File:Rotating polarizer animation.gif
Rotating_polarizer_animation.gif (500 × 500 pixels, file size: 1.67 MB, MIME type: image/gif, looped, 51 frames, 15 s)
Captions
Summary edit
DescriptionRotating polarizer animation.gif |
English: Animation shows how the intensity of the incoming vertically polarized light changes as a result of the rotation of a polarization filter. The precise dependency of the (normalized) intensity I on the rotation angle is given by Malus' law. Čeština: Animace ukazuje, jakým způsobem intenzita lineárně polarizovaného paprsku procházejího polarizačním filtrem závisí na natočení filtru. Přesná závislost (normalizované) intenzity I na úhlu natočení je dána Malusovým zákonem. |
Date | |
Source | Own work |
Author | JozumBjada |
Licensing edit
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
Source code edit
This animation was created using Wolfram language 12.0.0 for Microsoft Windows (64-bit) (April 6, 2019). The source code follows.
(* ::Package:: *)
(* ::Title:: *)
(*Polarizer*)
(* ::Text:: *)
(*Version: "12.0.0 for Microsoft Windows (64-bit) (April 6, 2019)"*)
(* ::Section:: *)
(*Constants*)
(* ::Input::Initialization:: *)
innerrad=0.8;
outerthick=.3;
innerthick=.2;
dist=2;
(* ::Input::Initialization:: *)
black=GrayLevel[0.3];
(* ::Input::Initialization:: *)
fontFamily="Times New Roman"(*"Adobe Devanagari"*);
fontSize=25;
(* ::Section:: *)
(*Polarizer*)
(* ::Input::Initialization:: *)
rim=ChartElementData["CylindricalSector3D"][{{0,2Pi},{innerrad,1},{-outerthick/2,outerthick/2}},1];
(*courtesy: suggestion by user 'kglr' at: https://mathematica.stackexchange.com/questions/153536/thick-annulus-ring-in-3d*)
(* ::Input::Initialization:: *)
coating=DensityPlot[y ,{x,-1,1},{y,-1,1},RegionFunction->(#1^2+#2^2<=1&),ColorFunction->(ColorData["Rainbow"][Mod[2#1,1]]&),PlotStyle->Opacity[.5],Frame->False];
coating=First@Cases[InputForm[coating],_GraphicsComplex,Infinity];
coating=Rasterize[Graphics@coating,ImageResolution->50,Background->None];
coating={Texture[coating],EdgeForm[None],Polygon[{{-1,-1,0},{1,-1,0},{1,1,0},{-1,1,0}},VertexTextureCoordinates->{{0,0},{1,0},{1,1},{0,1}}]};
(* ::Input::Initialization:: *)
filter={EdgeForm[None],
{Opacity[.5],LightBlue,Cylinder[{{0,0,-innerthick/2},{0,0,innerthick/2}},innerrad-.001]},
{coating},
{Gray,rim,Scale[rim,{1.03,1.03,.6}]},
{Darker[black],Cuboid[{innerrad,-0.02,0},{1.01,0.02,1.3outerthick/2}],Cuboid[{-innerrad,-0.02,0},{-1.01,0.02,1.3outerthick/2}]}
};
(* ::Section:: *)
(*Rest*)
(* ::Input::Initialization:: *)
arc[ang_]:=Module[{c=1,ampl=1.5,aux},
If[ang==0,Return[{}]];
aux=ParametricPlot3D[{ampl Cos[c t],ampl Sin[c t],0},{t,0,-ang}];
aux=First@Cases[InputForm[aux],_Line,Infinity];
If[ang>15Degree,Arrow[Tube[Reverse@First@aux,.02]],Tube[aux,.02]]
];
(* ::Input::Initialization:: *)
reticule[ang_]:={black,
Tube[Line[{{1,0,0},{2,0,0}}],.03],
Tube[Line[{{Cos[ang],-Sin[ang],0},2{Cos[ang],-Sin[ang],0}}],.03],
Arrowheads[.04],arc[ang],
Text[Style[ToString[NumberForm[N@ang/Degree,{3,1}]]<>"\[Degree]",fontSize,Black,Background->GrayLevel[1,.8],FontFamily->fontFamily],1.7{Cos[ang/2],-Sin[ang/2],0},{-.5,-.5}]
};
(* ::Input::Initialization:: *)
wave[ampl_,phase_]:=Module[{c=2\[Pi] /dist 5,aux},
aux=ParametricPlot3D[{ampl Sin[c t-phase],0,t},{t,0,dist}];
aux=First@Cases[InputForm[aux],_Line,Infinity];
{Red,Tube[aux,.05]}
];
(* ::Input::Initialization:: *)
label[ang_]:=Text[Style[Row[{"\!\(\*
StyleBox[\"I\",\nFontSlant->\"Italic\"]\) = ",ToString[NumberForm[Round[Cos[ang]^2,0.01],{3,2}],TraditionalForm]}],fontSize,FontFamily->fontFamily],ImageScaled@{0.7,0.85},{-1,0}]
(* ::Section:: *)
(*Scene*)
(* ::Input::Initialization:: *)
scene[ang_,phase_:0]:=Graphics3D[{
{(*rear wave*)
{Red,Opacity[.5],EdgeForm[None],Cylinder[{{0,0,-dist},{0,0,-1.01innerthick/2}},.6innerrad]},
Translate[wave[.55innerrad,phase],{{0,0,-dist}}]
},
(*polarizer*)
reticule[ang],
Rotate[{filter,{Opacity[Cos[ang]],wave[.55innerrad Cos[ang],phase]}},-ang,{0,0,1}],
{(*front wave*)
{Red,Opacity[0.5Cos[ang]^2],EdgeForm[None],Cylinder[{{0,0,1.01innerthick/2},{0,0,dist}},.6innerrad]},
{Opacity[Cos[ang]],Rotate[wave[.55innerrad Cos[ang],phase],-ang,{0,0,1}]}
}
},
(*intensity label*)
Epilog->label[ang],
(*options*)
Lighting->"Neutral",Boxed->False,PlotRange->{2.1{-.6,1},2{-1,.6},1.05dist{-1,1}},
ViewVertical->{1,0,0},ViewPoint->0.8{.5,1,1},ViewCenter->{{0.`,0.`,0.`},{0.36,0.4}},ViewAngle->0.83`
]
(* ::Input:: *)
(*Manipulate[scene[ang,phase],{ang,0,\[Pi]/2},{phase,0,2\[Pi]}]*)
(* ::Section:: *)
(*Export*)
(* ::Input::Initialization:: *)
angleTimeEvolution[t0_,t1_,t2_,t3_]:=Piecewise[{{0,#<t0},{Rescale[#,{t0,t1},{0,\[Pi]/4}],t0<=#<t1},{\[Pi]/4,t1<=#<t2},{Rescale[#,{t2,t3},{\[Pi]/4,\[Pi]/2}],t2<=#<t3},{\[Pi]/2,True}}]&
(*Plot[angleTimeEvolution[.2,.4,.6,.8][x],{x,0,1}]*)
(* ::Input:: *)
(*{time,frames}=AbsoluteTiming[ParallelTable[Rasterize[*)
(*scene[angleTimeEvolution[.2,.4,.6,.8][t],Rescale[t,{0,1},{0,4\[Pi]}]],*)
(*ImageResolution->100],{t,0,1,.02}]];*)
(*Print[time];*)
(* ::Input:: *)
(*file=Export["test6.gif",frames,AnimationRepetitions->Infinity,"DisplayDurations"->.3]*)
(* ::Input:: *)
(*FileSize[file]*)
(* ::Input:: *)
(*SystemOpen[file]*)
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 19:36, 16 August 2021 | 500 × 500 (1.67 MB) | JozumBjada (talk | contribs) | Cross-wiki upload from cs.wikipedia.org |
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