1. Suppose that a certain 20-year-old student has identical eyes and wears conta

Question

1. Suppose that a certain 20-year-old student has identical eyes and wears contact lenses of-2.50 D to correct her vision. While wearing these lenses, she can read without any problems-holding the book at the standard desired distance (25 cm) from her eyes. What is the minimum possible width of her focal range? That is, what is the minimum possible distance between her Near Point and her Far Point? a. b. Notice the calculations you did in part a. Now derive a general algebraic expression for the maximum Near Point an eye can have so that its Far Point can be properly corrected by a contact lens and yet the person can read while wearing this contact lens (and no other lenses) and still hold the book at the standard desired 25 cnm That is, write NPas a function of FP. Express all values in cm. (Test your solution with the numbers from a.) c. Now suppose that the above student's father is 50 years old, and his focal range is known to be this: NP = 18.0cm FP = 30.0 cm If the father uses contact lenses to properly correct his far vision, at what minimum distance must he hold a book to be able to read it while wearing those contact lenses (and no other lenses)? Considering the answer to c, it's probably (past) time for the father to make a choice. Either he gets reading glasses -so that he can simply put those on (while still wearing his contact lenses) and read a book at the standard desired 25 cm distance-while looking through both lenses at once; or he gets bi-focal eyeglasses-essentially two different half-lenses-where he looks through just one of them at a time (the upper for far viewing; the lower for near viewing) find the correction (in Diopters) for his contact lens and his reading glasses lens e. For the bifocals option, calculate the correction (in Diopters) for each part of the combined lens, using this logic The upper part must fully correct his far vision (without regard to how that blurs his near vision) The lower part must help correct his far vision as much as possible provided that he can read a book at the standard desired 25 cm distance

Explanation / Answer

1. a. contact lens power, P = -2.5 D

hence focal length fc = 1/P = -1/2.5 m = -0.4 m = -40 cm

far point , d = ?

hence form lens equation

1/v - 1/d = 1/fc

now, v = infinity ( theoretical far point)

hence

d = -fc = 40 cm

hence far point of the person is at 40 cm

near point is at x cm

hence

from lens equation

theoretical near point, n = -25 cm

hence

1/(-25) - 1/x = -1/40

x = -66.67 cm

hence width of focal field is 66.7 - 40 = 26.7 cm

b.

hence generally speaking

-1/25 + 1/NP = 1/f

also

FP = -f

hence

1/NP = -1/FP + 1/25

c. NP = 18 cm

FP = 30 cm

hence focal length of contact glasses = (-1/25 + 1/NP)^-1 = 64.285 cm

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