Question

A 55 year old man can focus objects clearly from 100 cm to 300 cm. Representing the eye as a simple lens 2 cm from the retina. What strength lens (focal length) must he wear in the lower part of his bifocal eyeglasses to focus at 25 cm?

• A. 33 cm
• B. 40 cm
• C. 50 cm
• D. 53 cm

Answer 1

Answer: (A)

33 cm

Answer 2

In order to see an object at 25 cm clearly, the dioptric power should be

F =+=$\frac { 1 } { 0.25 }$+$\frac { 1 } { 0.02 }$= 54 diopters,

and the combined power is the sum of the powers of the eye and the glasses,

F = F_eye = F_glasses.

Thus F_glasses = F – F_eye = 54 –$\frac { 1 } { 0.01961 }$= 3 diopters (F_eye =). He must wear 300ŗ far-sighted eyeglasses. The corresponding focal length is

F_glasses =$\frac { 1 } { \Phi _ { \text {glasses } } }$=$\frac { 1 } { 3 }$m = 33.3 cm.