Is the diffraction pattern of a vertical slit horizontal? 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?
My logic:-
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?
 A: The wider a slit, the narrower the diffraction pattern. So it makes sense that a tall rectangular slit makes a wide rectangular pattern. 
A: It is the narrowness in the horizontal dimension which cause horizontal diffraction.  The slits are only tall because they are not wide.
Incidentally, the diagram is wrong.  It shows light entering the full heights of the slits from top to bottom.  If it did that, the fringes would be tall too - like vertical lines.
A: To observe the diffraction from a slit assume that the vertical dimension of the slit is much larger than its horizontal dimension. To illuminate it you need a line source not a point source otherwise you will get 2-dimensional diffraction pattern not a simple 1-dimensional sinc thing.
The diagram shows that the rays break at $L_1$ and $L_2$, resp., implying a pair focusing (collimating) lenses at $L_1$ and $L_2$ distance. The one at $L_1$ converts the point source into a line source parallel with the long (here vertical) dimension of the slit. The one at $L_2$ collimates the emerging rays from the slit and project them at the screen for observation. The latter lens at $L_2$ focuses the rays that approximately homogeneous in the vertical dimension emerging from the slit into a vertically narrow and mostly horizontally distributed diffraction pattern on the screen for observation. The rays that emerge from the slit are diffracted horizontally but their distribution is nearly homogeneous in the vertical dimension because of the narrowness of the slit.
If there were no lens at $L_2$ you would see a mess on the screen, but if you looked straight into the slit the lens in your eye will collimate and you would see a diffraction pattern but do not do this or you will get badly burned.
