(* Content-type: application/vnd.wolfram.cdf.text *) (*** Wolfram CDF File ***) (* http://www.wolfram.com/cdf *) (* CreatedBy='Mathematica 10.0' *) (*************************************************************************) (* *) (* The Mathematica License under which this file was created prohibits *) (* restricting third parties in receipt of this file from republishing *) (* or redistributing it by any means, including but not limited to *) (* rights management or terms of use, without the express consent of *) (* Wolfram Research, Inc. 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Ademas de esto, \ podran cambiar a voluntad los valores de los parametros asociados, a saber:" }], "Text"], Cell[CellGroupData[{ Cell["el numero de rendijas, \[OpenCurlyQuote]N\[CloseCurlyQuote],", "Item"], Cell["el ancho de las rendijas, \[OpenCurlyQuote]b\[CloseCurlyQuote], y", \ "Item"], Cell["\<\ la separacion entre los centros de dos rendijas consecutivas, \ \[OpenCurlyQuote]a\[CloseCurlyQuote].\ \>", "Item"] }, Open ]], Cell["\<\ Asimismo podran elegir agrandar o achicar la region de observacion sobre la \ pantalla ajustando el valor del parametro denominado \[OpenCurlyQuote]rango \ horizontal\[CloseCurlyQuote]. Cabe destacar que este ultimo parametro solo \ modifica la representacion de los datos en pantalla, y no modifica en ninguna \ forma el fenomeno que se esta observando.\ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Que es lo que grafica la interfaz dinamica?", "Section"], Cell["\<\ En el grafico se presentan, superpuestas, dos curvas: una en azul y otra en \ naranja. La curva azul representa el patron de difraccion completo de N \ rendijas (identicas) de ancho \[OpenCurlyQuote]b\[CloseCurlyQuote] cuyos \ centros estan equiespaciados en una distancia \[OpenCurlyQuote]a\ \[CloseCurlyQuote]. Por otro lado, la curva naranja corresponde al patron de \ difraccion de una unica rendija de tama\[NTilde]o (ancho) \[OpenCurlyQuote]b\ \[CloseCurlyQuote]. \ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Codigo ", StyleBox["Mathematica", FontSlant->"Italic"], " e interfaz grafica dinamica" }], "Section"], Cell["\<\ Las lineas siguientes (de texto en tipografia de maquina de escribir) \ constituyen el codigo Mathematica que permite crear la interfaz dinamica para \ poder visualizar los patrones de difraccion de multiples rendijas finitas e \ interactuar con ella cambiando los valores de los parametros. Dichos valores \ pueden cambiarse utilizando los ' sliders', o bien directamente ingresando \ los valores deseados en las ' cajas de texto' asociados a cada magnitud.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"SetOptions", "[", RowBox[{"Manipulator", ",", RowBox[{"Appearance", "\[Rule]", "\"\\""}]}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"1", "/", "n"}], ")"}], RowBox[{"ChebyshevU", "[", RowBox[{ RowBox[{"n", "-", "1"}], ",", RowBox[{"Cos", "[", RowBox[{"b", " ", RowBox[{"k", "/", "2"}]}], "]"}]}], "]"}], RowBox[{"Sinc", "[", RowBox[{"a", " ", RowBox[{"k", "/", "2"}]}], "]"}]}], ")"}], "^", "2"}], ",", RowBox[{ RowBox[{"Sinc", "[", RowBox[{"a", " ", RowBox[{"k", "/", "2"}]}], "]"}], "^", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"k", ",", RowBox[{"-", "kmax"}], ",", "kmax"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}]}], ",", RowBox[{"PlotStyle", "\[Rule]", "\"\\""}], ",", RowBox[{"Axes", "\[Rule]", "False"}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"FrameTicks", "\[Rule]", RowBox[{"{", RowBox[{"True", ",", "False"}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"FrameLabel", "\[Rule]", RowBox[{"{", RowBox[{ "\"\\"", ",", "\"\\""}], "}"}]}], ",", RowBox[{"PlotLabel", "\[Rule]", RowBox[{"\"\\"", "<>", RowBox[{"ToString", "[", "n", "]"}], "<>", RowBox[{"If", "[", RowBox[{ RowBox[{"n", ">", "1"}], ",", "\"\< rendijas\>\"", ",", "\"\< rendija\>\""}], "]"}]}]}], ",", RowBox[{"Filling", "\[Rule]", RowBox[{"{", RowBox[{"1", "\[Rule]", "Axis"}], "}"}]}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"Automatic", ",", RowBox[{"{", RowBox[{"Thick", ",", "Dashed"}], "}"}]}], "}"}]}], ",", RowBox[{"ImageSize", "\[Rule]", RowBox[{"{", RowBox[{"500", ",", "350"}], "}"}]}], ",", RowBox[{"ImagePadding", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"40", ",", "20"}], "}"}], ",", RowBox[{"{", RowBox[{"40", ",", "20"}], "}"}]}], "}"}]}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n", ",", "2", ",", "\"\\""}], "}"}], ",", RowBox[{"Range", "[", "10", "]"}], ",", "SetterBar"}], "}"}], ",", "Delimiter", ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"a", ",", "0", ",", "\"\\""}], "}"}], ",", "0", ",", "2", ",", RowBox[{"Appearance", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"b", ",", "2.5", ",", "\"\\""}], "}"}], ",", "0", ",", "10", ",", RowBox[{"Appearance", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], "}"}], ",", "Delimiter", ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"kmax", ",", "10", ",", "\"\\""}], "}"}], ",", "1", ",", "100", ",", RowBox[{"Appearance", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], "}"}], ",", RowBox[{"ControlPlacement", "\[Rule]", "Right"}]}], "]"}]}], "Input"], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`a$$ = 0.835, $CellContext`b$$ = 2.52, $CellContext`kmax$$ = 10, $CellContext`n$$ = 2, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`n$$], 2, "Numero de rendijas (N):"}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}}, {{ Hold[$CellContext`a$$], 0, "Ancho de las rendijas (b):"}, 0, 2}, {{ Hold[$CellContext`b$$], 2.5, "Espacio entre rendijas (a):"}, 0, 10}, {{ Hold[$CellContext`kmax$$], 10, "Rango horizontal:"}, 1, 100}}, Typeset`size$$ = {500., {173., 177.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`n$122024$$ = 0, $CellContext`a$122025$$ = 0, $CellContext`b$122026$$ = 0, $CellContext`kmax$122027$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`a$$ = 0, $CellContext`b$$ = 2.5, $CellContext`kmax$$ = 10, $CellContext`n$$ = 2}, "ControllerVariables" :> { Hold[$CellContext`n$$, $CellContext`n$122024$$, 0], Hold[$CellContext`a$$, $CellContext`a$122025$$, 0], Hold[$CellContext`b$$, $CellContext`b$122026$$, 0], Hold[$CellContext`kmax$$, $CellContext`kmax$122027$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Plot[{(((1/$CellContext`n$$) ChebyshevU[$CellContext`n$$ - 1, Cos[$CellContext`b$$ ($CellContext`k/2)]]) Sinc[$CellContext`a$$ ($CellContext`k/2)])^2, Sinc[$CellContext`a$$ ($CellContext`k/ 2)]^2}, {$CellContext`k, -$CellContext`kmax$$, \ $CellContext`kmax$$}, PlotRange -> {0, 1}, PlotStyle -> "Detailed", Axes -> False, Frame -> True, FrameTicks -> {True, False}, FrameLabel -> {"Posicion en la pantalla", "Intensidad (irradiancia)"}, PlotLabel -> StringJoin["Patron de difraccion de ", ToString[$CellContext`n$$], If[$CellContext`n$$ > 1, " rendijas", " rendija"]], Filling -> {1 -> Axis}, PlotStyle -> {Automatic, {Thick, Dashed}}, ImageSize -> {500, 350}, ImagePadding -> {{40, 20}, {40, 20}}], "Specifications" :> {{{$CellContext`n$$, 2, "Numero de rendijas (N):"}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, ControlType -> SetterBar}, Delimiter, {{$CellContext`a$$, 0, "Ancho de las rendijas (b):"}, 0, 2, Appearance -> {"Labeled", "Open"}}, {{$CellContext`b$$, 2.5, "Espacio entre rendijas (a):"}, 0, 10, Appearance -> {"Labeled", "Open"}}, Delimiter, {{$CellContext`kmax$$, 10, "Rango horizontal:"}, 1, 100, Appearance -> {"Labeled", "Open"}}}, "Options" :> {ControlPlacement -> Right}, "DefaultOptions" :> {}], ImageSizeCache->{913., {201., 206.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Ideas para probar con la interfaz dinamica", "Section"], Cell["\<\ Aqui les dejo unas ideas que pueden ser utiles si quieren ver cosas \ divertidas empleando esta interfaz grafica, vinculadas con los temas que \ discutimos en las clases teoricas. Algunas que se me ocurren son las \ siguientes: \ \>", "Text"], Cell[CellGroupData[{ Cell["\<\ Observar el patron de difraccion correspondiente a dos rendijas de ancho \ infinitesimal: en el limite de \[OpenCurlyQuote]b\[CloseCurlyQuote] tendiendo \ a cero, deberiamos recuperar el patron de interferencia asociado a la \ experiencia de la doble rendija (infinitesimal) de Young. \ \>", "Item"], Cell["\<\ Manteniendo un ancho de rendija fijo, hacer que dos rendijas coincidan en su \ posicion. Esto podria lograrse haciendo \[OpenCurlyQuote]a = 0\ \[CloseCurlyQuote], y el patron que deberia observarse es el correspondiente \ al de la difraccion por una rendija finita, dado por la funcion seno cardinal \ al cuadrado. \ \>", "Item"], Cell["\<\ Provocar la perdida de un orden de interferencia (missing order): elegir un \ orden de interferencia n que queremos hacer desaparecer empleando para ello \ el orden m de difraccion. Establecer los valores de \[OpenCurlyQuote]a\ \[CloseCurlyQuote] y \[OpenCurlyQuote]b\[CloseCurlyQuote] para lograr la \ perdida del orden. Verificar que asi suceda, y observar que otros ordenes \ tambien se pierden con ese mismo par de valores de \[OpenCurlyQuote]a\ \[CloseCurlyQuote] y \[OpenCurlyQuote]b\[CloseCurlyQuote]. \ \>", "Item"], Cell["\<\ Estudiar como se modifican estos mismos resultados (los precedentes) si \ consideramos mas de 2 rendijas.\ \>", "Item"] }, Open ]] }, Open ]] }, Open ]] }, WindowSize->{1169, 681}, Visible->True, ScrollingOptions->{"VerticalScrollRange"->Fit}, ShowCellBracket->Automatic, CellContext->Notebook, TrackCellChangeTimes->False, FrontEndVersion->"10.0 for Mac OS X x86 (32-bit, 64-bit Kernel) (June 27, \ 2014)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[1486, 35, 131, 3, 83, "Title"], Cell[1620, 40, 61, 0, 43, "Text"], Cell[1684, 42, 155, 3, 49, "Text"], Cell[CellGroupData[{ Cell[1864, 49, 57, 0, 64, "Section"], Cell[1924, 51, 416, 8, 68, "Text"], Cell[CellGroupData[{ Cell[2365, 63, 76, 0, 28, "Item"], Cell[2444, 65, 83, 1, 28, "Item"], Cell[2530, 68, 125, 3, 28, "Item"] }, Open ]], Cell[2670, 74, 378, 6, 49, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[3085, 85, 62, 0, 64, "Section"], Cell[3150, 87, 494, 8, 68, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[3681, 100, 123, 5, 64, "Section"], Cell[3807, 107, 482, 7, 68, "Text"], Cell[CellGroupData[{ Cell[4314, 118, 3930, 108, 182, "Input"], Cell[8247, 228, 3491, 63, 424, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[11787, 297, 61, 0, 64, "Section"], Cell[11851, 299, 252, 5, 49, "Text"], Cell[CellGroupData[{ Cell[12128, 308, 309, 5, 45, "Item"], Cell[12440, 315, 339, 6, 45, "Item"], Cell[12782, 323, 533, 8, 62, "Item"], Cell[13318, 333, 129, 3, 28, "Item"] }, Open ]] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *) (* NotebookSignature DxpDt5aIqex2FBgUZingIrRI *)