A person is to be fitted with bifocals. She can see clearly when the object is b

Question

A person is to be fitted with bifocals. She can see clearly when the object is between 28.0cm and 0.8m from the eye. Since the upper portion of the bifocals should be designed to enable her to see distant objects clearly, what is the power they should have (in diopters)? (Assume there is no significant distance between the eye and the glasses lens.) The lower portion of the bifocals in the question above should enable her to see objects comfortably at 25.0cm. What power should they have (in diopters)?

Explanation / Answer

Apply lens equaiton

1/p + 1/q = 1/f

1/ inifinity +1/-0.6 m = 1/f

f = q = -0.6 m

power p = 1/ f in meters = 1/-0.6 m = -1.666 dipoters

(b)

from the thin lens equation

f = pq/ p+ q = ( 25 cm ) ( -28 cm)/ 25 cm - 28 cm = 2.33 * 10 ^2 cm = 2.33 m

power is p = 1/f = 1/2.33 = 0.429 dipoters

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