A person\'s eye can see clearly everything from 40 cm to 400 cm. Assume the diam

Question

A person's eye can see clearly everything from 40 cm to 400 cm. Assume the diameter of the eyeball is 2.5 cm. a. What is the range of focal length that this person's eye can produce? You want to build a bifocal lens to accommodate this person's vision. The top half of the lens is to be used for far vision to see infinity while the bottom half of the lens is to be used for near vision to see the ideal near point. b. What is the focal length of the top half of the lens? c. What is the focal length of the bottom half of the lens?

Explanation / Answer

here D = 2.5 cm = 0.025 m

as we know that

center of curvature = D / 2

= 0.025 / 2 = 0.0125 m

so the focal length

f = C / 2

= 0.0125 / 2 = 0.00625 m Ans

as we know that

1 / f = 1 / u + 1 / v

for top half of the lens v = infinity u = 400 cm = 4 m

1/ f = 1 / infinity - 1 / 4

f = - 4 m Ans

for bottom half the lens v = 25 cm = 0.25 m and u = 40 cm = 0.40 m

so 1 / f = 1 / 0.25 - 1 / 0.40

f = 0.66 m Ans

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