Double Slit Interference (slit width relevant)

[FreySmint]

Hi everyone,

So my quantum physics teacher gave this problem to solve as homework:

An experiment to watch neutron diffraction was made. The neutron wavelength measured was 18.45 Angstroms. The double slit was created by putting a thread in the middle of a single slit. The dimensions of the double slit were measured as 21.9, 104.1, 22.5 micrometers (left slit, thread, right slit). The slits are L meters away from the scanning surface that will detect the neutrons.
Calculate the interference figure on the scanning surface, not ignoring the width of the slits.
I guess I'll have to figure out an expression that gives an intensity that varies with a "y" (the length of the scanning surface) and probably integrate the width of the slits somewhere.
I really don't know how to do this, but my teacher said to use a computer to solve the equation...

Sorry for any misspelling or gramatical error, I'm translating all of this, as English is not my language.

Thanks in advance

 

[vela]

Use Huygens principle.

 

[jtbell]

Assuming that L is much larger than the dimensions of the slits, this is just like Fraunhofer diffraction in optics. A Fraunhofer diffraction pattern is calculated by evaluating an integral whose limits correspond to the edges of the slits. Some Google searching for things like "Fraunhofer diffraction integral" may help. You can probably find the derivation for two equal-width slits somewhere and modify it. I've seen it in intermediate-level optics textbooks such as Hecht or Pedrotti.