A person has a near point of NP = 65 cm and a far point of FP = 165 cm. The pers

Question

A person has a near point of NP = 65 cm and a far point of FP = 165 cm. The person wishes to obtain a pair of bifocal eyeglasses to correct these vision problems. The glasses will sit a distance d = 2.3 cm from the eyes. (a) Write a formula for the power, P_1, of the upper portion of the bifocals, in terms of the given quantities, that will enable the person to see distant objects clearly. (b) Calculate the power, P_1, of the upper portion of the bifocals in units of diopters. (c) Write a formula for the power, P_2, of the lower portion of the bifocals, in terms of given quantities, so that the person can clearly see objects that are located a distance N from his eyes. (d) Calculate the power, P_2, of the lower portion of the bifocals in units of diopters. Use N = 25 cm, which is for normal human vision.

Explanation / Answer

object distance s = (N-d)

image distance s' = -(65-d) cm

focal length = f2

from lens equation

1/s + 1/s' = 1/f2

1/(N-d) - 1/(65-d) = 1/f2

1/f2 = (65-N)/((65-d)*(N-d))

f2 = ((65-d)*(N-d))/(65-N) cm

power P2 = 1/f2   whre f2 is in m

f2 = ((65-d)*(N-d))/(65-N))

p2 = 1/f2 = (65-N)/((65-d)*(N-d)) <<<<----answer

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f2 = ((65-d)*(N-d))/(65-N))

f2 = ((65-2.3)*(25-2.3))/(65-25)

f2 = 35.58 cm

P2 = 1/0.3558 = +2.81

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