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

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 thesame focal power for her cornea (50 diopters) and for her variablelens (5 diopters), but Hannah suffers from myopia. She cannot focuson any object that lies more than 0.7 meters from her eyes sincethey are slightly longer -- the cornea to retina distance is larger-- than her sister's eyes. Considering this new far point, what isthe diameter of Hannah's eyes (in millimeters, to the nearest tenthof a millimeter) assuming Anna's eye diameter was ideally, again,20.0 mm? Hint: the focal power of the cornea remains the same forHannah as for Anna for focusing distant objects, but the farthestHannah can see (object distance) changes from infinity to 0.7meters.  

3) Assuming, instead, that the diameters of Hannah's myopic eyeswere 20.4 mm, but, again, that Hannah's eyes share the same focalpowers for her cornea and lens as Anna's, what would be Hannah'snear 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), whatpower corrective lenses would you prescribe to Hannah so that, whenwearing these lenses, her visual range was the same as Anna's (froma near point of 20 cm to a far point of infinity? Give your answerin units of diopters, to the nearest tenth of a diopter, with thecorrect sign.

5) One treatment of cataracts is to surgically remove thevariable lens of the eye. If we assume that the cornea's refractivepower focuses objects at infinite distances onto the retina of aperson who has had this surgery, what power correcting lenses wouldthey 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 tenthof a diopter and with the correct sign.