Geometrical mechanism for knife-edge and single-slit diffractions

Knife-edge diffraction and single slit diffraction have been studied extensively in history, but it is rare to find studies that explain how the two types of diffraction are linked and how knife-edge diffraction can evolve into slit diffraction. The current study fills this research gap. The stark differences between the knife-edge and single slit diffraction patterns pose a challenge to the traditional wave theory, but can be explained by extending the geometrical theory of diffraction for the knife-edge to the single slit. The extended theory predicts a transitional case from knife-edge to slit diffraction, and the transitional diffraction pattern is observed in experiments.