An optometrist prescribes corective contact lenses for a nearsighted patient. Th

Question

An optometrist prescribes corective contact lenses for a nearsighted patient. The patient cannot clearly see objects placed more than 2.50m from his eyes. Because of his age, the near point of the patient is 0.50m. Note that the optometrist needs to prescribe bifocal contact lenses. Near point of a normal eye is 0.25m.

a) The power of the upper part of the lenses is _______ diopters (pay attention to sign)

b) The power of the lower part of the lenses is _______ diopters (pay attention to sign)

c) The upper part is a ______ lens and the lower part is a ______ lens.

d) At the store, the technician made a mistake and gave the patient a pair of diveging contact lenses with a focal length of -4.00m. The near point of the patient wearing these contact lenses is

Explanation / Answer

Lower lens is for far sightdness. Since, near point shifts from 0.25 m to 0.5 m, we should find a lens which can produce an image at 0.5m when an object is placed in real at 0.25 m. since image is formed on the same side, v is negative in sign convention.

1/v - 1/u = 1/f

1/-0.5 - 1/-0.25 = 1/f ; f = 0.5 m

f is positive, so lens is convex.

Power (lower lens) = 1/f = +2 D

For upper part, when an object is at a distance beyong 2.5 m (infinity), image should form at 2.5 m for readability.

1/v - 1/u = 1/f

1/-2.5 - 1/(infinity) = 1/f

f = -2.5 m (concave lens)

Power = 1/f = -0.4 D.

d) f = -4 m ; u = -.25m

1/v = 1/f + 1/u = 1/-4 + 1/-.25

v = -23.53 cm

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