It’s been awhile since my Eye Physiology class, but considering that my area of expertise is vision, I should probably give this carrot question a go. I remember being in that class and thinking it was hilarious that this old wives tale actually came from something! Of course it’s not true that eating a lot of carrots will improve your visual acuity, but it’s interesting to note that this little tidbit of wisdom may have come from somewhere.
Carrots contain Vitamin A, which is necessary in the production of rhodopsin. Rhodopsin is formed from the combination of retinol and opsin, and it is what gives us our ability to see in dim light. So, eating carrots (or other foods rich in Vitamin A) is related to your ability to see in dimly lighted conditions.
I’m sure you remember from 6th-grade biology that the eye contains two types of receptors, rods and cones. Cones are used for seeing in bright light and they’re concentrated in the fovea, as they allow to you see what is directly in front of you. Rods are used in dim light and peripheral vision. Rhodopsin is related to your rods, so there you have it.