) + (1 / q)    = ......... diopters     when the contact lens is in place the objectdistance which yields a virtual image at the near point of the eyeis given by     p = q f / (q - f)        = ......... cm

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