Assuming they have the same demands on their vision (no inscribing the Lord’s Prayer on the head of a pin), would twins have similar vision problems? Or could one be nearsighted while the other was farsighted?
First of all, there are two sorts of twins, fraternal and identical. Fraternal twins are no more (or less) related than other full siblings, so yes, their vision can differ.
I assume you were referring to identical twins. Given they share the same DNA, they would tend to have the same vision, but not necessarially since they may not share the same exact environment. For example, if one twins worked inside, in an office, and the other worked in an occupation that had him/her out in natural sunlight a great deal the latter twin would be at higher risk for cataracts, for just one example. Even if they had the same environment, there may still be small variations in prescription. Mostly likely, you wouldn’t see extremes like one being farsighted and the other nearsighted.
my brother and I are twins and our eyesight is very different. We both have bad eyesight, but his prescription is not as extreme as mine. We can’t share glasses.
Identical (monozygotic) twins are more alike in their refractive indices than fraternal (dizygotic) twins, but they are far from having the same degree of myopia. One study of Finnish twins found
Cecil discusses the likelihood of myopia being environmental in origin in this column: Will sitting too close to the TV, reading with bad light, etc., ruin your eyes?