A pair of glasses is designed for a person with a far-point distance of 4.5 m so

Question

A pair of glasses is designed for a person with a far-point distance of 4.5 m so that she can read street signs 26.5 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

Part A)

We need to take objects at 26.5 m from the eye and reform the image 4.5 m from the eye on the same side of the lens as the object (thus virually)

The lens is 1 cm in front of the eye, so we need to use 26.49 and 4.49 for the object and image magnitudes

1/f = 1/26.59 + 1/-4.49

1/f = -.185109

Round to D = -.185 Diopters

Part B)

Now use 26.58 and 4.48

1/f = 1/26.58 + 1/-4.48

1/f = .185592

Thus round to D = -.186 Diopters

For the percent difference...

(.185109 - .185592)/(.185109) X 100% = .261%

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