In case 1, the optical axis is along the x direction. Left: a schematic of the birefringent plate, the rotation axis used to adjust the angle of incidence, and the two sheets of the index surface. Right: the geometry of wave vectors. The two circles and the ellipse are the intersections with the plane of incidence of the two sheets of the index surface and the unity sphere, all scaled by 2π/λ₀, such that they are the locus of the tips of wave vectors k′.