A student is not capable of focusing on objects closer than 0.44m from the eyes

Question

A student is not capable of focusing on objects closer than 0.44m from the eyes and no farther than 0.97m from them. To improve the vision, separate prescriptions are needed, one to correct for myopia, and the other to correct for hyperopia.

a) What is in meters the focal length of the lens needed to to enable the student to see objects that are 0.22m away from the eye? Express your answer in meters.

b) What is in diopters the power of that lens?

c) What is in meters the focal length of the lens needed to correct for the myopia? Express your answer in meters.

What if we want to design a bifocal for the student. The top portion will allow him to see far away objects. The lens then will be the lens you calculated in part c. To be able to see objects that are 0.22m away from the eye, we need to glue another lens at the bottom portion of this lens.

d) What power lens should we glue to the lens you have determined in part c, to enable the student to see objects that are 0.22m away from the eye?Express your answer in diopters.

Explanation / Answer

object distance s1 = 0.22 m

image distance s1' = -0.44 m

1/s1 + 1/s1' = 1/f1

1/f1 = (1/.25)-(1/.44)

f1 = 0.58 m <--------answer

b) powerof the lens P1 = 1/f1 = +1.73 D

c) s2 infinity         s2' = -0.97

1/s2 + 1/s2' = 1/f2

f2 = -0.97 m <<-----answer

d) P2 = -1/f2 = -1/.97 = -1.03 D

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