I used fluorescent posterboard for the "white" of the eyes. It is bent in concave shape to cover the interior sides of the box without seams.
For the iris/pupil, I used black foamcore and colored the iris with a fluorescent orange highlighter pencil. You could probably use Construction paper and glow-in-the-dark crayons instead. I think the drawn iris looks more realistic than the graphic, so I went with that.
I used bigger boxes for the final project. They are a bit deeper (about 5 in.), but mostly, they are wider.
I did a lot of tests with distance, iris size, etc before I secured everything.