A pair of glasses is designed for a person with a far-point distance of 2.5 m so

Question

A pair of glasses is designed for a person with a far-point distance of 2.5 m so that she can read street signs 29.5 m away. (The far-point distance is the distance from the eye at which you are just able to properly focus a distant object.)

(a) If the glasses are to be worn 1.0 cm from her eyes, what is the needed focal length?

(b) Compare this focal length (find the percent difference) to the focal length she would need if she chooses a style of glasses that fit on her face so that the lenses are instead 2.0 cm away from her eyes
.

Explanation / Answer

a) object distance, do1 = (2950 - 1) cm = 2949 cm

image distance, di1 = -(250 - 1) cm = -249 cm

So,

1/2949 + 1/(-249) = 1/f1

=> f1 = 2949 * 249 / (249 - 2949) = -272 cm

b) object distance, do2 = (2950 - 2) cm = 2948 cm

image distance, di2 = -(250 - 2) cm = -248 cm

So,

1/2948 + 1/(-248) = 1/f2

=> f2 = 2948 * 248 / (248 - 2948) = -270.8 cm

% difference from f1 = [(270.8 - 272) / 272] * 100 = -0.44 %

So, the required focal length when lenses are 2 cm away is 0.44 % less than the focal length needed for when they are 1 cm away.

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