Moiré Pattern of Two Straight Line Patterns

Manipulate[With[{u=Line[Table[{{i,-n/1.5},{i,n/1.5}},{i,-n/1.5,n/1.5}]]},Graphics[{Thickness[.5/n],
Rotate[u,a Degree],
Rotate[u,b Degree]},PlotRange->n/2 ,ImageSize->{450,450}]],
{{a,-4,"angle 1"},-20,20,Appearance->"Labeled"},
{{b,4,"angle 2"},-20,20,Appearance->"Labeled"},
Delimiter,
{{n,30,"lines"},10,70,1,Appearance->"Labeled"}]

CAPTION

The Moiré pattern formed using two sets of straight line patterns illustrates the interference fringes produced by interfering two plane waves. The spacing of the Moiré pattern depends on the angle between the two straight line patterns, just like the spacing of interference fringes depends upon the angle between two plane waves.  The spacing of the lines can be thought of as the wavelength of the two plane waves.  For a given angle between the two plane waves the smaller the wavelength, the smaller the spacing of the interference fringes.

DETAILS

Moiré patterns are a good way to illustrate the interference of two wavefronts. Moiré patterns show the difference between the two original patterns just like interference fringes show the phase difference between two interfering wavefronts. When the two patterns are in phase, bright regions result and when the patterns are a half-period out of phase, dark regions result.

THIS NOTEBOOK IS THE SOURCE CODE FROM

"Moiré Pattern of Two Straight Line Patterns" from the Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/MoirePatternOfTwoStraightLinePatterns/

Contributed by: James C. Wyant

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