It just occurred to me that when they’re talking about a “rational angle” they might be talking about a slope that can be specified rationally.
If you have a repeating three-dimensional crystal lattice, and a ray of light that is following an irrational slope, then it is guaranteed to intersect one of the cell units or vertices in that lattice.
If it did not intersect any nodes, then you would be able to express that slope rationally just by counting the number of vertical nodes over the number of horizontal nodes!
I’m assuming an infinite lattice here. For finite ones an irrational slope could still “sneak through”
If you have a repeating three-dimensional crystal lattice, and a ray of light that is following an irrational slope, then it is guaranteed to intersect one of the cell units or vertices in that lattice.
If it did not intersect any nodes, then you would be able to express that slope rationally just by counting the number of vertical nodes over the number of horizontal nodes!
I’m assuming an infinite lattice here. For finite ones an irrational slope could still “sneak through”