This topic seems to be more complicated than we've all been brought up to believe.
According to Wikipedia, carrots are not rich in Vitamin A; they're rich in carotene, which is converted in the small intestine to retinal, which is a form of Vitamin A. Carotene gets its name from the carrot, and it's what makes carrots orange; it can be synthesised by plants, but not by animals. So that's why we have to eat carrots to get our Vitamin A.
Wikipedia's most shocking assertion, however, is that "the belief that eating carrots improves night vision is a myth put forward by the British in World War II to mislead the enemy about their military capabilities."
© Haydn Thompson 2017