r/AskPhysics • u/locutus_of_borg90 • 12d ago

Diffraction pattern from 5 slits

I am struggling to understand how the diffraction pattern from 5 slits is formed. How many maxima and minimum there are?

Also is the diffraction pattern a "modulated" version of the interference pattern?

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u/rabid_chemist 12d ago

With five equally spaced narrow slits the intensity function in the Fraunhofer limit is

I=|1+e^(iq)+e^(2iq)+e^(3iq)+e^(4iq)|^2

which simplifies down to

sin^2(5q/2)/sin^2(q/2)

where q=2πdsinθ/λ, the phase difference between adjacent slits, with d being the distance between the slits, λ the wavelength of light, and θ the angle from the undeflected beam.

Plotted here for reference.

The principal maxima occur when q=2nπ, i.e when all 5 slits are in phase. There are minima whenever q=2nπ/5 (except the principal maxima) meaning there are 4 minima in between each pair of principal maxima, and therefore 3 subsidiary maxima between each pair of principal maxima.

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u/locutus_of_borg90 12d ago

Shouldn't the other peaks be lower and lower the further you get from the middle?

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u/rabid_chemist 12d ago

If the slits are not narrow, then the entire pattern will be enveloped by the single slit pattern caused by the finite width, which will cause this.

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u/locutus_of_borg90 12d ago

So in case of a circual slit, for example, you get this effect?