Constructive and Destructive Interference

Manipulate[Show[Graphics3D[{Opacity[.5],EdgeForm[],Polygon[{{{0,-2,-2},{0,-2,2},{0,0,2},{0,0,1.5`},{0,-1.15`,1.5`},{0,-1.15`,-1.5`},{0,0,-1.4`},{0,0,-2}},{{0,2,-2},{0,2,2},{0,0,2},{0,0,1.5`},{0,1.15`,1.5`},{0,1.15`,-1.5`},{0,0,-1.5`},{0,0,-2}},{{0,0.85`,-1.5`},{0,0.85`,1.5`},{0,-0.85`,1.5`},{0,-0.85`,-1.5`}}}],

Table[{Opacity[((Sin[4 d])^2)],Polygon[{{2,-2+d,-1.5},{2,-2+d,1.5},{2,-2+.05+d,1.5},{2,-2+.05+d,-1.5}}]},{d,0,4,.05}],
Polygon[{{0,-1,-1.},{0,-1,1.},{2,2Tan[θ]+1,1.},{2,2Tan[θ]+1,-1.}}],Polygon[{{0,1,-1.},{0,1,1.},{2,2Tan[θ]+1,1.},{2,2Tan[θ]+1,-1.}}],Red,Thickness[.01],Line[{RotationMatrix[θ,{0,0,1}].({t,0,Sin[10t]}/.t->Norm[{2,2Tan[θ]}])+{0,1,0},RotationMatrix[ArcTan[2,2+2Tan[θ]],{0,0,1}].({t,0,Sin[10t]}/.t->Norm[{2,2Tan[θ]+2}])-{0,1,0}}]}],ParametricPlot3D[{t,1,Sin[10t]},{t,0,Norm[{2,2Tan[θ]}]},PlotRange->All]/.Line[l_]:>Rotate[Line[l],θ,{0,0,1},{0,1,0}],ParametricPlot3D[{t,-1,Sin[10t]},{t,0,Norm[{2,2Tan[θ]+2}]},PlotRange->All]/.Line[l_]:>Rotate[Line[l],ArcTan[2,2+2Tan[θ]],{0,0,1},{0,-1,0}],Boxed->False,BoxRatios->{2,4,1},SphericalRegion->True],
{{θ,-0.732`},-.98,.46}]

CAPTION

Two waves are said to interfere with each other when they pass though the same medium at the same time; sometimes the waves reinforce each other and sometimes they cancel, depending on their relative phases.

The figure shows waves emerging from two slits that hit a screen and yield bright and dark strips  corresponding to constructive and destructive interference.

THIS NOTEBOOK IS THE SOURCE CODE FROM

"Constructive and Destructive Interference" from the Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/ConstructiveAndDestructiveInterference/

Contributed by: Enrique Zeleny

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