The claim that carrots can help your vision would seem to have some pretty solid scientific grounding. Retinal is essential for vision, and the beta-carotene in carrots offers a compound from which our body can produce the retinal our eyes require. However, eating carrots will only improve your eyesight if you are vitamin A deficient.
It turns out that the idea that carrots can improve your eyesight has its roots in a bit of British propaganda from World War II. After successfully using a new radar system to locate and shoot down German bombers, the British forces came up with the entirely false campaign stating that their pilots were eating carrots to improve their night vision in order to hide the existence of the radar system from the Germans. This campaign of disinformation was so successful that it took root and persists today.
From Can carrots help you see in the dark?