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Multiple-Slit Diffraction Using Wavenumber

Diffraction refers to various phenomena that occur when a wave encounters an obstacle or a slit. It is defined as the bending of light around the corners of an obstacle or aperture into the region of geometrical shadow of the obstacle. Multiple-slit diffraction occurs when a wave encounters several slits.

The normalized transmitted intensity decreases with the number of slits, the slit separation distance, wavenumber and the width of the slits. The normalized transmitted intensity varies sinusoidally with the diffraction angle.

Formula

QuantityVariable[Subscript[Style["I", Italic], "θ"]/Subscript[Style["I", Italic], "0"], "Unitless"] == (ChebyshevU[-1 + QuantityVariable["n", "Unitless"], Cos[(QuantityVariable["d", "Distance"]*QuantityVariable["k", "Wavenumber"]*Sin[QuantityVariable["θ", "Angle"]])/2]]^2*Sinc[(QuantityVariable["k", "Wavenumber"]*QuantityVariable["w", "Distance"]*Sin[QuantityVariable["θ", "Angle"]])/2]^2)/QuantityVariable["n", "Unitless"]^2

symbol description physical quantity
Iθ/I0 normalized transmitted intensity "Unitless"
n number of slits "Unitless"
d slit separation distance "Distance"
k wavenumber "Wavenumber"
θ diffraction angle "Angle"
w slit width "Distance"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Multiple-Slit Diffraction Using Wavenumber"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ ResourceObject["Multiple-Slit Diffraction Using Wavenumber"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Multiple-Slit Diffraction Using Wavenumber"], {QuantityVariable[ "\[Theta]","Angle"] -> Quantity[0.1`, "AngularDegrees"], QuantityVariable["n","Unitless"] -> 2}]
Out[3]=

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