A) Using the general approach (i.e., integrating waves from all sources in complex number form), derive...

A) Using the general approach (i.e., integrating waves from all sources in complex number form), derive the Fraunhofer diffraction amplitude produced by 4 very narrow slits of width "a", each being separated by distance "b".

B) Use Babinet's theorem to calculate the Fraunhofer diffraction amplitude of 4 very narrow rectangular plugs of width "a" and separated by "b". Here you do not have to relate the amplitude E_input to the slit diffraction amplitude E_L as done in the notes. Consider E_L an input parameter.

Expert Solution

4 narrow slits imply 4 diffracted waves. For one diffracted wave the amplitude is A₀

,

The path difference between two slits which is equilvalent to a phase difference of

for four slits . This is a finite geometrical series.

(b) I might not be much help with Babinet's theorem without your lecture notes. Here's something to go with nonetheless. According to Babinet's theorem diffraction due to 4 slits of width a and separated by b is equivalent to diffraction due to rectangular plugs of width a and separated by b.

genius_generous answered 2 years ago

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