How are the eyes the mirror of the soul?

It always surprised me how much emotion one can read in people’s eyes. How is this even possible? I can understand that facial expressions and body language “code” for emotions—that’s fairly obvious. But how does an eye convey fear, anger, shyness, happiness, intelligence, or interest?

Do you know of any study that tried to isolate the eyes from the rest of the face and test whether we can read emotions in them?

For instance, one cold take pictures of various people in different emotional states, crop everything but the eyes from the pictures, and then show these pictures to other people to see if they can guess the emotional state of pictured people.