Are carrots actually good for eyesight?

Are carrots good for eyesight? I was thinking about this today while running, and couldn’t come up with any reason outside of getting a particular vitamin. If that is the case, wouldn’t other food that carry this vitamin also be good? Do carrots just have that much more vitamin X than other foods? Do they improve your eyesight, or just prevent degradation?

I’m just trying to figure out why carrots are the poster-vegetable for eyesight, let me know what you know/think.