(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 8.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 64410, 1554] NotebookOptionsPosition[ 62696, 1496] NotebookOutlinePosition[ 63197, 1516] CellTagsIndexPosition[ 63154, 1513] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ RowBox[{ RowBox[{ StyleBox["(*", FontColor->RGBColor[0.6, 0.4, 0.2]], "\[IndentingNewLine]", StyleBox[ RowBox[{ RowBox[{ "Programma", " ", "di", " ", "esempio", " ", "di", " ", "calcolo", " ", "di", " ", "mode"}], "-", RowBox[{ "matching", " ", "usando", " ", "il", " ", "metodo", " ", "delle", " ", "matrici", " ", "di", " ", "propagazione", " ", RowBox[{"(", "ABCD", ")"}]}]}], "Title", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", "Title", FontColor->RGBColor[1, 0, 0]], "\[IndentingNewLine]", StyleBox["*)", FontColor->RGBColor[0.6, 0.4, 0.2]]}], StyleBox["\[IndentingNewLine]", FontColor->RGBColor[0.6, 0.4, 0.2]], StyleBox["\[IndentingNewLine]", FontColor->RGBColor[0.6, 0.4, 0.2]], StyleBox[ RowBox[{"(*", " ", StyleBox[ RowBox[{"si", " ", "lavora", " ", "in", " ", "mm"}], FontSize->16], " ", "*)"}], FontColor->RGBColor[0.6, 0.4, 0.2]], StyleBox["\[IndentingNewLine]", FontColor->RGBColor[0.6, 0.4, 0.2]]}]], "Input", CellChangeTimes->{{3.65434638353125*^9, 3.65434642946875*^9}}], Cell[BoxData[ StyleBox[ RowBox[{"(*", " ", RowBox[{ RowBox[{"Matrici", " ", RowBox[{"di", ":", " ", RowBox[{ "lente", " ", "sottile", " ", "di", " ", "focale", " ", "f", " ", RowBox[{"(", "Mf", ")"}]}]}]}], ",", " ", RowBox[{"propagazione", " ", "lunga", " ", "d", " ", RowBox[{"(", "Md", ")"}]}], ",", " ", RowBox[{ "passaggio", " ", "attraverso", " ", "una", " ", "superficie", " ", "sferica", " ", "di", " ", "raggio", " ", "R"}], ",", " ", RowBox[{ "che", " ", "delimita", " ", "due", " ", "mezzi", " ", "con", " ", "indici", " ", "di", " ", "rifrazione", " ", "n1", " ", "e", " ", "n2", " ", RowBox[{"(", "MnR", ")"}]}]}], " ", "*)"}], FontColor->RGBColor[0.6, 0.4, 0.2]]], "Input", CellChangeTimes->{{3.6543189957731247`*^9, 3.6543191519918747`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"Mf", "[", "f_", "]"}], ":=", RowBox[{"(", GridBox[{ {"1", "0"}, { RowBox[{ RowBox[{"-", "1"}], "/", "f"}], "1"} }], ")"}]}], ";", RowBox[{ RowBox[{"Md", "[", "d_", "]"}], ":=", RowBox[{"(", GridBox[{ {"1", "d"}, {"0", "1"} }], ")"}]}], ";", RowBox[{ RowBox[{"MnR", "[", RowBox[{"n1_", ",", "n2_", ",", "r_"}], "]"}], ":=", RowBox[{"(", GridBox[{ {"1", "0"}, { RowBox[{ RowBox[{"(", RowBox[{"n2", "-", "n1"}], ")"}], "/", "r"}], "1"} }], ")"}]}]}]], "Input"], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"(*", " ", RowBox[{ RowBox[{ RowBox[{ "matrici", " ", "esatte", " ", "per", " ", "lenti", " ", "piano"}], "-", RowBox[{"convessa", " ", "e", " ", "convesso"}], "-", "piana"}], ",", " ", RowBox[{"di", " ", "raggio", " ", "r"}], ",", " ", RowBox[{ "vetro", " ", "con", " ", "indice", " ", "di", " ", "rifrazione", " ", "nrf"}], ",", " ", RowBox[{"spessore", " ", "t"}]}], " ", "*)"}], FontColor->RGBColor[0.6, 0.4, 0.2]], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Mpc", "[", RowBox[{"nrf_", ",", "t_", ",", "r_"}], "]"}], ":=", RowBox[{"Dot", "[", RowBox[{ RowBox[{"MnR", "[", RowBox[{"1", ",", "nrf", ",", RowBox[{"-", "r"}]}], "]"}], ",", RowBox[{"Md", "[", RowBox[{"t", "/", "nrf"}], "]"}]}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Mcp", "[", RowBox[{"nrf_", ",", "t_", ",", "r_"}], "]"}], ":=", RowBox[{"Dot", "[", RowBox[{ RowBox[{"Md", "[", RowBox[{"t", "/", "nrf"}], "]"}], ",", RowBox[{"MnR", "[", RowBox[{"1", ",", "nrf", ",", RowBox[{"-", "r"}]}], "]"}]}], "]"}]}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.6543191827574997`*^9, 3.6543191838668747`*^9}}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"(*", " ", RowBox[{ "Si", " ", "definiscono", " ", "gli", " ", "alementi", " ", "ABCD", " ", "della", " ", "matrice", " ", "totale", " ", "del", " ", RowBox[{"sistema", " ", "'"}], RowBox[{"Mtot", "'"}], " ", RowBox[{"(", RowBox[{"che", " ", "costruiremo", " ", "dopo"}], ")"}]}], " ", "*)"}], FontColor->RGBColor[0.6, 0.4, 0.2]], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"mA", ":=", RowBox[{"Mtot", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"mB", ":=", RowBox[{"Mtot", "[", RowBox[{"[", RowBox[{"1", ",", "2"}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"mC", ":=", RowBox[{"Mtot", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"mD", ":=", RowBox[{"Mtot", "[", RowBox[{"[", RowBox[{"2", ",", "2"}], "]"}], "]"}]}], ";"}]}]}]], "Input", CellChangeTimes->{{3.6543195511012497`*^9, 3.6543195924918747`*^9}, { 3.6543204117262497`*^9, 3.6543204347574997`*^9}}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"(*", " ", RowBox[{ RowBox[{ "Si", " ", "suppone", " ", "di", " ", "partire", " ", "da", " ", "un", " ", "fuoco", " ", "del", " ", "fascio"}], ",", " ", RowBox[{"dove", " ", "il", " ", "waist", " ", RowBox[{"\[EGrave]", " ", "'"}], RowBox[{"win", "'"}]}], ",", " ", RowBox[{"e", " ", "di", " ", "arrivare", " ", "sul", " ", "fuoco"}], ",", " ", RowBox[{ RowBox[{ RowBox[{"con", " ", "waist", " ", RowBox[{"finale", " ", "'"}], RowBox[{ RowBox[{"wout", "'"}], ".", " ", "Il"}], " ", "parametro", " ", "di", " ", "fascio", " ", "q", " ", "\[EGrave]", " ", "quindi", " ", "immaginario", " ", "puro", " ", "sia", " ", "in", " ", "ingresso", " ", "che", " ", "in", " ", RowBox[{"uscita", ".", " ", "Valgono"}], " ", "quindi", " ", "le", " ", "relazione", " ", "BD"}], "+", FractionBox[ RowBox[{"AC", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["win", "4"]}], SuperscriptBox["\[Lambda]", "2"]]}], "=", "0"}], ",", " ", RowBox[{ "dove", " ", "\[Lambda]", " ", "\[EGrave]", " ", "la", " ", "lunghezza", " ", RowBox[{"d", "'"}], "onda"}], ",", " ", RowBox[{ RowBox[{"e", " ", "wout"}], "=", RowBox[{"win", "*", SqrtBox[ FractionBox["A", "D"]], " ", RowBox[{ RowBox[{"(", RowBox[{ "dimostrate", " ", "in", " ", "coda", " ", "a", " ", "questo", " ", "foglio"}], ")"}], ".", " ", "Queste"}], " ", "due", " ", "equazioni", " ", "definiscono", " ", "completamente", " ", "il", " ", "problema"}]}], ",", " ", RowBox[{ "che", " ", "avr\[AGrave]", " ", "quindi", " ", "due", " ", "incognite", " ", RowBox[{"libere", "."}]}]}], " ", "*)"}], FontColor->RGBColor[0.6, 0.4, 0.2]], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"wout", ":=", RowBox[{"win", "*", SqrtBox[ FractionBox["mA", "mD"]]}]}], "\[IndentingNewLine]", RowBox[{"equazione", ":=", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"mB", "*", "mD"}], "+", FractionBox[ RowBox[{ RowBox[{"\[Pi]", "^", "2"}], "*", RowBox[{"win", "^", "4"}], "*", "mA", "*", "mC"}], RowBox[{"\[Lambda]", "^", "2"}]]}], "\[Equal]", "0"}], ")"}]}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.6543196228199997`*^9, 3.6543198153668747`*^9}, { 3.6543198500699997`*^9, 3.6543199130074997`*^9}, {3.6543199544449997`*^9, 3.6543200172106247`*^9}, {3.6543200501168747`*^9, 3.6543200830387497`*^9}, { 3.6543207883981247`*^9, 3.6543208303981247`*^9}, {3.654414029671875*^9, 3.6544140809375*^9}}], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", StyleBox[ RowBox[{ StyleBox["(*", FontColor->RGBColor[0.6, 0.4, 0.2]], StyleBox[" ", FontColor->RGBColor[0.6, 0.4, 0.2]], RowBox[{ StyleBox["I", FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]], StyleBox[ RowBox[{"ESEMPIO", ":", " ", RowBox[{ "Adattamento", " ", "del", " ", "modo", " ", "con", " ", "due", " ", RowBox[{"lenti", ".", " "}]}]}], FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[0.6, 0.4, 0.2]]}], StyleBox["*)", FontColor->RGBColor[0.6, 0.4, 0.2]]}], "Subsubtitle"], StyleBox["\[IndentingNewLine]", "Text", FontColor->RGBColor[0.6, 0.4, 0.2]], StyleBox[ RowBox[{ StyleBox["(*", "Text"], " ", StyleBox[ RowBox[{ RowBox[{ "Il", " ", "sistema", " ", "ottico", " ", "complessivo", " ", "\[EGrave]", " ", "formato", " ", "da", " ", "una", " ", "propagazione", " ", RowBox[{"lunga", " ", "'"}], RowBox[{"d0", "'"}]}], ",", " ", RowBox[{"una", " ", "lente", " ", "di", " ", RowBox[{"focale", " ", "'"}], RowBox[{"f1", "'"}]}], ",", " ", RowBox[{"una", " ", RowBox[{"distanza", " ", "'"}], RowBox[{"d1", "'"}]}], ",", " ", RowBox[{"una", " ", "lente", " ", "di", " ", RowBox[{"focale", " ", "'"}], RowBox[{"f2", "'"}]}], ",", " ", RowBox[{"un", " ", "tratto", " ", "finale", " ", RowBox[{"lungo", " ", "'"}], RowBox[{ RowBox[{"d2", "'"}], "."}]}]}], "Text"], StyleBox[" ", "Text"], "*)"}], FontColor->RGBColor[0.6, 0.4, 0.2]], StyleBox["\[IndentingNewLine]", FontColor->RGBColor[0.6, 0.4, 0.2]], "\[IndentingNewLine]", " ", RowBox[{ RowBox[{"Mtot", ":=", RowBox[{"Dot", "[", RowBox[{ RowBox[{"Md", "[", "d2", "]"}], ",", RowBox[{"Mf", "[", "f2", "]"}], ",", RowBox[{"Md", "[", "d1", "]"}], ",", RowBox[{"Mf", "[", "f1", "]"}], ",", RowBox[{"Md", "[", "d0", "]"}]}], "]"}]}], " ", "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.6543194293668747`*^9, 3.6543195146949997`*^9}, { 3.6543203988043747`*^9, 3.6543204023512497`*^9}, {3.6543204695856247`*^9, 3.6543204863668747`*^9}, 3.6543205164762497`*^9, {3.6543205964606247`*^9, 3.6543206217418747`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"(", StyleBox[ RowBox[{ RowBox[{"*", " ", "Esempio", " ", "1", RowBox[{"a", ":", " ", RowBox[{ "conosciamo", " ", "il", " ", "waist", " ", "in", " ", "ingresso", " ", "e", " ", "quello", " ", "che", " ", "vogliamo", " ", "in", " ", "uscita", " ", RowBox[{"(", RowBox[{"'", RowBox[{"wf", "'"}]}], ")"}]}]}]}], ",", " ", RowBox[{ "le", " ", "focali", " ", "delle", " ", "due", " ", "lenti", " ", "e", " ", "la", " ", "lunghezza", " ", "totale", " ", "del", " ", "sistema", " ", "ottico", " ", RowBox[{ RowBox[{"(", RowBox[{"'", RowBox[{"dtot", "'"}]}], ")"}], ".", " ", "Le"}], " ", "incognite", " ", "sono", " ", "le", " ", "posizioni", " ", "delle", " ", RowBox[{"lenti", "."}]}]}], FontColor->RGBColor[0.6, 0.4, 0.2]], StyleBox[" ", FontColor->RGBColor[0.6, 0.4, 0.2]]}], StyleBox["*)", FontColor->RGBColor[0.6, 0.4, 0.2]]}], StyleBox["\[IndentingNewLine]", FontColor->RGBColor[0.6, 0.4, 0.2]]}]], "Input", CellChangeTimes->{ 3.6543206684918747`*^9, {3.6543207132106247`*^9, 3.6543207467106247`*^9}, { 3.6543208456324997`*^9, 3.6543209396637497`*^9}, {3.6543209722731247`*^9, 3.6543210285543747`*^9}, {3.6543210812418747`*^9, 3.6543210848043747`*^9}, {3.6543211775543747`*^9, 3.6543211859918747`*^9}, {3.6543212453356247`*^9, 3.6543212464449997`*^9}}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"(*", " ", RowBox[{"Definizione", " ", "dei", " ", "parametri", " ", "noti"}], " ", "*)"}], FontColor->RGBColor[0.6, 0.4, 0.2]], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Lambda]", "=", RowBox[{"0.78", " ", RowBox[{"10", "^", RowBox[{"-", "3"}]}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"win", "=", "0.8"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"wf", "=", "0.2"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"f1", "=", "100"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"f2", "=", "100"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"dtot", "=", "1500"}], ";"}]}]}]], "Input", CellChangeTimes->{{3.6543208898043747`*^9, 3.6543208899606247`*^9}, { 3.6543210333824997`*^9, 3.6543210944449997`*^9}, {3.6543211952262497`*^9, 3.6543211966324997`*^9}, {3.6543213337262497`*^9, 3.6543213456168747`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"(*", " ", RowBox[{ "Soluzione", " ", "delle", " ", "equazioni", " ", "del", " ", "sistema"}], " ", "*)"}], FontColor->RGBColor[0.6, 0.4, 0.2]], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"Solve", "[", RowBox[{ RowBox[{"{", RowBox[{"equazione", ",", RowBox[{"wout", "\[Equal]", "wf"}], ",", RowBox[{ RowBox[{"d0", "+", "d1", "+", "d2"}], "\[Equal]", "dtot"}]}], "}"}], ",", RowBox[{"{", RowBox[{"d0", ",", "d1", ",", "d2"}], "}"}]}], "]"}], " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Clear", "[", RowBox[{ "\[Lambda]", ",", "win", ",", "wf", ",", "f1", ",", "f2", ",", "dtot"}], "]"}]}]}]], "Input", CellChangeTimes->{{3.6543210505387497`*^9, 3.6543210726481247`*^9}, { 3.6543211135074997`*^9, 3.6543211155387497`*^9}, {3.6543211997418747`*^9, 3.6543212510856247`*^9}, {3.6543215950231247`*^9, 3.6543216152106247`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"d0", "\[Rule]", "1993.6273196655852`"}], ",", RowBox[{"d1", "\[Rule]", "189.60159550406345`"}], ",", RowBox[{"d2", "\[Rule]", RowBox[{"-", "683.2289151696486`"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"d0", "\[Rule]", RowBox[{"101.28013102107276`", "\[VeryThinSpace]", "-", RowBox[{"2580.883590983083`", " ", "\[ImaginaryI]"}]}]}], ",", RowBox[{"d1", "\[Rule]", RowBox[{"1297.4626869701408`", "\[VeryThinSpace]", "+", RowBox[{"2745.1333338357626`", " ", "\[ImaginaryI]"}]}]}], ",", RowBox[{"d2", "\[Rule]", RowBox[{"101.25718200878637`", "\[VeryThinSpace]", "-", RowBox[{"164.24974285267973`", " ", "\[ImaginaryI]"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"d0", "\[Rule]", RowBox[{"101.28013102107276`", "\[VeryThinSpace]", "+", RowBox[{"2580.883590983083`", " ", "\[ImaginaryI]"}]}]}], ",", RowBox[{"d1", "\[Rule]", RowBox[{"1297.4626869701408`", "\[VeryThinSpace]", "-", RowBox[{"2745.1333338357626`", " ", "\[ImaginaryI]"}]}]}], ",", RowBox[{"d2", "\[Rule]", RowBox[{"101.25718200878637`", "\[VeryThinSpace]", "+", RowBox[{"164.24974285267973`", " ", "\[ImaginaryI]"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"d0", "\[Rule]", "109.24635468163342`"}], ",", RowBox[{"d1", "\[Rule]", "1281.507290636733`"}], ",", RowBox[{"d2", "\[Rule]", "109.24635468163375`"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"d0", "\[Rule]", "640.753645318373`"}], ",", RowBox[{"d1", "\[Rule]", "218.4927093632678`"}], ",", RowBox[{"d2", "\[Rule]", "640.7536453183593`"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"d0", "\[Rule]", "550.479084958925`"}], ",", RowBox[{"d1", "\[Rule]", "215.47303055565413`"}], ",", RowBox[{"d2", "\[Rule]", "734.0478844854209`"}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{{3.6543213300074997`*^9, 3.6543213496324997`*^9}, 3.6543220564137497`*^9, 3.654340988625*^9, 3.654344976078125*^9, 3.654345133171875*^9, 3.654345613578125*^9, 3.654346011796875*^9}] }, Open ]], Cell[BoxData[ StyleBox[ RowBox[{ RowBox[{"(*", " ", RowBox[{ RowBox[{"Vengono", " ", "trovate", " ", "6", " ", RowBox[{"soluzioni", ".", " ", "Di"}], " ", "queste", " ", "2", " ", "sono", " ", "non", " ", "fisiche", " ", RowBox[{"(", RowBox[{"compaiono", " ", "parti", " ", "immaginarie"}], ")"}], " ", "ed", " ", "una", " ", "propone", " ", "una", " ", "distanza", " ", RowBox[{"negativa", ".", " ", "Rimangono"}], " ", "3", " ", "soluzioni", " ", "valide"}], ",", " ", RowBox[{ "tra", " ", "le", " ", "quali", " ", "si", " ", "pu\[OGrave]", " ", "scegliere"}]}], " ", "*)"}], "\[IndentingNewLine]"}], FontColor->RGBColor[0.6, 0.4, 0.2]]], "Input", CellChangeTimes->{{3.6543213966637497`*^9, 3.6543214583512497`*^9}, { 3.6543214887574997`*^9, 3.6543215513199997`*^9}, {3.654344991203125*^9, 3.65434499728125*^9}}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{ StyleBox["(*", FontColor->RGBColor[0.6, 0.4, 0.2]], StyleBox[ RowBox[{ StyleBox[" ", FontColor->RGBColor[0.6, 0.4, 0.2]], StyleBox[" ", FontColor->RGBColor[1, 0, 0]]}]], RowBox[{ StyleBox[ RowBox[{ RowBox[{"II", " ", RowBox[{"ESEMPIO", ":", " ", RowBox[{ "Adattamento", " ", "del", " ", "modo", " ", "a", " ", "quello", " ", "di", " ", "una", " ", "cavit\[AGrave]"}]}]}], ",", " ", RowBox[{"usando", " ", "tre", " ", RowBox[{"lenti", ".", " "}]}]}], FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[0.6, 0.4, 0.2]]}], StyleBox["*)", FontColor->RGBColor[0.6, 0.4, 0.2]]}], "Subsubtitle"], StyleBox["\[IndentingNewLine]", FontColor->RGBColor[0.6, 0.4, 0.2]], StyleBox[ RowBox[{"(*", " ", RowBox[{ RowBox[{ "Uso", " ", "di", " ", "tre", " ", "lenti", " ", "sottili", " ", "per", " ", "adattare", " ", "il", " ", "modo", " ", "a", " ", "quello", " ", "di", " ", "una", " ", "cavit\[AGrave]", " ", "ottica", " ", RowBox[{"lunga", " ", "'"}], RowBox[{"lung", "'"}]}], ",", " ", RowBox[{ RowBox[{ "composta", " ", "da", " ", "uno", " ", "specchio", " ", "di", " ", "ingresso", " ", "piano"}], "-", RowBox[{"concavo", " ", "di", " ", "fused", " ", "silica", " ", RowBox[{"(", RowBox[{"indice", " ", "di", " ", "rifrazione", " ", "1.445"}], ")"}]}]}], ",", " ", RowBox[{"raggio", " ", "di", " ", RowBox[{"curvatura", " ", "'"}], RowBox[{"raggio", "'"}]}], ",", " ", RowBox[{"spessore", " ", "6.35", "mm"}]}], " ", "*)"}], FontColor->RGBColor[0.6, 0.4, 0.2]], StyleBox[" ", FontColor->RGBColor[0.6, 0.4, 0.2]], StyleBox["\[IndentingNewLine]", FontColor->RGBColor[0.6, 0.4, 0.2]], "\[IndentingNewLine]", RowBox[{"Mtot", ":=", RowBox[{"Dot", "[", RowBox[{ RowBox[{"Md", "[", "lung", "]"}], ",", RowBox[{"Mpc", "[", RowBox[{"1.445", ",", "6.35", ",", RowBox[{"-", "raggio"}]}], "]"}], ",", RowBox[{"Md", "[", "d3", "]"}], ",", RowBox[{"Mf", "[", "f3", "]"}], ",", RowBox[{"Md", "[", "d2", "]"}], ",", RowBox[{"Mf", "[", "f2", "]"}], ",", RowBox[{"Md", "[", "d1", "]"}], ",", RowBox[{"Mf", "[", "f1", "]"}], ",", RowBox[{"Md", "[", "d0", "]"}]}], "]"}], " "}]}]], "Input", CellChangeTimes->{{3.6543192713981247`*^9, 3.6543194020543747`*^9}, { 3.6543216571637497`*^9, 3.6543216866949997`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"\[IndentingNewLine]", StyleBox[ RowBox[{"(*", " ", RowBox[{ RowBox[{"Esempio", " ", "2", RowBox[{"a", ":", " ", RowBox[{ "conosciamo", " ", "il", " ", "waist", " ", "in", " ", "ingresso", " ", "e", " ", "calcoliamo", " ", "quello", " ", "della", " ", "cavit\[AGrave]", " ", RowBox[{"(", RowBox[{"'", RowBox[{"wcav", "'"}]}], ")"}]}]}]}], ";", " ", RowBox[{ "fissiamo", " ", "le", " ", "focali", " ", "delle", " ", "tre", " ", "lenti", " ", "e", " ", "le", " ", "prime", " ", "due", " ", RowBox[{"distanze", ".", " ", "Le"}], " ", "incognite", " ", "sono", " ", "la", " ", "posizione", " ", "dell", " ", "aterza", " ", "lente", " ", "e", " ", "quell", " ", "adella", " ", RowBox[{"cavit\[AGrave]", "."}]}]}], " ", "*)"}], FontColor->RGBColor[0.6, 0.4, 0.2]], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"f1", "=", "300"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"f2", "=", "50"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"f3", "=", "125"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"d0", "=", "60"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"d1", "=", "300"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"win", "=", "0.4"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Lambda]", "=", RowBox[{"0.78", " ", RowBox[{"10", "^", RowBox[{"-", "3"}]}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"lung", "=", "10"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"raggio", "=", "200"}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"wcav", ":=", RowBox[{"Sqrt", "[", RowBox[{"\[Lambda]", " ", RowBox[{ SqrtBox[ RowBox[{"lung", "*", RowBox[{"(", RowBox[{"raggio", "-", "lung"}], ")"}]}]], "/", "\[Pi]"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"N", "[", "wcav", "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.6543202843512497`*^9, 3.6543203255543747`*^9}, { 3.6543217092731247`*^9, 3.6543218207106247`*^9}, {3.6543218932574997`*^9, 3.6543219820231247`*^9}, {3.6543220686637497`*^9, 3.6543220833824997`*^9}, { 3.6543221240074997`*^9, 3.6543221273668747`*^9}, {3.654345093796875*^9, 3.654345104328125*^9}}], Cell[BoxData["0.104030519019755`"], "Output", CellChangeTimes->{{3.6543220805856247`*^9, 3.6543220841793747`*^9}, 3.654340988671875*^9, 3.654344976125*^9, 3.65434513321875*^9, 3.654345613625*^9, 3.65434601184375*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{"Solve", "[", RowBox[{ RowBox[{"{", RowBox[{"equazione", ",", RowBox[{"wout", "\[Equal]", "wcav"}]}], "}"}], ",", RowBox[{"{", RowBox[{"d2", ",", "d3"}], "}"}]}], "]"}], " ", "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.6543202537731247`*^9, 3.6543202547418747`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"d2", "\[Rule]", "100.1578240660559`"}], ",", RowBox[{"d3", "\[Rule]", RowBox[{"-", "518.1474748711815`"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"d2", "\[Rule]", "88.95809032882285`"}], ",", RowBox[{"d3", "\[Rule]", RowBox[{"-", "66.36011143579412`"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"d2", "\[Rule]", "259.6066458538469`"}], ",", RowBox[{"d3", "\[Rule]", "280.16226363462937`"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"d2", "\[Rule]", "207.53448362625193`"}], ",", RowBox[{"d3", "\[Rule]", "300.1380024172323`"}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{{3.6543202490699997`*^9, 3.6543202755543747`*^9}, 3.6543203512106247`*^9, 3.6543220881168747`*^9, 3.65434098890625*^9, 3.654344976484375*^9, 3.654345133390625*^9, 3.654345613765625*^9, 3.654346011984375*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"\[IndentingNewLine]", StyleBox[ RowBox[{"(*", " ", RowBox[{ RowBox[{"Esempio", " ", "2", RowBox[{"b", ":", " ", RowBox[{ "si", " ", "trova", " ", "il", " ", "fuoco", " ", "finale", " ", RowBox[{"(", RowBox[{"posizione", " ", "e", " ", "waist"}], ")"}], " ", "al", " ", "variare", " ", "della", " ", "posizione", " ", "della", " ", "terza", " ", "lente"}]}]}], ",", " ", RowBox[{ "con", " ", "d2", " ", "variabile", " ", "tra", " ", "200", "mm", " ", "e", " ", "300", "mm", " ", RowBox[{"(", RowBox[{"ovvero", ",", " ", RowBox[{ "intorno", " ", "alla", " ", "posizione", " ", "suggerita", " ", "precedentemente", " ", "dalla", " ", "terza", " ", "soluzione"}]}], ")"}]}]}], " ", "*)"}], FontColor->RGBColor[0.6, 0.4, 0.2]], StyleBox["\[IndentingNewLine]", FontColor->RGBColor[0.6, 0.4, 0.2]], "\[IndentingNewLine]", RowBox[{ RowBox[{"xout", ":=", RowBox[{"d3", "/.", RowBox[{"Solve", "[", RowBox[{"equazione", ",", "d3"}], "]"}]}]}], "\[IndentingNewLine]", RowBox[{"wf", ":=", RowBox[{"wout", "/.", RowBox[{"{", RowBox[{"d3", "\[Rule]", "xout"}], "}"}]}]}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Plot", "[", RowBox[{ RowBox[{"(", RowBox[{"d0", "+", "d1", "+", "d2", "+", "xout"}], ")"}], ",", RowBox[{"{", RowBox[{"d2", ",", "200", ",", "300"}], "}"}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}], " ", "\[IndentingNewLine]", RowBox[{"Plot", "[", RowBox[{ RowBox[{"(", "wf", ")"}], ",", RowBox[{"{", RowBox[{"d2", ",", "200", ",", "300"}], "}"}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}], " "}]}]], "Input", CellChangeTimes->{ 3.6543226397574997`*^9, {3.654340839421875*^9, 3.654340962640625*^9}, { 3.654341044703125*^9, 3.654341059859375*^9}, {3.65434110209375*^9, 3.6543412370625*^9}}], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], LineBox[CompressedData[" 1:eJwV1Xk4ldsXB3BTcg0XXRQhIU0UuYW6sRpIkszTRWWI8xrPLkUd83HIpQwZ IkJCkllRkaQSiWQoKUMZ8pMQEspvnb/O83nO877v3vu71trrHb1NXbg4ODiE OTk42L9fZqacbVpokJFoKFUpehFKyv6zUHlFg+DGc2bGLyMhalN3oVIrDbbN 7ggSyokE5wx5Hrk2GjQyJw7Hh0eCtpjXv5KvaXBu+onrvHskrImqLlvVToPR A26xdItImF7m4Rd8Q4ODuiteiO+LhJe+xidXdNBg3YfQObttkRB8ckR4vpMG n+vfXrgsGAm23Ttcp7poEKsS+1P0VwT8fTSwdqybBmVpBpTFRASMaop7fnhH g9DRL5dq2iOgvuhEQ1cPDRR/7Dla8zQCrikWrm17T4Oln65latURYCxyoKn+ Aw0C39+vNMyKgHsjPhvzB2jgzWyRpHwjINb+YWDWIA1kWHe0Zd0jgHqzsiv1 Ew3CmqeU/zwZAbKPMpgxQzQQ3HCkMP5oBLCSXg6QLzT42uii0LMpAix1N13b O0WDT577pIOHWaD64PT3XdM0qFNp06z7yAJ+tUcGqt9p4L85V39tNwtqpS1/ ys/SoPLGR2vZRhYozYRZ8v2kwdaPy8s6t1kwm90n8oaDAppt5zpzXxZUBFhH DXCiZ56a23mxgFi/5p7kogA++2Wec2XBhNCTOcEVFNgqWB8fsmHBqF9ur94f FIQ2n+KJ1WFBr5Fn/n1RCrbsmr/wTIgFDQsLOtnyFBxnCa9PLA+H0M7T1SUK FAT0Ob86UhQO+0rGdzxSpOBfLq1xgVvhUOvycUOvEgVvXay68jLCoartsYDE VgocpeW2G0SFQ2FuZPdFdQpiTdUSpZzCIcFUwpt+kIKyjpWu66Xweet77z11 KXD/Xei7SiIcRh2s9Sk9ChL4jUv4VoWDtnvqeid9CqwYZzx5+MNhLEy2w9yQ gr2PCdFYYAJUKmlpmlPAs1v6Q9B7Jkys1uBedqKgX10r+1AWEw5/sEqODqNg LVf3mdsaTLDWV1LKYFLgp3eM2/hvJriVz1QUh1PQVfBu/IcqE1gX49rbIygI nt5babKFCQ07m4UkoylIH9ltryzDBJ1L2sybVyjoblFy9uNmwk6dDfTamxQw s5R197eHwfqsaYPJ5xQcccipjzoXBlKZib1LjRQoKJrGjJwJA7Hrml5/NFGg O/TaTY+EAW96YJz8Swq2/W7T5fcMg7EU/rfmbbi/rn37CxzDoCJW3qX6LQWW vztK9I3CQC/YNCj0CwXzQ+6bx5XCgDpeVi4m4A4qU/uf630IheZ5xnDlYXfQ 43iwWdYpFIyaM3Oux7iDV+W6x8mTIfDFr1WZt8Udhi775a5ICIEZOQVKRcAD /K7LPw7YFwLyXG070o084H579OnL08HgWhvx9GKMByS94nMJKQmG1vKUT7Wv PUDbZNXdZe9gyLvx6m6FmCdUjLmcGt4VDMlewuYbzTzB98JQZDhvMNwitxiD SZ6gueLUxuA7QfDGxMhbqssTYuID1dXtgmAdZfg1VcoL/re9oeKFQBD0Mrzl eu29IG+otK3rSSCUUukyqde84FBRsvQJViDkxynmZvZ7QWPBzivWhwPhXsLd eQU5b+jQWFW8TTwQNGI9OdwcvMFTIaRj+3AAvHsakDCT5Q17B7c/8b8XAAld KZO/+r0hsPJdbtLlANCMZY3nrfIBEc/1QRJuAeCww2yP2t8+cJ452NdyMABE 9m/45mfmA6bVn1c0KwWA2cSNUWdfH+j6styo+kcAyPNtOiSc6AP00/26CpMM 2HJdm0OqwgeC91m7db9jwJN2zuXGTh84Ir9KkLeBAaOnmxx3zfpAoVNgX30p AzJKdQT1V9NhUGfBfm0mA/rt7kut0aBD4S9fOWYcA2zDn4fpW9Lhb9ULKYNM BrgYhOyQ8aPDfi310e9+DFhigF5JMh22cD3JdPRmgKZyroJWCh34xx85/IP2 fS/AWY/OVs3SkEBPaHU/eHOVDhJPf2g1eTFgYM5T7UcaHa656gWro5/5pElr Z+L3vRaEBDwZEOs8N92cT4etTwu4XlEMUDQsvD5STQcjxQ+/s04xcL4xfnve p4PzRNG7UHSEtqH9DHpB9udLJ/SY6rgU50M6WLT2L21Al4grJ0nV0uGfaOeQ 2y4M+KfvdvTRejrw9V9Y88CZAebktn95Ex2GD6nbjDsygJlSYBb0HvejarWU eJwBHnl/Fi6h1YsyLgSize8SnvO9dLBvERB2RSt07K4884EOn4ke0UTXCzdL UH10UNRs2tzrwIBl1v/emX+ig4HpWZuN6PO+yie2/I8OV/ZMZby0Y4AjM7Yq D+1zmDftHtogYUZkwzgdauFRQTZasvTh43Vf8fvLgiv80VXjhgri3+gwF5Kf o4SedfIcXp6mw5ITLTr8Xwb4mBZ5dC7QYZRcHTSxZUDTX5st7RfpUPdL48Fe tGLnDZ0h9M3NtgWb0W+trq6aXaJD7HPxl5xosGdWiS3ToWv9gHS5DQOE3Wx5 zLkJbNUM/yaJLgrgvdYuQICI7tSYt2IAn05IuK0gAUbdYNcw2pFjyWsQ3d7v H92Jlgib2jctRCA2xkSrHB0Y2TsiKkIgP0b+qjfaKKFM3USMQJPdds9xSwZ8 zXdobpUmwGVsrzdnwYDfQZ5FRjIEnnlNxI+i/7RixLWgJc+snu5Bb1uRatUs S8DWTn70EdrrZOenZ3IEnDkqyqLQk5KGSzWKBPyfRtcqoKejtFQKlQnIXfNP djJnAJejvshWFQJVV8a2W6NXaVl9v4W2uRnYY4jeMXKmOm8bAb27nKd2oU8f KNG9oUqg7YSwJT96ZlHJIfVvAq8MtiRXmjFgzkPscuQ/BNKq05iS6MWYmO88 ewlYSoVGiqA5inmtQ9Dnjan0lWj+qXm589oEZLaoL8yaMkDW90OZOxDg0z4S 9AatF5DbZXSQwD6+moo49JGMdXua0RKHdz+/iDZ+lHL9kC6BEt/wsRC0Led/ bqBHQLXSz4mgvcK9F9T0CYRO+smao5NjNGXFDQkobxa7K4W+VlQaGofmnfv2 5i90duuWEaGjBE6lnuISQheKypTwGhGwe7w6btmEAXWJnPvnjxGIX6vmO4Qe TW9yeW9GwE03yKIC/bX2QJOVOQHNoEsXitDTfQ+3daANjvKW5aOX1hf/eGmB 61FTME5Hi+QmXKy1wuclHhhHoDWL7O5k/Uvgv1d3Tjigi0PGszfZEeBxC1aw QStZMFKK0Q95aD/N0OJLaWE19gSGMz0+HmZ/7/B7m3fHMR/htuhdaErG/diJ E5if69CIGnpgcuHgCFo6dspCBd2WLKU6e5KAy+uPlCL6zpANr6gznkdx5rm/ 0IrVXxaT0SFKHJQw+lq0/5SsC4EdoRreAugo9au9yqcIdIXJlnGj3ULelum7 EVDa4yg5a8yAPnO3/FZ0vZV49hTactN8uiUNz7M4ZO8EWrd19UVnioBI69nC EbS8jNXxYA8CM3pu1Hv01clh85WeBCYKzke+RYs0nDW4hJ75tLG6E71MJe28 5kVgtvKAaRv6rLbSVgVvAlOPC+63oCdE78oVoOcj03c2o3urOgWqfAhEaq12 eoY2i3bh1KFj/2QkiTegm47Pzj1FV1XE9zxGV/OKD74hWI/zU2k16CRz86pv ZzDfdZ8XK9FCmz7fOetLoPxY/74KNHPx9I1faBHjPall6NPZCZcEzhHoHfwd Uowe81VgxqNl/jghWoR2PFzuL+mH80JJtLwQbTzZ7rzRH+vlgrlKAbrxiaNt EXrqaN+KW2id5OljO88TaDl2ezIPfZcK1X2INntd8TUXvU171Z4DFwgsKswv 3UTfFM1WbULvTqXLsi09pKZkwiBwMULGNAd9perx2rdoB5hPvoEWiDYRPR6A /SP1+1s2WtPXl+MDesLhuhPbpxyufrMNJDBtKTiShU44VPPxLZqLf/95tutU B1osgwjcDt4rw/aE5IqaDrRmw2JrJnot9+ZC02ACFR/949nWHzdMa0N/6alw Zvtsp0+UUQj2X8MtPbZzaq/4v0SfybPQZPt1XpWbQSgBsbhKLbZ/x/ZaNaLl Lj8zYFv5PMchvTCcDyXh7mzbOinuakBrc0+msR1hqL9hP5NAZgpXL9sVOz3E 6tA/g+9vZa93UDaWWzucQGuL2H9si/BVTD9Au8T9ucD23qnuAS0WgaKPOX7s 86B6FtvuoT1edPCyzy/lybq6nRGY/6m0HLafFR4oLke/fjFrwj7v74muGWqR BDL4B/5k52HkVsxQuYj9Eehwj50fw+SN+210wcBYNjvfW7t/2G6OIlAWvJSe j+YR0tHa8B8B054b9ez62DHnuOkG2qRJffw2+ngfa/X6aAI6J/duuIO+X/pq VjqGwN250qfs+htNnf6cig5UXa1SihZnSnSsuUQgJ2LsBrtefSwdysQu43wS bHvEru8MndCsePT+C73O99DNm3JjRWJxvxePSFajlRa/egnGEVgQ0it5iDb/ LOoQhd7U3Bxfiw5p2XmULx7XW5nPrGP33/WArTwJmE+uXRK73+IPCo0uXsH9 adjT2f1ap6LW7Z+I/ycZvmpFf5WwePYD/dOBsbudXS9fruV8TyLA6o2Dbnb+ Mcon/5dCwNBZl3uQnUf3kZ6ea3hffLY6sYCuWdPj5ZqO622I+us3O09bN+4Z tGY86x0nzqu7vUxloesEjpx5kf4HmmuwJlAni4D3b+GVUujU8e0KOTcxH+F9 Ntrs+a5Se081l8Dbh+oaB9DgbWhYg45pKt2ojx6ecvPtysP7/AWAKXrHj6zn fAUEUvt1jrmimznFPDyL2PcPGbiClj2QzbGArm80G05FE6ZqIquYQLIB81cm es3Ko7XXS/B9P+sd76CdBVki7WUEOByN+J6z7xOJ+Ypd93CeJ/778Bf6mDXr 8BO0C7/HZx72fXZV7OOxKgIHxy/LCqL1pdVW0qpxnv3D/YJ9/11ZT9mkPSBQ t11tThM94jj/deNDAh1KZ4sAvTuHFVqBVlIr9dNH9yvduN1Sg/N3aGG/NVrd TQ1sawms0+M6cALNuvWoYxg9rjhl7oZ+N3aUdvoRztO+J34+aGXl3l/L6PaO s0V+6P8DtWXAZw== "]], LineBox[CompressedData[" 1:eJwV13c8VW8YAHCkUhQhKykjqSQ7KTxKoiRJSFGK4hzrHumXspIR914j2dFQ ShEJ2UppkJTsUZKQVTLKiN9z/vL5fo57znmf9b5H+qS7uSMXBwdHDScHB/33 x/iow5FaZzB7YH/QUz0McnKZhze/d4YzCV1KR86HQbhCc6Z8nTP0mW4ybk0N A4dUGe61H5zhlPSmwOiSMNAVdjsq/tEZPI4myzt9CgOx8KJcwXpncCtK8t/U Hwa/57mX8n1yhtzN9VdeTIfBOy8z+4UNzpDK3mRXyBsOAfZ9/H8bncFyca3c vw3hYNOsema0yRkkvRtG87eGg/p+v/KBZmdQOCwWlWUQDv1aK107W52Bu9ex tfhYOFQ+OvGyqc0ZbCYSLk6cCYfrcpmrPrQ7g0GsnW4JFQ5mAruqKzudobzL skcoNBye9nmsv//VGbyvqpu2PwyHKNtSv1vdzvBo+Xzb8bxwID4tbkr6hs8L +kfeLw0HqYrUIPZ3Z2DIT1peexcOIXHvvlI/nCHuV/z5TQPhcIJPbJvLgDOY Jl+MXD8aDtqBp6IcB/H3ldr+//6Ew4jrtK71sDMUWg936ixkguVuhes6o85g +/WFo7YUE5RLPMc0fzvDzuJBRWU5JixVqdirPOYMbcpL2pZuZEK5pOWUzIQz 7GrZWk9pMEF+/LIlz5QzrC7VClu3jwkTt78IfOIgoGt58e8nFBPyfK3Dv3IS 8GzXlqDC/5hAWX9c8IuLAKpnvjPDhwkjy15M8i0kYGhB9dLDIUzoP5/eYbiE gNg4y6a2BCZ0mLreL15BwIdMyoqjhAlJG3ql3woSEBUwdGBRBROOcB9PbhYi oJXv+7H5SiY0FZlFjK8kwNloorqmmgkf5NTPKkkQcHrZC4HGVia8nJ7Wuy1D wLEvxNH2CSYENnoW5cgSYD7wsU1pign6OUOqFXIEmLYu/3p+Ftfr+HldhzwB 8vb160e5WFD44TmvyCYCVu3s7j3Hz4LM9CvNYWoE8LQdlZqUZ0GMuYg7w4CA 56d0iqPMWFBu/bTddTcB2zWeBtSYs6DfztqIMCSgfrHhOs7DLNAlk6RPGRHg YpBiaHuEBQOXpRosTAgYPjnMbLNnAeTLb9OyIOCcT5/ZBIMFZMnru+qHCXA0 q8/s8WRB3HMnQRVLjLeu97M6LxYM1T4Y3GBNwH5BSifRmwXxvUqpq44RkD98 5810AAtGRLcumD9FQPKImwNnJAvEpVrcZxwIIPmSTR9HscBAzrvjjyMB/i7S cbZXWZCkXJL/6wwBDaK69g9jWbDbWM+pmyTgc+7RDsnrLLh+YU9tlScBLYIF aXb3WWDcaRXPuozx5biVGV3OAmsjefnUIAJu5z8X+lvBAqcn43nZwQRYt/sZ H33OgpCw6Pr6UALaSHtdsZcseKlRs0ycRcCW9ydEXd+yQC9CN+juNcxf6eWQ K59YYDrFJ/Q0loDq8fjVFQ0ssHNov/UmjgDhCsmfvxtZ4KN9vmIwgYBPW6OO mLewoLj38bRKCgGSR8t+/epggYbeOkb5XQLuX3gulPsd1/tgbL4unYC5jtn5 8l4WWKysjPh6j4Ae7S3+b/tYQA3aZXI/ICCV22Nv8w8W5MQn9O19RMB7Rb6U pmEWbPrFa9dcgOuP+LHPaYIF0rd+7/31moD+Vd9FJ7nYIHEztmP2DV4PqLxQ vIANwje03JZUYzyD9Jb6crNhUYpftMw7vC6ZVDq7kA0DCUtbLD4QYPgwpqaX hw15UTKORS0EiL4Zs3NazoasyKrJqlZcv06iwAp+NqRHOF2pb8P3+WUnXYhO YD16ONhBQKbVMMm5gg2+V7R/r/5KQI2f4ESAEBsMA8z9A38QMFZA7dQUY4Oe /4RA5AABcZrVGq/QWn4Jt5MHCeAzGnpiIc6GjT6fq/KGCfjN8dDGVYIN/OcJ vr5RAiokU+LZkmxocQ9M3DdNwJuGkwPMtWz46LZuk/UM1psy89FCaTZUu74p dZjF9RoxZf3QpeTyLt85Apb3/lAgZdhw60ySfA4XCWnl3J815NhAHM99IsxL gjDpVB25ng0fwny1+PlIUM4tqx1Ba+QZlS1ZRsIZ71PVJgps4Fjy5dXcchL4 tcbyF25gQ1wub1u/IAmfK15cIjeyoXKhI0eZBAkHq37q8Wxmg4KycvDTVSQk jEtFWaHZNjNLciVJ6PpwZ/Qu2jo7WuieFAmK/EdG9JTYMGJdLh8tQ8KRm1YT Tlswn5mi+x03kmBxx9Y5SoUNAU3dH49vIuEDQ83zI/o7xyNLG0USBr60pa1Q ZUPOYYMTB5RI2L8pyy8SbTjv4blNlQT5GhOdS2psyNyw46+aGgnv7TNvlqBX WCz2VVInwWDvC/UJdMf9lBBZTRJYtt1jjupsoMyrE5dpk5C3h/unjgbG3ydW imc7CfOR+6YYaJ17J9K4dpBweFWWzl00z+xk5h8dErqj9nkv0WRD6l3ZZ1/1 SQja4Nj+Bl3z16c335iEkckrIKfFBpErXuyqvSSoqte8O4A+Ieqm3rgP11vy LegCelzjeOD4fhLYz+p9a9GSnvpSauYY38zXBc7b2HCaS7tq5yF8nu9gVQQ6 J1rVxdyChNMx0rxP0AY5ssUMSxIm/xbumEK7DC+0zLEhoSGh1s5Hmw0FPnOz FUdJUEisgWQ0B9+ftLpjJES6RZwsQl/b2D86YkdCscRKYgxdeqaavfkUCa2l iRl227Gf/lSq6ziQoP1O78F/aLOQknYTRxKM5jrGItE9dzI3uJwhITWfcboc zdcdUfWAJMGyrK5PcAcbLBmhLsUuJLScWnxAHn2TI0Co2hXr6dqvxdvQ6msY 9j/cSRD7Juh5DO33yJlnyoOE6IOO613Rb3ROZvNQmL/xZBVf9LFjh/6tP0uC VUHjvmR0+uC+O1u9SFh6rcc2A/3rgsG+PedIuLzh59sCdFCiRuLp8yT89372 SR36vYISnPMm4dp/c2rtaLFC+b7gC5hfwakVveisJlGNuz4keBS+HJxC/3UU 6MjzJeHs7dAfXDps2DnBc/mlHwmf9Ncb86JZQZwbG/xJmL6TwCuEbhKa/vAt gITX5nUqEui1ab//G7tEwtX9ZaVr0YTqoNSCyySoiRzKkkfnPf9WJRhEgki2 P7cies6sw0UmmATBG8ovlNFGXQ1CqiEknBs/OKCOvupeW6wfSkLHnvcXtNAd c1X2B6+QsLYiwms7Wj6inMc+jAQ5gYvtOmiP1U+zPcJJyL3snaWHLs7Mtgxg kmD4120I0Nw77v+LZOH79ugm6qNNa27eucHGeBytyaPNHfJcNyUC/99JyYR2 CXS3JEVife9hnKZ/T81weSZEkdD70Iibvr9CgeyyuGgSbuo6ydPP/+xhcC/m Kgk77wbWaqNjNznqR8fgei4ZT29Fm/QGt0dcI8HE0zWLXh/XrXQvViwJQxKp ffT6C4++5g+Pw/6SCM+g4+Mu0p8RGk/CL9EvY+vp9X7kMQhOICGg3Pi1DB0P 5obPgYkkvHrmJbeajpfh3vMBSSRA2zI+UTqenKSgXzLG+2OJnwA6/1ymoXcK Cc8fzSym8+uiUtt1LhXny+mONdOYf5mh4Qtnb+D6bnhUjaIj7Ldku9/C588b ln5BG0iaGbveJqEy4sPyJvRMk8c3Io2E257XR2vQTia5oqfvYr1KBhB0PUot /vT4VDoJlFAL50N04/Oxffb3ML7VvzfdQO/cqhFwLIOE2c192iFoSZnCfvMs Esxt2ywOoOs7WgLNHmG/L7eNAXRY/JSkaTbO2+veziroSb7tB40fk6DU3P55 BbruT1mRXj4JJanxc7XYnyG5nw/pFGC9ftdfWore4To/rP2UhMzx9bkZ6Pvd IKNZRELF5h8tl9GBtS/CFctIqO/pilZDa13pkdtYjv1awx8phf65c2HF+goS Fo3+UFyCPlZoOCbznAQJ07cmnThPNNPeHhWvIuGbmqLiJfSP83WKi2qxH/S7 Pz/FeRX++uXbOXROanBWCnqjSPHpP+9J0NgfqnAZTTy5c7P/A84/m6B1+9ED w97CNQ1Y311HjDpxXg6dlJuN7MD3t5CMH9mK+4uJd434EAnVjs/OtOC8jkh2 cxIcxucPfk7NQysNnFrIO4LzmF8jKgrtHmqqN/sT53GuVNoe9K/nsk8+j5Hw N77/Wi7uD6Oa75PSZkgoNyubu4j7x/haWWIzrwtoStkEf1Fmg3fD7g3b+Vyg rKh2QQ56LtSp32iZC0QMcekGoBf/zDrtwO8Cwrdd+tagJcq0TiULucAVU02J Y7j/wRHTY0skXeB+1hXbN7hfMqO9Tb8rusBndfPNnrjfynB9UE0xdQGtrKF6 eVk2CH2V+J5wwAX25XozhnG/537mGH/NzAXPW2t+PEH3+s7MMM1dQPlwkQOg H0zJV12wdAGFuFXXrPC8oDbqa2Vth/c/899S/zVYv12bfITcXEDCT+Lfk1Vs OFMeWhXGdoEWccuDlXi+qXuS8K38owvkHI9tM+Fkw7209wV5wq5wNevEToUR PA+78VusP+QK017Sfr3tLMigMny641xBv/SWh8AbFnw6aOou0eQKUYEXJ6vz WbCGMBlOknCD5dn+rj63WdDh4762w9YN9o5766vgefkxkbI66bobXCqWlq73 Z8H9aLn0m11uYJGV+LDPjQVPYwr+yq51B8kyZuev4yzYGuXK4WTnDt3pWrOC +D3QWuUbM37LHQobVYtHd+H3Q1PCr39d7iCh6aWXupUFWlEhQ/cEPaCoIzVD eROed1UPbVdR9wDP7+LjA2tYILBz3c/zhzygfPfm6K0iLDg0ktbv4OUB1k86 RKL4WCDDo7CHP9YDnr1qDrTiZsHGG7ocEnke0OH6MZ7jHxNe1HPOv2n0wHz5 JX3E76F+z+qTmhMeoJGvLf/pJxNSH+vxGYkyYDAv85zgABO6jhVLiG1lQKbj Pb4T35lgE/z6spElAwbuXNS2/8oEN5fApjq00D4plYPowEM6G6ysGHCt77Gq Pvqh9JP3jtYM+LXgrqU0erYsVfyyDQN8msKku7uYkDLplV1mx4Dd3a+eO6K7 zsi1q55hwDPXrjVeX5jguPeS6urzDJg1qhx90onfq3s++CWjO5fdv3APPb1r TY24N97fP58vGR2hU3ZK5AIDvnzTNwlEFypPXeP3YcDI7JTWQfRSUcYfzgAG JIXlvv7VwYScbydKe0MZ4L8mPUcTPesDhjnxDFgupeDQ2cYELcV02W0JDBi1 KDxYj/Zq5+WsRHdsv238Gj2yrbnkUyIDQnb7WD9Gf510VfmTzACnUPHfwehX HsmSujcZsCfoopAKOsph8nfNfQZsKpznisTv03dCxz5YZDBgUdRFrWD0khfP szrRlf0S5y+iA6XZTj8fYLxPl610Qnt9lv0smMWA2IyT1fpoG+uDb488xvhl PxX908IEOZPMG31FDHic+k3TuYX+3veZcy1mAN/5g40n0KG6JrbjaNN3B32t 0QPKQxKcpQwQzVgwsAeds1IxTqKcAYcSOTTXo3d8ecjaX8kAXVgQ39fMBAvq ofeTavw9hxXljg4hL7Zsq8F47xACJ/RTh31bn6EFApRF7dESVoPj794xQGEm 9Ks5umv7Jo/e9wx4Penfq4l2WfjwtPgnBqyw0c3hQAclPDjk386AoVuHtJKb 8Pq95Zmz6ICVJXGxaIsCivtCB66vQPpfJFq2QTv/bCcD8m71fQ1CV/LXiBBf sF651Hnd0fMhg60W3xhw8nV5uwH6gpfiiY2DDLA0l3OZbGTCyaCownvotWpi b0bRe2PGBdYNMaAutmfTMFr8cenzNcMMUBXl4u1BFw6ZyK78yYATUUrr69ET p1x7538z4JzszqZstIf5I5fGaQYkmCxYzEBXC22wtJ3B/Oj18Lmi5RrT9L6j l3R+XOWMbrFKFJyYxXhL1lrYo8E2qFB4ngHib8XVzNH8TjbcFgsoaL5VdkMD 7bShcbgdvV+wQEMVXTlwoPkUNwVbLNIalNDnXHc/8FxIwTE7y80K6M+UslnM YgqmxCaMV6Ef+S66Xs9LweyRaqUFaB69S8E2fBQMBtod4qDjwTHr1o3e0l0X 8K+BCSKXR/V/L6PAz9Fg8g/a70pH3woBCsy99+0bRrcYW31MpL3/ZsEAWpW3 vlh6BQVRt15t7Ef3sl+zVQQpsBq/tPkb2jQmV+2gMAXDnuHXW9H3LTavbkUP nd9p2ozmErm/yH4lBdlWz3ga0QUJKa0eIhT0fFqc8AEtlXrFP0qMgkCllDVv 0MP37WrqJCl4djblYyF6zt/1kelqCgaMMxWfopdb+UTXojvCTSLz0UoLk6xq pCjgSdtB5qLd7Bu/vVpLgeLFYt9Men1aPa92S1PAN6u28iE6gn8s4yXaOkYj LwOdXSbgUSlDwV/bdzz30L/ETWbL5CgIaF/PdxvNMWrzZcc6Chghz7/cRAu8 ca4sQW+fay2+gVY+F3qlSJ4C4SeBoSlo2B9Haq2nYOKGgPd1tJncXdOnaIsi MSoZzaivFM5XoGDbp6sXEtGBGR//qG2ggDeYKzwBfTWgqy0XPV7VdzMenas0 dzNnIwV3jyz/Hov+Hb5tc6YiBRtiHr66Ssf3pJHAps0UcIfeW0FbcJvVWAZ6 upnfIZrOX9/ZontKFBTOrF0Thd5Zfvm6/BYKtIJeh0aizWOv+t9F6zY2/olA e+7K2Z2mTMEh3XUjbHSQRIWCjAoFkcscztK+NlrLewudI7SIi/adNx0ja1Qx X4pL41novBuDH1PRc+ruarRfnpvOW61GwUce9WYmumH/koTr6MYgq0DaPXJi F1ep4/XgFnXa4zPydkno8v78kXA09ycNfXENCirCR7JpCz8wkEtAbzS+dJ62 3KVDi0U1KQjhdDWirW59ciAWHRSds4a2wRZGrfBWChY2750LQ1ssCsiJQYvn aPfQduiMiBHUooBrxu8jba+8lHPR6M1xIq9ohzAzjwhso0DzBEcl7biTJTsi 0YNbt1fRTt9WvWa5NgUGs1V1tAsEWrnYaBfWja+0X/X1fefdTkHp61fTtJvK J9+Eo0vY2qvo9+uNXZi5ZAcFq8undtKedBGOvIJ+o7WAoj3DZo9x6+D9AlXv 0ebIXmR9Ca281/4b7YUf/Ev/oeUuRcjT8Vs6+nftBV0KgsWKPGjzC1LBk+gi zq7ntIXVBn9QehSYKnFJ0PmR8urMxa8DeCmm/oW2bJylaD86pVjfhM6vwtO6 iw76FNSdMXxGW3XquYHtTgqWPlIuo+tlq8T2jFa0k6KwIV1PO7bnLbPcRUFl wEAjbUPf9CZTAwpG/yOX0vW4L3XN9ho0xSmcTdusIuHGnt0U7FJ6aEPXrw0n 0wkMKRDSv/UqBn1chru2lDb/XMg1Ol+7fFW27aGAMNttSveDW7D7tIoRBfNz EaNxdP2m99s9Qiccjqyl++f8a/sXG40p2PHbK4fur8AlFizZvRSo1o+GJ6Hj 2VpSK00oWLwo9Goq+vqjx4HR6DmH63fp/r5dt7Fv2X4K3J9GVtD9n7lidc4i UwrSBfh40tDPYjl3/j1AAUeM7iA9P6oKLqSfNaNgK1Neg54v1c1jS0fRvFt6 gh/Q9S/e++nHQexH647tWej+lGrH9kOYf+u0KXp+DZfvqraywPlYt+pCHt3v X0qVGtD8BfacBehZ6ew/7w5TIJZ7UK6InkfpMWHlVhSszb1bUoHWenQs69ZR Cu6ka215T8+3S0O3FY7h/Ua2GdLzVv6wT0I2WqJwg2M9euVs8uUyW9x/rtcV N9HPM24/0nqcgrgTAlVf0Fnfjyxa4UCBg56BxRjdb0U/ZuLREqZXf0zQ8WJ5 j0o5UlCsVhzyFx2ultiheBrr0/5qC73fOF1qyTVywv3qOLTx4H4ks9rqeIAL BQ2Xz1qsRSf+6rVY7ErBdddXp2XRAi/P7Y1Ah5V3Bsij54k4jetueP9LVu8U 0R2FjbyFHhiP5RbPtqHjLCwKf57F+cphueowmpd1cMVxXwqubci+Fo3W8vLi 6ESnc49ZxaJP2yX+tPHD+lVskU5EP1P+Wmvpj/PGMvDtTXq/bfQIN71EgVnv NqccdLdU1ALdYArc6iy6P6CLH7+fkGRTsDxjW6UInj/6k373JKFDuvKtVqFX Bok0iEVQcNLtydgatIelXa5wJPZPopLeBrT8zLAbXzTmL2qJ3A70VYNl/TPX cL4zveROoYnmfW1t1ykwnN07lY8uE2tzO5OC+bQZ+leCFrBxWjCO9nl/aWkl uqAjSHHZDQoUYi9vf4/m6i7z07uF9c9VNtuLThraInvnLgWpFu3T4ngeq+EU dnF9hPOhheoIRkvtus0xjTb24+hkoakg5diQbPz/DKvvMWixxfvLb+RQ0HvA dtlttANfiEB9LgUrpW8Vl6NnRf7maT6l4HTr9ytT6APWIcYv0KYlbgs58bx5 O1H484FCXM/2zDAetJGkymLnIgp29uhliKKvSRNHkktw/4y6a6CJ7jv5d3h9 Ke6/ItlzOmjtOyGBeWiRLyef7UZ3yac9rC2j4MqylzaH0WpOKmBTTsGJL25q tuiQjIqGXrRdTbmQI7p1YL+zZwX2x5XcGRe0omLHv3l00DujwbPo/wEzKYyE "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{205., 460.}, PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]], "Output", CellChangeTimes->{{3.6543226431481247`*^9, 3.6543226566168747`*^9}, 3.654340994671875*^9, {3.654341047921875*^9, 3.654341066125*^9}, 3.65434125271875*^9, 3.654344986390625*^9, 3.654345143234375*^9, 3.65434562359375*^9, 3.654346021765625*^9}], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], LineBox[CompressedData[" 1:eJwV0Hs41IkaB3DUJktL5UiTMIjawyZb6NT2vnu2taMiRW6hRMvvx5iZn6Pj WFTGmeSSOo7YWZLLFruSWrlfKtNZ21AkM4yZcimX2dzH5efUsXP+eJ/3+Tzf P77P82We4Rw/q6WhoRGuvv//cdVMqF8HgWtD2wi6tgcq76edsHtGIM2MfFNh LYHU7dJy6+cEcmIYwaJvJRB6w2K1eSeBN3d89ygtRwIHDKNObu4i0HcD07b6 oQSMU+vub3hBoJ2u8IrxWwnMrqz+WK+bwBidjsOma6TQHuMR/NFLApm0IjDP SgoXgkf1l3oITF5gz78/KQV/qUPYjITA/deUTH6MFHa7JTYrpQSKM3SThjKk MOb8J7aij0CLK6N1ogYpPK44LZLICNSuC9S62CWFPKvyLZ39BAbUOW3OGJGC h8FXTx8rCHQ+xTnX+0kv1IxybUoHCayLTazK9euFq4GNiYVDBDb6bF3HiugF sltbIhwmMG8qzbAgvhdMW24kZ7wl0Huk+Jn/jV4QXG8fpMbVe3X+9PLyq17w /np73hczBP7Nxazstlcf2DdEzznOEiiStzmWnOmDj3e1HLKfI9CnPD03jtsH zSbetMU8gUTRQkt9Wh9Yq/jea2kCC7z8ze487IP5otcG3RokzvvVW7lsk0FV gm/qoCaJVaGLp3kOMqB8u1ZNa5Fow4KbSSCDyXWtC3ofkSjaOe7q7yeDsdhb chcdEqcmH+yeTZOB3J1dWr+eRLK9lnF4Qgai5WUosiCx0fbu0YfF/ZB13IjD O6jOvSBRNSmHZt+afvbXJO7RD242WZLDWJAvi3QhMX92ZuKApgIORAiZISwS le9W2LyNClDyTV96HSFRKls2ueakAHxgvdfZi0S9RdExcaICJjc5rVoJIfF0 qbf2DzqvwFXhk5POJ/GbUCNe4MbXwCycPTT9K4no8tpIen0AyFP3fzHUjUD9 /SrX9ZmDIF6KH3ngGoHdFoGHM9lD4C6+WVKQEYF7f2TYmfkOw3jsc9s1HREo ShV/nv/ZG1CZW5J2upFoV2+v+ezDG7DQ6nTId4/EAbKserX8LYQ1X3pyOSMS 776xHUwqG4Hnv+QON3dFYjp/98EawSjcLn5WXWXIxkqzGYPyoDHIidL3svFk o66gdfwLm3Eoo8rih66z8QnnsmiDhhK6j7lzGBI29pyL8pj+TQlm5JEJISMK fTR/dttf8jvI4znm8sAoLHcIoh3j3sE9Mn+rMC8Ks31dLIVfTkDpNatbNwfU +fdJdPbmSajJql6yNOdgDXt435bhSXC6ytYID+JgZ4NWW1bpFPQ9SchSFXLw UntSdSBMQ5Ykd/rDAAf5f7/26GDxNDhfFby7vYGLe3LsjVL0ZyDIwXPfrt1c 9PyOT3b+YwYM/rptKtaTiww2a2JWPgOek8VjoTFc5IfvmDzHmgWLtdu/0c9W 5+uUJ6Tls/BpwQENRhUXQ2TKsC/156D1heZKWw8XdzjbhRjEzcFY9NMzjvNc lJ8PHm9UzMGNe6DH2sTD7ebXWZ2uKhgIqGcYO/HQKTj80KMKFfj/81c+y5uH MU1pKU3r5+HsoYsOW2N5KHQOqbVImIf38ehSmcPD/m7RrdDBebA6Ul4wWsdD cal8xMB9AZJzf/I838/D3010PvutdgG4xysie5Z5OOmo958Ak0WYKA0SPzeh 8FJC1qcBKYuwEGmYmbKfQio+dZXjxCI4VwTcKTxJoeIicyfDYwl004+tP5VA YbKgKzCiYQlI6WGZLI/CSvKeZ7YZDU3GsqiwfArbN20r9GLSYOAfvkqltudT namNljRUy5Nt1xVQ2Gxsnf4vaxq0hpoSoZBCY48ycaYdDcJ3Oy1LfqRwU2vX qdR9NIg1DSPZFRR+YhomP+9Dg+lXRRrLaqN4zAn8aKCS7bMFdyk8zZJl/c+f BmNtt+aCSgodUvXcEoJoCNUTGLy4T2Eu444o7iwN742WqhxrKJzu7GmLiabh qK/AtVVtN8XRP++JoaHoe8NXR2spFG7Ze0V1jgaWyS5too7CW2v8TkTH0fBv Jun3QwOFJRc6xrgXaRg9szRh00ihn/ZDd3s+DX8pESRVqR3NZT6YSqZhwLr4 544m9Z6P7flRKTR8Hr4L/ZvVfTmvlHapNAjKWl6OqF1o/d/jE2k09CndiOgW CulvBQ3lGTTY2so/rKid63bBKjKThj8AP0Qt6A== "]], LineBox[CompressedData[" 1:eJwV0Hk81fkeBnBLi6KL7iEjxMHRSM2hheY2fT7tKEsqRLLE5ffFcc7Pq6s7 l0q2RNKlUJa0iGrEz4mEcxImu7MhS6W6M5bbKkpGGfPH83pe7z+efx6TgAi3 IBUlJaV/z+WvHp34EHiwg8LtCR4jLqe6oYxJObC6k8K7ESS+eVk3nFnZe4fT RWHKxHI3wYACAvPZ84wlFLo6rJSGlCpgM4vn/Z10bj/a3f/1tAL0zlQzS2UU PnXmx3qHKGB8dt5iDTmFya9G/XV3K6D9qKv/fAWFoSumYg9yFXDSf1hzqptC 89kj6jFKCvDqtQn+0EOh8fyojuoxOaxzOi4a66XQgC16Z9gjhxE7nfCnfRRG vy2Marwrh0elfo09/RTmXN0Q1pEnh1yzO8slAxQucikyT0qVg6vWttZHTynk 65mzW0LlUDXMtyh+QaEK73mUJVcO6T61xwtfUlj5Rnt8O1sORL6w59IrCn2z Yl3us+RgJM6PP/sbhUkBQlbGtAwSL7a/oEcpHJW4Pc9qkYH7jpW5P32gML3P Vj4jkAG3JvLjhnEKg3/0t5AHy2CxtdiR+5HCXZYrbCU+MhAZuH9hT1K49cCa QjtHGXAm4tzVvlBY4B6ln28mg8mrz7XkSgSpsszormdSEMZ4nnmhTJD3m2ab vFsKtKdU9b0KQZOAztrxdim8XdLwSWM+wZjPPsExNVIYOVY0uHMRQbdvySPl OVIYdA4vfqBN0PWTg1jLSwqN09NwlU2wVtnMJWFYAqe6I6vLTAkWKtcXKYYk sKXstY3YjOCD7fNjuf0SEAU9Mx/kENxcwlZodEjgvqReXXcVwY3OnR/2Vkjg TtHp3uS1BJ2qnXpexkogw003QrCdYL/l8hpVztzes2ogfAfB8daUyRFjCYwc 9rQnOwm++5vfY8VyCWwOvWRyxJ5g9FHVZ2JtCYzFGSn27yHYbGPs2vBHF+A9 zka7/QSnDdNHEku74O0yW9XZIwSze4+qGBl0gcNTj6zUOILDce5iraWd4GnP 4eTHE8yaV+qStagTQiomhHcTCHYoLipzlDshMfm8TJZEMEGoHev9vgMa17ct +S6V4K01at/MujoA0jbH38gkOLlTc6NpWgesB3OB6AbBM74lEQHaHWBSOO74 /vHcn5f/K7aybAf9KxcGZ5oJ9jZZl4SZtgOrwI63qJWgzOI6KTdohwV5x8+z 2wmmzr474KDZDmPZi5/slxAcdDT+Uj7RBsJ0dlD1E4J+M2aL/R62wc6TbidO jRIMkXq3zHq1AfFlKljqoUgHzYSq5rZC21T07/ccQrG0P6mlzqsFnNuuXC84 G4r/2tKi42TRDKPHuqwWdITiySTbgRzOY5gwNiWr1cOwZptUorf1V2CrSGzy nMNQi7odqvBtgmBRUlPy2TBk5XIZ1fxG6KrIfiWShmF8/3yP7wcb4Oa1zkoh KxwHVO8FrLJqgCye5n6LfeH4RHST45jxCErokuiXF8MxZdM5Nf+pepDvdY7Q 7wlHNcc/Vn/m18MKsufNJX0ecn82+M/G4YcwGB1hPOjDwwyt21UbQh5COckz vJTLw+gPqV2t78VQfN6s6MoQD5N2PezMURdDVUbllKlxBJ76nOCpsUUEtunh SiGHIzBrxxpf9/g66GuKyZgojMBA+vbarvpayOjJfv91KAKfnA18xNapBbv0 xNc3l/KxcamC+zagBg7b7PuH9To+Eonp/31rH4DWVvN3x/bx8cSk5u1Ziwew 7+21kcCjfNyU56/7Q1o1sNVW7tK8wEe1W0vK5fOqwbJgs5K+kI/hC5Ldrsfd hwaZ8mxzNx/rz6lHrv9aBSORrQEbJvl4OfKCR198FeSXg4b9MgG6+tr7pC+s gqFDD/T1bAVoE+hhuCqrErwSHsfZuwvQ7zLPedHqSghyjLUxPCZA46YR1fWi ezATjTvLsgS45+jfXTK97oHZnjsFw9UCjDZad+jMuBDis2/tOzEgwDzhm0yL dCHw3UrDuqcFyI6yMEmzFcKb4sNtXQY09jV0G//aXwGfwljnTm+icaWwyVI3 qQLsSg/9Uug9Z/GyX4ptK0A9da+2bwyNTjE/+e/4HwOkd3d/fy6NYdy0uo/Z DNTp9fOC82g0LBNUFWcxoOUVojoxZ/rYguc+FxmoHIy3WlJAo9Zqo6rmDAZU XtYdh0IafcTfkq+kMXDp9Q+m12/QuKV1L+MZz0CbMissvJTGu5bc9rEIBoy2 XVWannO+6/fkBo8BOp57IfEujV4Tt9b5hTOgt9BJVFBGo3iHqUsPYSBQI1FL xtBonTKa3RjEwIzulHBDFY2++UNRJd4MuHgmOjTM2arIpP+fXgxczWE9c7lP IyvFK8TsIAP2BtYLqWoadfTT1a64M5BpQg5erqHxiI6WR85eBoYDpt5Y1M79 V6ej5+nKwI/XE08J52z2rG3eMhcGhjjXbnfU0dipzPG/sIeBtSHW6CWiscf+ vmT/bgYSS8SK3+fMPdcbynJkoG/MiYoU03hz5mcbhT0DVlaDX2f/ck2OWeYu Bv4EjK+ZSw== "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{205., 0.05}, PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]], "Output", CellChangeTimes->{{3.6543226431481247`*^9, 3.6543226566168747`*^9}, 3.654340994671875*^9, {3.654341047921875*^9, 3.654341066125*^9}, 3.65434125271875*^9, 3.654344986390625*^9, 3.654345143234375*^9, 3.65434562359375*^9, 3.654346026359375*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"\[IndentingNewLine]", StyleBox[ RowBox[{"(*", " ", RowBox[{"Esempio", " ", "2", RowBox[{"c", ":", " ", RowBox[{"si", " ", "trova", " ", RowBox[{"l", "'"}], "ultima", " ", "lente", " ", "fissando", " ", "lo", " ", "spazio", " ", RowBox[{"disponibile", ".", " ", "\[IndentingNewLine]", RowBox[{"Puo", "'"}]}], " ", "servire", " ", "per", " ", "trovare", " ", "valori", " ", "ragionevoli", " ", "di", " ", RowBox[{"focale", "."}]}]}]}], " ", "*)"}], FontColor->RGBColor[0.6, 0.4, 0.2]], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"Clear", "[", "f3", "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"dtot", "=", "600"}], ";"}], "\[IndentingNewLine]", RowBox[{"Solve", "[", RowBox[{ RowBox[{"{", RowBox[{"equazione", ",", RowBox[{"wout", "\[Equal]", "wcav"}], ",", RowBox[{ RowBox[{"d2", "+", "d3"}], "\[Equal]", "dtot"}]}], "}"}], ",", RowBox[{"{", RowBox[{"f3", ",", "d2", ",", "d3"}], "}"}]}], "]"}], " "}]}]], "Input", CellChangeTimes->{{3.65434478184375*^9, 3.6543447904375*^9}, { 3.6543448459375*^9, 3.654344846890625*^9}, {3.654344878609375*^9, 3.654344891328125*^9}, {3.65434530821875*^9, 3.654345322625*^9}, { 3.65434574428125*^9, 3.654345748859375*^9}, {3.65434579303125*^9, 3.6543458566875*^9}, {3.654345919984375*^9, 3.65434594015625*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"f3", "\[Rule]", "139.40915456981372`"}], ",", RowBox[{"d2", "\[Rule]", "284.3809339781812`"}], ",", RowBox[{"d3", "\[Rule]", "315.6190660218188`"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"f3", "\[Rule]", "144.69620742079823`"}], ",", RowBox[{"d2", "\[Rule]", "233.371154062853`"}], ",", RowBox[{"d3", "\[Rule]", "366.628845937147`"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"f3", "\[Rule]", RowBox[{"-", "704.6192603618526`"}]}], ",", RowBox[{"d2", "\[Rule]", RowBox[{"-", "418.90339735741344`"}]}], ",", RowBox[{"d3", "\[Rule]", "1018.9033973574135`"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"f3", "\[Rule]", RowBox[{"-", "4489.153453679011`"}]}], ",", RowBox[{"d2", "\[Rule]", RowBox[{"-", "1289.649887863416`"}]}], ",", RowBox[{"d3", "\[Rule]", "1889.649887863416`"}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{ 3.654345025375*^9, 3.65434516875*^9, 3.654345657078125*^9, 3.654345745078125*^9, {3.654345779796875*^9, 3.654345794421875*^9}, 3.654346047*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"(*", " ", RowBox[{ RowBox[{ "NSolve", " ", "\[EGrave]", " ", "pi\[UGrave]", " ", "veloce", " ", "di", " ", "Solve"}], ",", " ", RowBox[{"e", " ", "sufficientemente", " ", "accurato"}], ",", " ", RowBox[{ "ma", " ", "pu\[OGrave]", " ", "essere", " ", "che", " ", "non", " ", "trovi", " ", "tutte", " ", "le", " ", RowBox[{"soluzioni", "."}]}]}], " ", "*)"}], FontColor->RGBColor[0.6, 0.4, 0.2]], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"Clear", "[", "f3", "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"dtot", "=", "600"}], ";"}], "\[IndentingNewLine]", RowBox[{"NSolve", "[", RowBox[{ RowBox[{"{", RowBox[{"equazione", ",", RowBox[{"wout", "\[Equal]", "wcav"}], ",", RowBox[{ RowBox[{"d2", "+", "d3"}], "\[Equal]", "dtot"}]}], "}"}], ",", RowBox[{"{", RowBox[{"f3", ",", "d2", ",", "d3"}], "}"}]}], "]"}], " "}]}]], "Input", CellChangeTimes->{ 3.65434586603125*^9, {3.654345929859375*^9, 3.6543459620625*^9}, 3.6543460734375*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"f3", "\[Rule]", RowBox[{"-", "4489.153453679019`"}]}], ",", RowBox[{"d2", "\[Rule]", RowBox[{"-", "1289.6498878634175`"}]}], ",", RowBox[{"d3", "\[Rule]", "1889.6498878634175`"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"f3", "\[Rule]", "139.40915456981384`"}], ",", RowBox[{"d2", "\[Rule]", "284.3809339781814`"}], ",", RowBox[{"d3", "\[Rule]", "315.6190660218186`"}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{ 3.654345886859375*^9, {3.654346070109375*^9, 3.654346120234375*^9}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"\[IndentingNewLine]", StyleBox[ RowBox[{"(*", " ", RowBox[{ RowBox[{ RowBox[{"Esempio", " ", "2", RowBox[{"d", ":", " ", RowBox[{ "Si", " ", "\[EGrave]", " ", "visto", " ", "che", " ", "f3"}]}]}], "=", RowBox[{ RowBox[{"139.4", " ", "e", " ", "f3"}], "=", RowBox[{"144.7", " ", "darebbero", " ", "buoni", " ", RowBox[{"risultati", ".", " ", "Si"}], " ", "ottimizza", " ", "la", " ", "posizione", " ", "delle", " ", "due", " ", "ultime", " ", "lenti"}]}]}], ",", " ", RowBox[{ "sempre", " ", "fissando", " ", "lo", " ", "spazio", " ", "disponibile"}], ",", " ", RowBox[{"con", " ", "una", " ", "lente", " ", "disponibile", " ", RowBox[{"(", RowBox[{"f3", "=", "125"}], ")"}], " ", "vicina", " ", "ai", " ", "risultati", " ", RowBox[{"precedenti", "."}]}]}], " ", "*)"}], FontColor->RGBColor[0.6, 0.4, 0.2]], StyleBox["\[IndentingNewLine]", FontColor->RGBColor[0.6, 0.4, 0.2]], "\[IndentingNewLine]", RowBox[{ RowBox[{"Clear", "[", "d1", "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"f3", "=", "125"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"dtot", ":=", "900"}], ";"}], "\[IndentingNewLine]", RowBox[{"NSolve", "[", RowBox[{ RowBox[{"{", RowBox[{"equazione", ",", RowBox[{"wout", "\[Equal]", "wcav"}], ",", RowBox[{ RowBox[{"d1", "+", "d2", "+", "d3"}], "\[Equal]", "dtot"}]}], "}"}], ",", RowBox[{"{", RowBox[{"d1", ",", "d2", ",", "d3"}], "}"}]}], "]"}], " "}]}]], "Input", CellChangeTimes->{ 3.65434477628125*^9, {3.65434487540625*^9, 3.6543449316875*^9}, { 3.65434505596875*^9, 3.654345056875*^9}, {3.654345198640625*^9, 3.6543451990625*^9}, {3.65434528634375*^9, 3.654345287484375*^9}, { 3.65434537353125*^9, 3.65434537365625*^9}, {3.654345976046875*^9, 3.65434598453125*^9}, {3.654346133*^9, 3.654346146859375*^9}, { 3.65434621025*^9, 3.654346307765625*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"d1", "\[Rule]", RowBox[{"-", "326.15090738200604`"}]}], ",", RowBox[{"d2", "\[Rule]", "187.92347233864768`"}], ",", RowBox[{"d3", "\[Rule]", "1038.2274350433584`"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"d1", "\[Rule]", RowBox[{"314.686294955374`", "\[VeryThinSpace]", "+", RowBox[{"125.96724830806068`", " ", "\[ImaginaryI]"}]}]}], ",", RowBox[{"d2", "\[Rule]", RowBox[{"438.71039697131795`", "\[VeryThinSpace]", "-", RowBox[{"195.2331247745441`", " ", "\[ImaginaryI]"}]}]}], ",", RowBox[{"d3", "\[Rule]", RowBox[{"146.60330807330806`", "\[VeryThinSpace]", "+", RowBox[{"69.26587646648343`", " ", "\[ImaginaryI]"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"d1", "\[Rule]", RowBox[{"314.686294955374`", "\[VeryThinSpace]", "-", RowBox[{"125.96724830806068`", " ", "\[ImaginaryI]"}]}]}], ",", RowBox[{"d2", "\[Rule]", RowBox[{"438.71039697131795`", "\[VeryThinSpace]", "+", RowBox[{"195.2331247745441`", " ", "\[ImaginaryI]"}]}]}], ",", RowBox[{"d3", "\[Rule]", RowBox[{"146.60330807330806`", "\[VeryThinSpace]", "-", RowBox[{"69.26587646648343`", " ", "\[ImaginaryI]"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"d1", "\[Rule]", "346.9988377096238`"}], ",", RowBox[{"d2", "\[Rule]", "262.20692920380486`"}], ",", RowBox[{"d3", "\[Rule]", "290.79423308657135`"}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{ 3.65434525575*^9, 3.65434536009375*^9, 3.654345431953125*^9, { 3.6543459768125*^9, 3.6543459853125*^9}, 3.654346070328125*^9, { 3.65434612259375*^9, 3.654346148296875*^9}}] }, Open ]], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", "\[IndentingNewLine]", StyleBox[ RowBox[{ StyleBox["(*", FontColor->RGBColor[0.6, 0.4, 0.2]], StyleBox[" ", FontColor->RGBColor[0.6, 0.4, 0.2]], StyleBox[ RowBox[{ RowBox[{ RowBox[{"DIMOSTRAZIONE", " ", "DELLE", " ", "RELAZIONI", " ", "BD"}], "+", FractionBox[ RowBox[{"AC", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["win", "4"]}], SuperscriptBox["\[Lambda]", "2"]]}], "=", RowBox[{ RowBox[{"0", StyleBox[ RowBox[{" ", " "}]], "e", StyleBox[ RowBox[{" ", " "}]], " ", "wout"}], "=", RowBox[{"win", "*", SqrtBox[ FractionBox["A", "D"]]}]}]}], FontColor->RGBColor[1, 0, 0]], StyleBox[" ", FontColor->RGBColor[0.6, 0.4, 0.2]], StyleBox["*)", FontColor->RGBColor[0.6, 0.4, 0.2]]}], FontSize->18], StyleBox["\[IndentingNewLine]", FontColor->RGBColor[0.6, 0.4, 0.2]], StyleBox["\[IndentingNewLine]", FontColor->RGBColor[0.6, 0.4, 0.2]], StyleBox[ RowBox[{"(*", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ "La", " ", "relazione", " ", "che", " ", "descrive", " ", "la", " ", "trasformazione", " ", "del", " ", "parametro", " ", "complesso", " ", "q", " ", "del", " ", "fascio", " ", "operata", " ", "dal", " ", "sistema", " ", "ottico", " ", "\[EGrave]", "\[IndentingNewLine]", RowBox[{"(", "1", ")"}], " ", "qout"}], " ", "=", " ", RowBox[{ FractionBox[ RowBox[{ RowBox[{"A", " ", "qin"}], " ", "+", " ", "B"}], RowBox[{ RowBox[{"C", " ", "qin"}], " ", "+", " ", "D"}]], " ", "\[IndentingNewLine]", "Per", " ", "ipotesi"}]}], ",", " ", RowBox[{ RowBox[{ "in", " ", "ingresso", " ", "siamo", " ", "nel", " ", "fuoco", " ", "del", " ", RowBox[{"fascio", ".", " ", "qin"}], " ", "\[EGrave]", " ", "quindi", " ", "immaginario", " ", "puro", " ", "e", " ", "si", " ", "pu\[OGrave]", " ", "scrivere", " ", "come", " ", "\[IndentingNewLine]", "qin"}], " ", "=", " ", RowBox[{ RowBox[{ RowBox[{"-", SubscriptBox["iz", "in"]}], " ", "dove", " ", SubscriptBox["z", "in"]}], "=", RowBox[{ RowBox[{ RowBox[{ FractionBox[ RowBox[{"\[Pi]", " ", SuperscriptBox["win", "2"]}], "\[Lambda]"], " ", "\[EGrave]", " ", "il", " ", "parametro", " ", "confocale", " ", RowBox[{ RowBox[{"(", "reale", ")"}], ".", " ", "Lo"}], " ", "stesso", " ", "vale", " ", "in", " ", RowBox[{"uscita", ".", " ", "La"}], " ", RowBox[{"(", "1", ")"}], " ", "si", " ", "pu\[OGrave]", " ", "quindi", " ", "scrivere", " ", "come", "\[IndentingNewLine]", RowBox[{"(", "2", ")"}]}], " ", "-", SubscriptBox["iz", "out"]}], " ", "=", " ", RowBox[{ FractionBox[ RowBox[{ RowBox[{ RowBox[{"-", "iA"}], " ", SubscriptBox["z", "in"]}], " ", "+", " ", "B"}], RowBox[{ RowBox[{ RowBox[{"-", "iC"}], " ", SubscriptBox["z", "in"]}], " ", "+", " ", "D"}]], " ", "\[IndentingNewLine]", "che"}]}]}]}], ",", " ", RowBox[{"razionalizzata", " ", RowBox[{"(", RowBox[{ "tenendo", " ", "conto", " ", "che", " ", "gli", " ", "elementi", " ", "di", " ", "matrice", " ", "sono", " ", "reali"}], ")"}]}], ",", " ", RowBox[{ RowBox[{ RowBox[{"diventa", "\[IndentingNewLine]", RowBox[{"(", "3", ")"}]}], " ", "-", SubscriptBox["iz", "out"]}], " ", "=", " ", RowBox[{ RowBox[{ FractionBox[ RowBox[{"BD", " ", "+", " ", RowBox[{ SuperscriptBox[ RowBox[{"(", SubscriptBox["z", "in"], ")"}], "2"], "AC"}], " ", "-", " ", RowBox[{"i", " ", SubscriptBox["z", "in"], " ", RowBox[{"(", RowBox[{"AD", " ", "-", " ", "BC"}], ")"}]}]}], RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"C", " ", SubscriptBox["z", "in"]}], ")"}], "2"], " ", "+", " ", SuperscriptBox["D", "2"]}]], "\[IndentingNewLine]", "La", " ", "richiesta", " ", RowBox[{"Re", "[", "qout", "]"}]}], "=", RowBox[{ RowBox[{ RowBox[{"0", " ", "comporta", " ", "quindi", "\[IndentingNewLine]", RowBox[{"(", "4", ")"}], " ", "BD"}], " ", "+", " ", RowBox[{ SuperscriptBox[ RowBox[{"(", SubscriptBox["z", "in"], ")"}], "2"], "AC"}]}], " ", "=", " ", RowBox[{"0", "\[IndentingNewLine]", "che"}]}]}]}], ",", " ", RowBox[{"sostituendo", " ", RowBox[{"l", "'"}], "espressione", " ", "di", " ", SubscriptBox["z", "in"]}], ",", " ", RowBox[{ RowBox[{ RowBox[{"si", " ", "scrive", "\[IndentingNewLine]", RowBox[{"(", "5", ")"}], " ", "BD"}], "+", FractionBox[ RowBox[{"AC", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["win", "4"]}], SuperscriptBox["\[Lambda]", "2"]]}], "=", RowBox[{"0", "\[IndentingNewLine]", "Riprendendo", " ", "la", " ", RowBox[{"(", "3", ")"}], " ", "ed", " ", "utilizzando", " ", "la", " ", RowBox[{"(", "4", ")"}]}]}], ",", " ", RowBox[{ RowBox[{"abbiamo", "\[IndentingNewLine]", RowBox[{"(", "6", ")"}], " ", SubscriptBox["z", "out"]}], " ", "=", " ", RowBox[{ FractionBox[ RowBox[{" ", RowBox[{ SubscriptBox["z", "in"], " ", RowBox[{"(", RowBox[{"AD", " ", "-", " ", "BC"}], ")"}]}]}], RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"C", " ", SubscriptBox["z", "in"]}], ")"}], "2"], " ", "+", " ", SuperscriptBox["D", "2"]}]], "\[IndentingNewLine]", "Utilizzando", " ", "la", " ", RowBox[{"(", "4", ")"}]}]}], ",", " ", RowBox[{ "il", " ", "denominatore", " ", "si", " ", "pu\[OGrave]", " ", "scrivere", " ", "come", " ", FractionBox["D", "A"], RowBox[{"(", RowBox[{"AD", "-", "BC"}], ")"}], " ", "e"}], ",", " ", RowBox[{ "semplificando", " ", "col", " ", "numeratore", " ", "ed", " ", "utilizzando", " ", "le", " ", "espressioni", " ", "di", " ", SubscriptBox["z", "in"], " ", "e", " ", SubscriptBox["z", "out"]}], ",", " ", RowBox[{ RowBox[{"si", " ", "ottiene", "\[IndentingNewLine]", RowBox[{"(", "7", ")"}], " ", "wout"}], "=", RowBox[{"win", "*", SqrtBox[ FractionBox["A", "D"]], "\[IndentingNewLine]", "Notiamo", " ", "che", " ", RowBox[{"(", RowBox[{"AD", "-", "BC"}], ")"}], " ", "\[EGrave]", " ", "il", " ", "determinante", " ", "della", " ", "matrice", " ", "del", " ", "sistema", " ", "ottico"}]}], ",", " ", RowBox[{"e", " ", "vale", " ", "sempre", " ", "1."}]}], "\[IndentingNewLine]", "*)"}], FontColor->RGBColor[0.6, 0.4, 0.2]]}]], "Input", PageWidth->PaperWidth, CellChangeTimes->{{3.654414091515625*^9, 3.65441415059375*^9}, { 3.654414188421875*^9, 3.654414722796875*^9}, {3.6544147546875*^9, 3.6544150609375*^9}, {3.654415097015625*^9, 3.65441516990625*^9}}] }, WindowSize->{1186, 680}, WindowMargins->{{14, Automatic}, {-2, Automatic}}, PrintingCopies->1, PrintingPageRange->{32000, 32000}, PrintingOptions->{"Magnification"->1., "PaperOrientation"->"Portrait", "PaperSize"->{705.6, 777.6}}, FrontEndVersion->"8.0 for Microsoft Windows (32-bit) (February 23, 2011)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[557, 20, 1129, 31, 239, "Input"], Cell[1689, 53, 851, 20, 52, "Input"], Cell[2543, 75, 624, 25, 42, "Input"], Cell[3170, 102, 1374, 39, 112, "Input"], Cell[4547, 143, 1246, 35, 132, "Input"], Cell[5796, 180, 2843, 71, 250, "Input"], Cell[8642, 253, 2451, 66, 152, "Input"], Cell[11096, 321, 1523, 37, 72, "Input"], Cell[12622, 360, 1006, 26, 172, "Input"], Cell[CellGroupData[{ Cell[13653, 390, 1018, 27, 112, "Input"], Cell[14674, 419, 2246, 51, 69, "Output"] }, Open ]], Cell[16935, 473, 907, 19, 72, "Input"], Cell[17845, 494, 2659, 70, 112, "Input"], Cell[CellGroupData[{ Cell[20529, 568, 2477, 61, 360, "Input"], Cell[23009, 631, 225, 3, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[23271, 639, 392, 11, 72, "Input"], Cell[23666, 652, 977, 25, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[24680, 682, 2040, 52, 192, "Input"], Cell[26723, 736, 14529, 244, 236, "Output"], Cell[41255, 982, 5415, 94, 240, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[46707, 1081, 1451, 32, 152, "Input"], Cell[48161, 1115, 1196, 31, 50, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[49394, 1151, 1139, 30, 112, "Input"], Cell[50536, 1183, 632, 17, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[51205, 1205, 2071, 50, 172, "Input"], Cell[53279, 1257, 1788, 40, 50, "Output"] }, Open ]], Cell[55082, 1300, 7610, 194, 860, "Input"] } ] *) (* End of internal cache information *)