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

Here we have the information of the far point distance =2.5m

image distance = 29.5m

case a:

distance from her eyes to lens = 1cm

object distance u = 2.5m - 1 cm

= 2.5 - 0.01

= 2.49 m

here both object and image are on the same side ,so we need to take 'u 'as negative

From Lens formula we have,

1 / f = 1/ u + 1/v

= - 1/ 2.49 + 1/ 29.5

= - 0.4016064257 + 0.03389830508

= - 0.3677

f = - 2.719548 m

The required focal length is 2.719 m and the power of lens = 0.3677 Diopters

case b :

here u = 2.5m - 0.02m

= 2.48 m

v = 29.5m

1 / f = 1/u + 1/v

= - 1/ 2.48 + 1/ 29.5

= - 0.40322580645 + 0.03389830508

= 0.033898

power of lens = 1/f = 0.033898 diopters

focal length f = 29.5m

comparison gives us,

% difference = (26.780/29.5 ) * 100

= 90.78

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