Why Are Paul Atreides's Eyes Blue?

Paul Atreides's eyes are blue because of the spice. Once he joins the Fremen he lives on their diet, which is full of melange, and over time it stains both the whites and the irises of his eyes a deep blue. The Fremen call it the Eyes of Ibad. Paul wasn't born with them. At the start of Dune his eyes are green. (Dune; Dune (appendix))

The spice turns the eyes blue#

Frank Herbert defines the condition in the glossary at the back of Dune. The Eyes of Ibad are a "characteristic effect of a diet high in melange wherein the sclerae (whites) and irises of the eyes turn a deep blue (indicative of deep melange addiction)." (Dune (appendix))

It's gradual. The more spice someone eats, and the longer they eat it, the deeper the blue goes, until no white is left in the eye at all. On Arrakis, where melange is in the food, the drink and the air of the deep desert, everyone born to the sietch ends up with it. (Dune)

Paul starts with green eyes#

At the very start of Dune, the Reverend Mother Gaius Helen Mohiam studies fifteen-year-old Paul before testing him. Among the family features she reads in his face are directly staring green eyes, like those of the Old Duke, his paternal grandfather. (Dune)

So when Paul and his mother flee into the desert, he looks like what he is, a wet-world noble. When Stilgar first sizes him up, the naib lists what marks him as an outsider: "He is full-fleshed. He has lived on much water. He has lived away from the father sun. He has not the eyes of the Ibad." (Dune)

When Paul's eyes change#

Paul's exposure to spice starts early on Arrakis, and it gets much heavier once he lives in the desert. In a stilltent the night after his father's death, the spice in the air sets off his prescience. After that he eats and breathes it every day among the Fremen. (Dune)

Herbert marks the change later in the book. Facing Stilgar's blue-within-blue eyes, Paul thinks that his own eyes are already starting to take on the same mask of colour from the spice. By the time he is a Fremen war leader, his eyes are as blue as theirs. (Dune)

Lady Jessica's green eyes go the same way during her years in the sietch. (Dune)

Blue eyes, but not a superpower#

It's easy to read the blue as a sign of Paul being special. The book doesn't support that. The same eyes belong to every Fremen child, and off Arrakis they belong to spice addicts like the Harkonnen Mentat Piter de Vries, whose eyes have no white left at all. Gurney Halleck, living with smugglers who could get off-world food, has only a touch of the colour. (Dune)

The far end of the scale is the Spacing Guild. In Dune Messiah the Navigator Edric attends the conspirators' meetings floating in a tank of orange spice gas. (Dune Messiah)

What the blue does show is dependence. Melange is addictive, and once someone's eyes are fully blue they are bound to it for life. Our reading, and it's only a reading, is that the change works as a quiet symbol for Paul: the moment his eyes match the Fremen's, he belongs to Arrakis and to the spice, and he can never go back to being the green-eyed boy from Caladan. (Dune)

For what the spice does to Paul's mind rather than his eyes, see Paul Atreides's powers. (Dune)