In Born's Atomic physics, he makes the comment on the single slit diffraction that
For diffraction patterns to show themselves, it is necessary that the width of the slit employed should be of the order of magnitude of the wavelength of the light.
Why is this?
Thanks!
If the slit is much smaller than the wavelength, there will not be significant path-length difference between beams passing through different points inside the slit. If the slit is much larger than the wavelength, most of the beam passing through the slit will not be affected by the edges of the slit. I also guess that Born had in mind Fraunhofer diffraction (https://en.wikipedia.org/wiki/Fraunhofer_diffraction#Diffraction_by_a_slit_of_infinite_depth ).
Typically the order of magnitude of angular spread of a fringe in a pattern can be given by lambda/Width. If lambda is much smaller than width the diffraction pattern will be difficult to see. In the other case of lambda much greater than the width the entire screen would be covered by just the first fringe.
