1) Identical twins Anna and Hannah visit you at the optical clinic. Anna, whose eyes can...

1) Identical twins Anna and Hannah visit you at the optical clinic. Anna, whose eyes can easily focus on distant objects (her far point), is also able to focus on objects within 20 cm of her eyes (her near point). Assuming the diameter and, hence, the distance between the cornea and retina, of Anna's eye is 20 mm, what is the range (in diopters) of Anna's vision? The limits of this range correspond to the total refractive power of her eyes at their far point and and the refractive power at their near point.

a) from 50 to 50.5 diopters

b) from 50 to 55 diopters

c) from 50 to 60 diopters

d) from 0 to 5 diopters

2) Hannah's eyes have the same range as her sister's, with the same focal power for her cornea (50 diopters) and for her variable lens (5 diopters), but Hannah suffers from myopia. She cannot focus on any object that lies more than 0.7 meters from her eyes since they are slightly longer -- the cornea to retina distance is larger -- than her sister's eyes. Considering this new far point, what is the diameter of Hannah's eyes (in millimeters, to the nearest tenth of a millimeter) assuming Anna's eye diameter was ideally, again, 20.0 mm? Hint: the focal power of the cornea remains the same for Hannah as for Anna for focusing distant objects, but the farthest Hannah can see (object distance) changes from infinity to 0.7 meters.

3) Assuming, instead, that the diameters of Hannah's myopic eyes were 20.4 mm, but, again, that Hannah's eyes share the same focal powers for her cornea and lens as Anna's, what would be Hannah's near point (to the nearest tenth of a cm, in cm) if Anna's, again, is 20 cm?

4) Now assuming Anna's far point was found to be 0.8 m (i.e., her eyes can't focus on any object more than 0.8 m away), what power corrective lenses would you prescribe to Hannah so that, when wearing these lenses, her visual range was the same as Anna's (from a near point of 20 cm to a far point of infinity? Give your answer in units of diopters, to the nearest tenth of a diopter, with the correct sign.

5) One treatment of cataracts is to surgically remove the variable lens of the eye. If we assume that the cornea's refractive power focuses objects at infinite distances onto the retina of a person who has had this surgery, what power correcting lenses would they need to be able to read text at a 21-cm near-point distance? Again, give your answer in units of diopters, to the nearest tenth of a diopter and with the correct sign.

Expert Solution

genius_generous answered 1 year ago

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