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diff --git a/Master/texmf-dist/doc/generic/pst-optic/more_docs/pst-optic-examples.tex b/Master/texmf-dist/doc/generic/pst-optic/more_docs/pst-optic-examples.tex new file mode 100644 index 00000000000..bd0464c9835 --- /dev/null +++ b/Master/texmf-dist/doc/generic/pst-optic/more_docs/pst-optic-examples.tex @@ -0,0 +1,653 @@ +%% $Id: pst-func-doc.tex 64 2008-12-08 22:14:27Z herbert $ +\documentclass[11pt,english,BCOR10mm,DIV13,bibliography=totoc,parskip=false,smallheadings + headexclude,footexclude,oneside]{pst-doc} +\usepackage[utf8]{inputenc} +\usepackage{pst-optic,pst-text} +\usepackage{hyperref} +\let\pstOpticFV\fileversion +\lstset{pos=t,wide=true,language=PSTricks,basicstyle=\footnotesize\ttfamily} +\let\belowcaptionskip\abovecaptionskip +% +\begin{document} + +\title{\texttt{pst-optic}} +\subtitle{Lenses and Mirrors -- examples; v.\pstOpticFV} + +\author{Manuel Luque \\Herbert Vo\ss} +\docauthor{Herbert Vo\ss} +\date{\today} +\maketitle + +\tableofcontents + +\clearpage + +\part{Lenses} +\section{A simple colored System} + +\begin{itemize} +\item $\mathrm{\overline{AB} = 2\ cm}$ +\item $\mathrm{\overline{OA} = -10\ cm}$ +\item $\mathrm{\overline{OF'} = 3,333\ cm}$ +\item $\mathrm{\overline{XO} = 2\ cm}$ +\end{itemize} + +\begin{LTXexample} +\begin{pspicture}(-8.5,-3)(8.5,3) +\rput(0,0){\lens[focus=3.333,OA=-10,AB=2,XO=2,xLeft=-8.5,xRight=8.5,rayColor=red]} +\pnode(!XO 2.5){L1} \pnode(!XO -2.5){L2} +\psOutLine[length=2](L1)(B'){END} \psBeforeLine[length=2](B')(L2){START} +\pspolygon[style=rayuresJaunes,linestyle=none](B)(L1)(END)(START)(L2) +\rput(0,0){\lens[focus=3.333,OA=-10,AB=2,XO=2,xLeft=-8.5,xRight=8.5,rayColor=red,arrowsize=0.2]} +\end{pspicture} +\end{LTXexample} +\xLcs{psOutLine}\xLcs{psBeforeLine} + +\clearpage +\section{A Magnifier} + +\begin{LTXexample} +\begin{pspicture}(-8,-5)(8,3) +\rput(0,0){\lens[lensGlass=true,lensWidth=0.4,focus=4,AB=0.5,OA=-2.8,XO=2,drawing=false] + \psline[linewidth=0.5pt](xLeft)(xRight)} +\pnode(!XO 2.5){L1} \pnode(!XO -2.5){L2} +\psOutLine[length=5.5,linestyle=none](B')(L1){END1} +\psBeforeLine[length=6,linestyle=none](L2)(B'){START} +\pspolygon[style=rayuresJaunes,linestyle=none](B)(L1)(END1)(START)(L2) +\psline[linewidth=1.5\pslinewidth,arrowinset=0]{->}(A)(B) +\uput[270](A){A} \uput[90](B){B} +\psline[linewidth=1.5\pslinewidth,arrowinset=0,linestyle=dashed]{->}(A')(B') +\uput[270](A'){$\mathrm{A'}$} \uput[90](B'){$\mathrm{B'}$} +\psset{linecolor=red,arrowsize=0.2} +\pcline[nodesepB=-4](B)(O)% Mittelpunktstrahl +\psline[linecolor=red,linestyle=dashed](B)(B')% ruckwaertige Verlaengerung +\Arrows(B)(O)% Mittelpunktstrahl +\psOutLine[length=2,arrows=->](B)(O){END6}% Mittelpunktstrahl +\psline(B)(I)(F')\psOutLine(I)(F'){END2}\Arrows(I)(F')\Arrows(B)(I) +\psOutLine[length=1,linestyle=dashed](I')(B'){END3} +\psline[linestyle=dashed](B)(F)\psline(B)(I')\Arrows[arrows=->>](B)(I') +\psline[linestyle=dashed](B')(I')\psline[linestyle=dashed](B')(I) +\psOutLine[length=2,arrows=->>](B')(I'){END4}\psOutLine[length=4](B')(I'){END5} +\rput(8,0){\psset{linecolor=black}\eye} +\end{pspicture} +\end{LTXexample} +\xLcs{psOutLine}\xLcs{psBeforeLine}\xLcs{eye}\xLcs{lens}\xLcs{Arrows} + +\clearpage +\section{Two Lenses} + +This is a simple system with two lenses, where the \Lcs{lens} macro is used only once. +The second lense (the left one) is drawn by the \Lcs{psline} macro. + +\begin{LTXexample} +\begin{pspicture}(-8,-5)(8,3) +\rput(0,0){\lens[lensScale=0.6,drawing=false,focus=1.5,OA=-1,XO=5,nameF={},nameFi={},AB=-1] + \psline[linewidth=1pt](xLeft)(xRight)} %image intermediaire A1B1 au foyer F'1 +\psline{->}(4,0)(4,-1) %lentille 2 +% \psline[linewidth=2\pslinewidth,linecolor=blue]{<->}(5,1.5)(5,-1.5) +%On place les points essentiels +\pnode(-6,0){O1} \pnode(-6,2.5){E1L1} \pnode(-6,-2.5){E2L1} +\pnode(4,0){A1} \pnode(4,-1){B1} +\rayInterLens(O1)(B1){5}{Inter1L2}%intersection de O1 avec la lentille L2 +\pcline[nodesepB=-2](Inter1L2)(O1)%rayon venant de l'infini jusqu'e la lentille L2 +\Parallel(B1)(O1)(E1L1){B1infty}%rayon parallele au precedent et passant par E1L1 +\Parallel(B1)(O1)(E2L1){B2infty}%rayon passant par E2L2 +%intersection de la droite passant par E1L1 et B1 avec la lentille L2 +\rayInterLens(E1L1)(B1){5}{InterE1B1L2}\psline(E1L1)(InterE1B1L2) +%intersection de la droite passant par E2L2 et B1 avec la lentille L2 +\rayInterLens(E2L1)(B1){5}{InterE2B1L2} +\psline(E2L1)(InterE2B1L2) +\psline[linestyle=dashed]{->}(A')(B')\psline[linestyle=dashed](InterE1B1L2)(B') +\psline[linestyle=dashed](InterE2B1L2)(B')\psline[linestyle=dotted](B')(O) +\psOutLine[length=3](B')(InterE1B1L2){END}\psBeforeLine[length=3](InterE2B1L2)(B'){START} +\pspolygon[style=rayuresJaunes,linestyle=none](B1infty)(E1L1)(InterE1B1L2)% + (END)(START)(InterE2B1L2)(E2L1)(B2infty) +\uput[90](A'){$\mathrm{A'}$}\uput[270](B'){$\mathrm{B'}$} +\uput[90](A1){$\mathrm{A_1}$}\uput[270](B1){$\mathrm{B_1}$} +\uput[225](O1){O1}\uput[45](O){O2}\uput[90](F){$\mathrm{F_2}$} +\uput{0.4}[150](F'){$\mathrm{F'_2}$}\uput{0.6}[90](A1){$\mathrm{F'_1}$} +\psline[linecolor=red](B1infty)(E1L1)(InterE1B1L2)(END) +\psline[linecolor=red](B2infty)(E2L1)(InterE2B1L2)(START) +\rput(8,0){\eye} +\psline[linewidth=2\pslinewidth,linecolor=blue,arrowsize=0.2,arrowinset=0.5]{<->}(-6,-2.5)(-6,2.5) +\end{pspicture} +\end{LTXexample} +\xLcs{psOutLine}\xLcs{psBeforeLine}\xLcs{eye}\xLcs{lens}\xLcs{Arrows}\xLcs{rayInterLens} + +\clearpage +\section{Real Image} + +\begin{LTXexample} +\begin{pspicture*}(-7.5,-3)(7.5,3) +\rput(0,0){\lens[lensGlass=true,lensWidth=0.5,lensType=DVG,XO=0,AB=2,OA=-4,focus=-6,spotAi=270,spotBi=90]% + \psline[linewidth=1pt](xLeft)(xRight)} +\psline[linecolor=red,linestyle=dashed](I')(F)% Verlaengerung des Brennstrahls +\psOutLine[length=7](B')(I){END}\psBeforeLine[length=7](I')(B'){START}% permet de definir START +\pspolygon[style=rayuresJaunes,linestyle=none](B)(I)(END)(START)(I') +\psline(B)(I)(END) \psline(B)(I')(START) +\end{pspicture*} +\end{LTXexample} +\xLcs{psOutLine}\xLcs{psBeforeLine}\xLcs{lens} + +\clearpage +\section{Virtual Image} + +\begin{LTXexample} +\begin{pspicture*}(-7.5,-6.5)(7.5,7.5) +\rput(0,0){\lens[lensType=DVG,lensWidth=0.75,lensHeight=7,focus=-2,OA=-6,AB=4,XO=-1,lensGlass=true, + rayColor=red,yBottom=-5,yTop=5,drawing=false] + \psline[linewidth=1pt](xLeft)(xRight)} +\pnode(!XO 2.9){L1} \pnode(!XO -2.5){L2} +{ \psset{length=4,linestyle=none} + \psOutLine(B')(L1){A1} \psOutLine(B')(L2){A2} + \pspolygon[style=rayuresJaunes,linestyle=none](B)(L1)(A1)(A2)(L2) + \psset{linecolor=red,linestyle=solid} + \psline(B)(L1)(A1) \psline(B)(L2)(A2) \psline[linestyle=dashed](B')(L1) + \psline[linestyle=dashed](B')(L2) } +\psline[linestyle=dashed]{->}(A)(B) \psline{->}(A')(B') +\uput[90](B){B}\uput[90](B'){$\mathrm{B'}$}\uput[270](A){A}\uput[270](A'){$\mathrm{A'}$} +\end{pspicture*} +\end{LTXexample} +\xLcs{psOutLine}\xLcs{psBeforeLine}\xLcs{lens} + +\clearpage +\section{A Microscope} + +\begin{LTXexample} +\begin{pspicture}(-7.5,-5.5)(7.5,3) +\rput(0,0){\lens[focus=1.5,OA=-2,AB=0.5,XO=-5,lensGlass=true,lensWidth=0.4, + yBottom=-4,yTop=4,drawing=false,lensScale=0.4,nameF=F_1,nameFi=F'_1] + \psline[linewidth=1pt](xLeft)(xRight)} +\pnode(! XO 1){UPlens1} \pnode(! XO -1){DOWNlens1} +\Transform +\rput(0,0){\lens[focus=2,XO=3,lensGlass=true,lensWidth=0.4,yBottom=-4,yTop=4,drawing=false, + nameF=F_2,nameFi=F'_2,spotF=90,spotFi=90]} +\psline{->}(A1)(B1)\psline{->}(A'1)(B'1)\uput[270](A1){A}\uput[90](B1){B} +\uput[270](B'1){$\mathrm{B_1}$}\uput{0.7}[90](A'1){$\mathrm{A_1}$} +{\psset{linecolor=red} + \rayInterLens(I11)(B'1){3}{Inter1L2}\rayInterLens(B1)(O1){3}{Inter2L2} + \rayInterLens(UPlens1)(B'1){3}{Inter3L2}\rayInterLens(DOWNlens1)(B'1){3}{Inter4L2} + \psline(B1)(I11)(B'1)(Inter1L2)\psline(B1)(Inter2L2)\psline(B1)(UPlens1)(Inter3L2) + \psline(B1)(DOWNlens1)(Inter4L2) + \psset{length=5} + \Parallel(B'1)(O)(Inter3L2){B1inftyRigth}\Parallel(B'1)(O)(Inter4L2){B2inftyRigth} + \Parallel(B'1)(O)(Inter2L2){B3inftyRigth}\Parallel(B'1)(O)(Inter1L2){B3inftyRigth} + {\psset{length=-5,linestyle=dashed} + \Parallel(B'1)(O)(Inter3L2){B1inftyLeft}\Parallel(B'1)(O)(Inter4L2){B2inftyLeft} + \Parallel(B'1)(O)(Inter2L2){B3inftyLeft}\Parallel(B'1)(O)(Inter1L2){B3inftyLeft} + \pcline[nodesep=6](B'1)(O)} + \pspolygon[style=rayuresJaunes,linestyle=none](B1)(UPlens1)(Inter3L2)% + (B1inftyRigth)(B2inftyRigth)(Inter4L2)(DOWNlens1) + \psline(B1)(UPlens1)(Inter3L2)(B1inftyRigth)\psline(B2inftyRigth)(Inter4L2)(DOWNlens1)(B1)} +\rput(7,0){\eye} +\end{pspicture}% +\end{LTXexample} +\xLcs{psOutLine}\xLcs{psBeforeLine}\xLcs{lens}\xLcs{rayInterLens}\xLcs{Parallel} + + +\clearpage +\section{Telescope} + +\begin{LTXexample}[wide=false] +\telescope[mirrorFocus=10,posMirrorTwo=8,yBottom=-8] +\end{LTXexample} + +\xLcs{telescope} +\begin{LTXexample}[wide=false] +\telescope[mirrorFocus=6,posMirrorTwo=5,yBottom=-5] +\end{LTXexample} + +\clearpage +\section{Lightspeed measured by Foucault} +1849 Foucault (1819-1868) determines with the following configuration the speed of the light. + + + +\begin{LTXexample} +\begin{pspicture}(-8,-3.2)(7,4.5) +\rput(0,0){\lens[lensWidth=1,lensGlass=true,lensHeight=6,focus=4,drawing=false,AB=2.5]} +{\psset{linewidth=0.5pt,linestyle=dashed,arrowsize=5pt,arrows=|<->|} + \psline(-8,0)(4,0)\pcline(-7.75,-3)(0,-3)\lput*{:U}{2f} + \pcline(0,-3)(4,-3)\lput*{:U}{f}\pcline(7,0)(7,4)\lput*{:U}{f} + \pcline(4,5)(5,5)\lput*{:U}{s}\pcline(5.25,2.3)(5.25,2.8)\lput*{:U}{s} } +\uput[90](0,3){\Large L}\uput[45](-7.7,3){\Large B}\uput[45](-7.7,-2){\Large E} +\uput[270](3,-0.5){\Large D}\uput[-45](4,0){\Large A=F}\uput[270](3,2){\Large S} +\uput[90](4,4){\Large Sp}\uput[90](3.5,3.25){\Large B'}\uput[0](6.3,2.25){\Large B''} +\uput[-90](6,1.1){\Large M}\psarc[linewidth=0.5pt](-7.75,2.5){0.5}{-90}{0}\qdisk(-7.55,2.3){1pt} +\rput{210}(F'){\mirrorTwo} +{\psset{fillstyle=solid,fillcolor=lightgray} + \rput{210}(4,2.5){\psframe(-1,0)(1,0.2)}\psframe(-8,-3)(-7.75,3) + \psframe(3,4)(3.8,4.2)\psframe(4.2,4)(5,4.2) } +{\psset{linewidth=1pt,linecolor=red,arrows=->,arrowsize=5pt} + \arrowLine[linecolor=blue,arrowOffset=-0.2](F')(4,2.5){2} + \arrowLine[linecolor=blue,arrowOffset=-0.2](4,2.3)(6,2.3){1} + \qdisk(6,2.3){2pt} + \psline[linestyle=dashed,arrows=-](F')(5.1,4)\psline[linestyle=dashed,arrows=-](5,2.8)(6,2.8) + \arrowLine(4,4)(F'){3}\arrowLine[linecolor=blue,arrowOffset=-0.2](I)(F'){2} + \arrowLine(F')(I){2}\arrowLine[linecolor=blue,arrowOffset=-0.3](-7.75,2.5)(I){3} + \arrowLine(I)(-7.75,2.5){3} } +\psframe(5.5,1.1)(6.5,3.5) +\multido{\r=1.3+0.2}{12}{\psline(6.1,\r)(6.5,\r)} +\end{pspicture} +\end{LTXexample} + +Sp chink; \\ +D rotating mirror;\\ +L collecting lens;\\ +E end mirror;\\ +S half diaphanous mirror;\\ +M scale + + +\clearpage +\part{Mirrors} + +\section{High Beam Light\label{beamlight}} +\begin{LTXexample} +\begin{pspicture}(-1.5,-5.5)(10,5.5) +\rput(0,0){\beamLight[drawing=false,mirrorDepth=4.75,mirrorWidth=0.1,mirrorHeight=10,linecolor=lightgray]} +\makeatletter +\pst@getcoor{Focus}\pst@tempf +\psset{linewidth=1pt,linecolor=red} +\multido{\n=60+5}{18}{% + \mirrorCVGRay[linecolor=red,mirrorDepth=4.75,mirrorHeight=10,linewidth=1pt](Focus)(!% + /XF \pst@tempf pop \pst@number\psxunit div def \n\space cos XF add \n\space sin neg){Endd1} + \psOutLine[arrows=->,length=.25](Endd1)(Endd1''){Endd2}% + \mirrorCVGRay[linecolor=red,mirrorDepth=4.75,mirrorHeight=10,linewidth=1pt](Focus)(!% + /XF \pst@tempf pop \pst@number\psxunit div def \n\space cos XF add \n\space sin ){End1} + \psOutLine[arrows=->,length=.25](End1)(End1''){End2}} +\makeatletter +\end{pspicture} +\end{LTXexample} +\xLcs{beamLight}\xLcs{mirrorCVGRay}\xLcs{psOutLine} +\clearpage +\section{Low Beam Light} + + +\begin{LTXexample} +\begin{pspicture}(-1.5,-5)(10,5) +\rput(0,0){\beamLight[drawing=false,mirrorDepth=4.75,mirrorWidth=0.1,mirrorHeight=10,linecolor=lightgray]} +\psset{linewidth=1pt,linecolor=red} +\multido{\n=70+5}{20}{% + \psline(2.75,-0.2)(! \n\space cos 2.75 add \n\space sin ) + \mirrorCVGRay[linecolor=red,mirrorDepth=4.75,mirrorHeight=10,linewidth=1pt](2.75,-0.2)% + (! \n\space cos 2.75 add \n\space sin ){End1} + \psOutLine[arrows=->,length=.25](End1)(End1''){End2}} +\end{pspicture} +\end{LTXexample} +\xLcs{beamLight}\xLcs{mirrorCVGRay}\xLcs{psOutLine}\xLkeyword{mirrorDepth}\xLkeyword{mirrorHeight} + + + +\clearpage +\part{Refraction} + +\section{Vertical Medium} + +Refrectionnumbers are $n_1=1$ and $n_2=1.5$: + +\begin{LTXexample} +\begin{pspicture}[showgrid=true](-5,-3)(5,3) +\pnode(-1,-2.5){A}\pnode(1,-2.5){B}\pnode(1,2.5){C}\pnode(-1,2.5){D} +% \rotateFrame(A)(B)(C)(D){10} +\uput[-135](A){A}\uput[-45](B){B}\uput[45](C){C}\uput[135](D){D} +\pspolygon[fillcolor=lightgray,fillstyle=solid,linecolor=blue](A)(B)(C)(D) +% 1. +\refractionRay(-3,-3)(-2,-2)(D)(A){1}{1.5}{END} +\psset{linecolor=red,linewidth=2pt,arrowsize=5pt,arrows=->} +\arrowLine(-3,-3)(END){2}\ABinterCD(END)(END')(C)(B){Out} +\arrowLine(END)(Out){1}\refractionRay(END)(Out)(C)(B){1.5}{1}{Q} +\arrowLine(Q)(Q'){1}\psOutLine[length=2](Q)(Q'){End} +% 2. +\refractionRay(-3,0)(-2,0)(A)(D){1}{1.5}{END} +\psset{linecolor=green,linewidth=2pt,arrowsize=5pt,arrows=->} +\arrowLine(-3,0)(END){2}\ABinterCD(END)(END')(C)(B){Out} +\arrowLine(END)(Out){1}\refractionRay(END)(Out)(C)(B){1.5}{1}{Q} +\arrowLine(Q)(Q'){1}\psOutLine[length=2](Q)(Q'){End} +% 3. +\refractionRay(-3,3)(-2,2)(D)(A){1}{1.5}{END} +\psset{linecolor=blue,linewidth=2pt,arrowsize=5pt,arrows=->} +\arrowLine(-3,3)(END){2}\ABinterCD(END)(END')(C)(B){Out} +\arrowLine(END)(Out){1}\refractionRay(END)(Out)(C)(B){1.5}{1}{Q} +\arrowLine(Q)(Q'){1}\psOutLine[length=2](Q)(Q'){End} +\end{pspicture} +\end{LTXexample} +\xLcs{refractionRay}\xLcs{arrowLine}\xLcs{ABinterCD}\xLkeyword{length} + +\clearpage +\section{Horizontal Medium} +Refrectionnumbers are $n_1=1$ and $n_2=1.5$: + +\begin{LTXexample} +\begin{pspicture}[showgrid=true](-5,-4)(5,3) +\pnode(-2.5,-1){A}\pnode(2.5,-1){B}\pnode(2.5,1){C}\pnode(-2.5,1){D} +%\rotateFrame(A)(B)(C)(D){10} +\uput[-135](A){A}\uput[-45](B){B}\uput[45](C){C}\uput[135](D){D} +\pspolygon[fillcolor=lightgray,fillstyle=solid,linecolor=blue](A)(B)(C)(D) +% 1. +\refractionRay(-3,3)(-2,2)(C)(D){1}{1.5}{END} +\psset{linecolor=red,linewidth=2pt,arrowsize=5pt,arrows=->} +\arrowLine(-3,3)(END){2}\ABinterCD(END)(END')(B)(A){Out} +\arrowLine(END)(Out){1}\refractionRay(END)(Out)(B)(A){1.5}{1}{Q} +\arrowLine(Q)(Q'){1}\psOutLine[length=2](Q)(Q'){End} +% 2. +\refractionRay(0,3)(0,1)(C)(D){1}{1.5}{END} +\psset{linecolor=green,linewidth=2pt,arrowsize=5pt,arrows=->} +\arrowLine(0,3)(END){2}\ABinterCD(END)(END')(A)(B){Out} +\arrowLine(END)(Out){1}\refractionRay(END)(Out)(B)(A){1.5}{1}{Q} +\arrowLine(Q)(Q'){1}\psOutLine[length=2](Q)(Q'){End} +% 3. +\refractionRay(3,3)(2,2)(C)(D){1}{1.5}{END} +\psset{linecolor=blue,linewidth=2pt,arrowsize=5pt,arrows=->} +\arrowLine(3,3)(END){2}\ABinterCD(END)(END')(B)(A){Out} +\arrowLine(END)(Out){1}\refractionRay(END)(Out)(B)(A){1.5}{1}{Q} +\arrowLine(Q)(Q'){1}\psOutLine[length=2](Q)(Q'){End} +\end{pspicture} +\end{LTXexample} +\xLcs{refractionRay}\xLcs{arrowLine}\xLcs{ABinterCD} + +\clearpage + +\section{Parallel Rays and a sloping medium} +Refrectionnumbers are $n_1=1$ and $n_2=1.5$: + +\begin{LTXexample} +\begin{pspicture}[showgrid=true](-7,-1)(5,6) +\pnode(0,0){A}\pnode(2,0){B}\pnode(2,5){C}\pnode(0,5){D} +\rotateFrame(A)(B)(C)(D){40} +\uput[-135](A){A}\uput[-45](B){B}\uput[30](C){C}\uput[135](D){D} +\pspolygon[fillcolor=lightgray,fillstyle=solid,linecolor=blue](A)(B)(C)(D) +\psset{linecolor=red,linewidth=2pt,arrowsize=5pt,arrows=->} +\multido{\r=1.10+0.28}{8}{% + \refractionRay(-6.00,\r)(-3.00,\r)(A)(D){1}{1.5}{End} + \arrowLine(-6.00,\r)(End){2}\ABinterCD(End)(End')(C)(B){Out} + \arrowLine(End)(Out){1}\refractionRay(End)(Out)(C)(B){1.5}{1}{Q} + \psline(Q)(Q')\psOutLine[length=3](Q)(Q'){End}} +\end{pspicture} +\end{LTXexample} +\xLcs{refractionRay}\xLcs{arrowLine}\xLcs{ABinterCD}\xLcs{polygon} + +\clearpage + +\section{A Prisma} +Refrectionnumbers are $n_1=1$ and $n_2=1.5$: + + +\begin{LTXexample} +\begin{pspicture}[showgrid=true](-7,0)(5,6) +\pnode(-3,1){A}\pnode(1,1){B}\pnode(-1,5){C}\uput[-135](A){A}\uput[-45](B){B}\uput[30](C){C} +\pspolygon[fillcolor=lightgray,fillstyle=solid,linecolor=blue](A)(B)(C) +\psset{linecolor=red,linewidth=2pt,arrowsize=5pt,arrows=->} +\multido{\rA=0.6+0.2,\rB=1.5+0.2}{7}{% + \refractionRay(-6,\rA)(-4,\rB)(C)(A){1}{1.5}{END}\arrowLine(-6,\rA)(END){2} + \ABinterCD(END)(END')(C)(B){Out}\arrowLine(END)(Out){1} + \refractionRay(END)(Out)(C)(B){1.5}{1}{Q}\psline(Q)(Q')\psOutLine[length=3](Q)(Q'){End}} +\end{pspicture} +\end{LTXexample} +\xLcs{refractionRay}\xLcs{arrowLine}\xLcs{ABinterCD}\xLcs{psOutLine} + + +\section{A Prisma for Dispersion} +The following figure shows the light dispersion with realistic values for the refractions numbers of the different light colors. +\bigskip + +\begin{tabular}{ @{}l l l l l l @{}} + & darkblue & bluegreen & yellow & red & darkred \\ +$n$ for glass & 1.528 & 1.523 & 1.517 & 1.514 & 1.511 +\end{tabular} + +\begin{landscape} +\begin{LTXexample}[wide=false] +\begin{pspicture}[showgrid=true](-7,0)(14,6) +\pnode(-6,1){A}\pnode(-2,1){B}\pnode(-4,5){C}\uput[-135](A){A}\uput[-45](B){B}\uput[30](C){C} +\pnode(12.5,0.5){E1}\pnode(12.5,5.5){E2} +\psframe[fillcolor=lightgray,fillstyle=solid](E1)(12.75,5.5)\pspolygon[fillcolor=lightgray,fillstyle=solid,linecolor=blue](A)(B)(C) +\psset{linecolor=black,linewidth=2pt,arrowsize=5pt,arrows=->} +\pnode(-7,1){P1}\pnode(-6,2){P2}\ABinterCD(P1)(P2)(C)(A){END}\arrowLine(P1)(END){2} +\psset{linecolor=blue,linewidth=0.5pt,arrowsize=2pt,} +\refractionRay(P1)(P2)(C)(A){1}{1.528}{END}\ABinterCD(END)(END')(C)(B){Out}\arrowLine(END)(Out){1} +\refractionRay(END)(Out)(C)(B){1.528}{1}{Q}\psline(Q)(Q')\ABinterCD(Q)(Q')(E1)(E2){END}\arrowLine(Q)(END){4}\qdisk(END){1.5pt} +\psset{linecolor=green} +\refractionRay(P1)(P2)(C)(A){1}{1.523}{END}\ABinterCD(END)(END')(C)(B){Out}\arrowLine(END)(Out){1} +\refractionRay(END)(Out)(C)(B){1.523}{1}{Q}\psline(Q)(Q')\ABinterCD(Q)(Q')(E1)(E2){END}\arrowLine(Q)(END){4}\qdisk(END){1.5pt} +\psset{linecolor=yellow} +\refractionRay(P1)(P2)(C)(A){1}{1.517}{END}\ABinterCD(END)(END')(C)(B){Out}\arrowLine(END)(Out){1} +\refractionRay(END)(Out)(C)(B){1.517}{1}{Q}\psline(Q)(Q')\ABinterCD(Q)(Q')(E1)(E2){END}\arrowLine(Q)(END){4}\qdisk(END){1.5pt} +\psset{linecolor=red} +\refractionRay(P1)(P2)(C)(A){1}{1.511}{END}\ABinterCD(END)(END')(C)(B){Out}\arrowLine(END)(Out){1} +\refractionRay(END)(Out)(C)(B){1.511}{1}{Q}\psline(Q)(Q')\ABinterCD(Q)(Q')(E1)(E2){END}\arrowLine(Q)(END){4}\qdisk(END){1.5pt} +\end{pspicture} +\end{LTXexample} +\end{landscape} + + +\clearpage +\section{Refration with different Angles} +Refrectionnumbers are $n_1=1$ and $n_2=1.5$: + +\begin{LTXexample} +\begin{pspicture}[showgrid=true](-6,-5)(6,5) +\pnode(-6,-1){A}\pnode(6,-1){B}\pnode(6,1){C}\pnode(-6,1){D} +\uput[-135](A){A}\uput[-45](B){B}\uput[30](C){C}\uput[135](D){D} +\pspolygon[fillcolor=lightgray,fillstyle=solid,linecolor=blue](A)(B)(C)(D) +\psline[linewidth=0.5pt](0,-5)(0,5) +\psset{linecolor=red,linewidth=1.5pt,arrowsize=5pt,arrows=->} +\multido{\n=30+5}{25}{% + \refractionRay(5;\n)(0,1)(C)(D){1}{1.5}{END}\arrowLine(5;\n)(END){2} + \ABinterCD(END)(END')(B)(A){Out}\arrowLine(END)(Out){1} + \refractionRay(END)(Out)(B)(A){1.5}{1}{Q}\psline(Q)(Q')\psOutLine[length=3](Q)(Q'){End}} +\end{pspicture} +\end{LTXexample} + + + + + +\clearpage +\section{Great difference in the Refractionsnumbers} + +Refrectionnumbers are $n_1=1$ and $n_2=4$: + + +\begin{LTXexample} +\begin{pspicture}[showgrid=true](-5,-1)(2,6) +\pnode(0,0){A}\pnode(2,0){B}\pnode(2,5){C}\pnode(0,5){D}\rotateFrame(A)(B)(C)(D){45} +\uput[-135](A){A}\uput[-40](B){B}\uput[45](C){C}\uput[135](D){D} +\pspolygon[fillcolor=lightgray,fillstyle=solid,linecolor=blue](A)(B)(C)(D) +\refractionRay(-2.5,-1)(-2,1)(A)(D){1}{4}{END} +\psset{linecolor=red,linewidth=2pt,arrowsize=5pt,arrows=->} +\arrowLine(-2.5,-1)(END){2}\ABinterCD(END)(END')(C)(B){Out}\arrowLine(END)(Out){1} +\refractionRay(END)(Out)(C)(B){4}{1}{Q}\arrowLine(Q)(Q'){1}\psOutLine[length=2](Q)(Q'){End} +\end{pspicture} +\end{LTXexample} + + +\clearpage + +\section{Total Reflection} + +Refrectionnumbers are $n_1=2$ and $n_2=1$: + +\begin{LTXexample} +\begin{pspicture}[showgrid=true](-8,-3)(8,6) +\pnode(-8,1.5){A}\pnode(8,1.5){B}\uput[45](A){A}\uput[135](B){B}\pnode(0,0){START} +\psframe[fillcolor=lightgray,fillstyle=solid,linecolor=blue](-8,-1.5)(B) +\psset{linecolor=red,linewidth=1.5pt,arrowsize=5pt,arrows=->} +% \multido{\n=20+5}{16}{% +\multido{\n=20+5}{29}{% + \refractionRay(START)(1;\n)(A)(B){1.5}{1}{END}\arrowLine(START)(END){2} + \arrowLine(END)(END'){1}\psOutLine[length=3](END)(END'){Q}\arrowLine(END')(Q){3}} +\end{pspicture} +\end{LTXexample} + +\clearpage + + +\section{Total Reflection with a sloping medium} + +Refrectionnumbers are $n_1=2$ and $n_2=1$: + + +\begin{LTXexample} +\begin{pspicture}[showgrid=true](-8,-6)(8,6) +\pnode(-6,1.5){A}\pnode(6,1.5){B}\pnode(6,-1.5){C}\pnode(-6,-1.5){D} +\rotateFrame(A)(B)(C)(D){30}\uput[90](A){A}\uput[135](B){B}\pnode(0,0){START} +\pspolygon[fillcolor=lightgray,fillstyle=solid,linecolor=blue](A)(B)(C)(D) +\psset{linecolor=red,linewidth=1.5pt,arrowsize=5pt,arrows=->} +\multido{\n=50+5}{29}{% + \refractionRay(START)(1;\n)(A)(B){2}{1}{END}\arrowLine(START)(END){2} + \arrowLine(END)(END'){1}\psOutLine[length=3](END)(END'){Q}\arrowLine(END')(Q){3}} +\end{pspicture} +\end{LTXexample} + +\clearpage + +\part{Spherical Optic} + + +\section{Refraction at a Spherical Surface} + +\subsection[Simple Example]{Construction for finding the position of the image point P' of a point object P formed by refraction at a sperical surface} + + +\begin{LTXexample} +\begin{pspicture*}[showgrid=true](-10,-4)(3,4) +\rput(0,0){\lensSPH[lensType=CVG,lensHeight=12,lensWidth=10,yBottom=-6,yTop=6,xLeft=-6,xRight=6,drawing=false]} +\psset{linecolor=red,linewidth=1.5pt,dotstyle=|} +\pnode(-9,0){P}\psdots(P)\uput[-90](P){P}\psline(P)(xRight)\lensSPHRay(P)(-5,2){1}{9}{Q} +\psline(P)(Q)(Q')\psdots(Q)\uput[90](Q){B}\ABinterCD(Q)(Q')(0,0)(5,0){P'} +\psdots(Q')\uput[-90](P'){P'}\psline[linewidth=0.5pt,linecolor=black](Center')(Q) +\psline[linewidth=0.5pt,linecolor=black](Q)(Q|0,0)\psdots(Center')\uput[-90](Center'){C} +\end{pspicture*} +\end{LTXexample} +\xLcs{lensSPH}\xLcs{lensSPHRay}\xLcs{ABinterCD} + + +\clearpage +\subsection[Height of an Image]{Construction for determining the height of an image formed by refraction at a sperical surface} + +\begin{LTXexample} +\begin{pspicture*}[showgrid=true](-13,-3)(3,5) +\rput(0,0){\lensSPH[lensType=CVG,lensHeight=12,lensWidth=10,yBottom=-4,yTop=4,xLeft=-5,xRight=5,drawing=false]} +\psset{linecolor=red,linewidth=1.5pt,dotstyle=|} +\pnode(-12,0){P}\psdots(P)\uput[-90](P){P}\pnode(-12,4){Q}\psdots(Q)\uput[90](Q){Q} +\psline[linecolor=blue,linewidth=3pt,arrows=->](P)(Q)\psline(P)(xRight) +\lensSPHRay(Q)(Center'){1}{9}{S1}\lensSPHRay(Q)(-5,0){1}{9}{S2}% +\psline(Q)(S1')\psline(Q)(S2)(S2')\ABinterCD(Q)(S1')(S2)(S2'){Q'} +\pnode(Q'|0,0){P'}\psline[linecolor=blue,linewidth=3pt,arrows=->](P')(Q') +\uput[90](P'){P'}\uput[-90](Q'){Q'}\psdots(Center')\uput[90](Center'){C} +\end{pspicture*} +\end{LTXexample} +\xLcs{lensSPH}\xLcs{lensSPHRay}\xLcs{ABinterCD} + + +\clearpage +\section{Thin Convergent Lenses} + +If the two spherical surfaces are close enough we can call such a lense a +\textbf{thin lens}. The following figure shows the behaviour of such a lense with real rays. + +\begin{LTXexample} +\psset{xunit=0.75cm} +\begin{pspicture*}[showgrid=true](-10,-4)(10,4) +\rput(0,0){\lensSPH[lensType=CVG,lensHeight=7,lensWidth=1.25,yBottom=-5,yTop=5,xLeft=-12,xRight=12,% + AB=2,OA=-9,refractA=1,refractB=2,drawing=true,rayColor=red]} +\end{pspicture*} +\end{LTXexample} +\xLkeyword{refractA}\xLkeyword{refractB}\xLkeyset{lensType=CVG}\xLkeyword{AB} + +\clearpage + +\section{Thick Convergent Lenses} + +There is no real image possible. + +\begin{LTXexample} +\begin{pspicture}(-10,-4)(10,4) +\rput(0,0){\lensSPH[lensType=CVG,lensHeight=7,lensWidth=2,yBottom=-5,yTop=5,xLeft=-12,xRight=12,% + AB=2,OA=-9,refractA=1,refractB=2,drawing=true,rayColor=red]} +\end{pspicture} +\end{LTXexample} +\xLkeyword{refractA}\xLkeyword{refractB}\xLkeyset{lensType=CVG}\xLkeyword{AB} + + +\clearpage + +\section{Thin Divergent Lenses} +If the two spherical surfaces are close enough we can call such a lense a \textbf{thin lens}. The following figure shows the behaviour of such a lense with real rays. + +\psset{unit=1cm} +\begin{LTXexample} +\begin{pspicture*}[showgrid=true](-6,-3)(6,3) +\rput(0,0){\lensSPH[lensType=DVG,lensWidth=0.1,lensDepth=0.2,AB=1,OA=-5,drawing=true,rayColor=red]} +\end{pspicture*} +\end{LTXexample} +\xLcs{lensSPH}\xLkeyset{lensType=DVG}\xLkeyword{AB} + + +\clearpage + +\section{Thick Divergent Lenses} + +There is no real image possible. + +\begin{LTXexample} +\begin{pspicture*}[showgrid=true](-6,-3)(6,3) +\rput(0,0){\lensSPH[lensType=DVG,lensWidth=1,lensDepth=1,AB=1,OA=-5,drawing=true,rayColor=red]} +\end{pspicture*} +\end{LTXexample} +\xLcs{lensSPH}\xLkeyset{lensType=DVG}\xLkeyword{AB} + +\clearpage +\section{\nxLcs{mirrorCVG}} + +\begin{LTXexample} +\begin{pspicture*}[showgrid=true](-1,-5)(8,5) +\rput(0,0){\mirrorCVG[mirrorType=SPH,drawing=false,yBottom=-4,yTop=4,mirrorHeight=8,mirrorDepth=3] + \qdisk(Center){2pt}\qdisk(Focus){2pt} + \uput[-90](Center){Center}\uput[-90](Focus){F}\psline(O)(xRight)} +\multido{\rA=-3.50+0.25}{5}{% + \mirrorCVGRay[mirrorType=SPH,linecolor=red](6,\rA)(4,\rA){E} + \psOutLine[linecolor=red,length=4](E')(E''){EEnd}} +\multido{\rA=-2.25+0.25}{19}{% + \ABinterSPHLens(6,\rA)(4,\rA)(Center){Ptemp} + \reflectionRay[mirrorType=SPH](5,\rA)(Ptemp){E} + \psline[linecolor=red](6,\rA)(Ptemp)(E)\psOutLine[linecolor=red,length=6](Ptemp)(E){EEnd}} +\multido{\rA=2.50+0.25}{5}{% + \mirrorCVGRay[mirrorType=SPH,linecolor=red](6,\rA)(4,\rA){E} + \psOutLine[linecolor=red,length=4](E')(E''){EEnd}} +\end{pspicture*} +\end{LTXexample} +\xLcs{mirrorCVG}\xLkeyset{mirrorType=SPH}\xLcs{ABinterSPHLens}\xLcs{refractionRay} + + +\clearpage +\section{\nxLcs{mirrorDVG}} + + +\begin{LTXexample} +\begin{pspicture*}[showgrid=true](-5,-5)(8,5) +\rput(0,0){% + \mirrorDVG[mirrorType=SPH,drawing=false,yBottom=-4,yTop=4,mirrorHeight=8,mirrorWidth=0.25,mirrorDepth=2.5] + \qdisk(Center){2pt}\qdisk(Focus){2pt}\uput[-90](Center){C}\uput[-90](Focus){F} + \psline(xLeft)(xRight)} +\multido{\rA=-3.00+0.25}{25}{% + \ABinterSPHLens(7,\rA)(4,\rA)(Center){Ptemp}\reflectionRay[mirrorType=SPH](5,\rA)(Ptemp){E} + \arrowLine[linecolor=red,linewidth=1.5pt](7,\rA)(Ptemp){1} + \psline[linecolor=red,arrows=->,linewidth=1.5pt](Ptemp)(E) + \psOutLine[linecolor=red,length=6,linewidth=1.5pt,arrows=->](Ptemp)(E){EEnd} + \psOutLine[linecolor=red,length=3,linestyle=dashed,linewidth=0.5pt](E)(Ptemp){EEnd}} +\end{pspicture*} +\end{LTXexample} +\xLcs{mirrorDVG}\xLkeyset{mirrorType=SPH}\xLcs{ABinterSPHLens}\xLcs{refractionRay} + +\bgroup +\raggedright +\nocite{*} +\bibliographystyle{plain} +\bibliography{pst-optic-doc} +\egroup + +\printindex + +\end{document} |