Question

What is the problem with focus when someone is nearsighted? Farsighted? Which type of lens would correct each problem, concave or convex?

Answer 1

When someone is nearsighted the focal length of eye lens decreases which we say as a power. If someone is farsighted the focal length increases. This actually not a perfect answer because eye can change it focal length accordingly. The problem arises when eye cannot differentiate near and far object and cannot change its focus accordingly.
Today glass to correct this is made of a special type of lens called meniscus lens. But for simplicity to correct nearsighted we need a divergent lens to diverge light from distant object that is concave.To correct farsighted we need a convergent lens to diverge light from distant object that is convex.