How did the rumor that carrots improve your eyesight start?

During World War II, the British Royal Air Force (RAF) announced that their pilots were eating lots of carrots to enhance their night vision and maintain their accuracy. But the truth was that the British were successful in defeating the German air force at night not because of carrots but because of a new radar technology they had developed. To keep this secret, the British government spread the rumor that carrots improved eyesight.