I am familiar with the mathematical aspects of single slit diffraction pattern, at the undergraduate level.
Consider the following pictorial representation from the book Optics, by Hecht:
The fact that I find puzzling here is - even though the slit is shown vertical, the pattern on the screen is shown horizontal. Is this correct? Why so?
The reason why I find this strange is because of a translational symmetry argument. Any two points vertically separated by some distance have the same horizontal attributes. So, one expects the pattern also to have this sort of vertical symmetry, irrespective of what happens along the horizontal axis.
Am I mistaken? If yes, can someone please point out why is the vertical slit producing a horizontal pattern here?