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 1.2m 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

The distance of far point x = 1.2m

To view distant objects, Concave lens of local length -1.2 should be used.

f= -x = -1.2m

Power of lens = 1/f = 1/(-1.2m) = -0.83D

Next it is given that the person cannot see within 28cm

given u= -25 cm v= -28 cm f = ?

Using lens formulae 1/f = 1/v - 1/u

1/f = -1/28 - (-1/25) = -1/28 + 1/25 = 3/700

Therefore f = 700/3 = 233.33 cm = 2.33 m

Power of the lens = 1/f = 1/2.33 = +0.4285D

Therefore aa convex lens of power +0.4285D can be used to correct the vision

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