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+\documentclass[12pt]{article}
+\usepackage[T1]{fontenc}
+\usepackage[latin1]{inputenc}
+\usepackage[vtex]{geometry}
+\usepackage{graphicx}
+\usepackage{subfigure}
+\usepackage{pstcol}
+\usepackage{pst-optic}
+\usepackage{pst-text}
+\usepackage{url}
+\usepackage{amsmath}
+\usepackage{tabularx}
+\usepackage{lscape}
+\usepackage{fancyhdr}
+\pagestyle{fancy}
+\lfoot{\small\ttfamily\jobname.tex}
+\cfoot{}
+\rfoot{}
+\renewcommand{\headrulewidth}{0pt}
+\renewcommand{\footrulewidth}{0pt}
+\usepackage{listings}
+\lstset{language=TEX,basicstyle=\ttfamily\footnotesize,%
+ extendedchars=true,numbers=left,numberstyle=\tiny}
+\usepackage{multicol}
+\let\myPart\part
+\renewcommand{\part}[1]{%
+ \clearpage\myPart{#1}%
+}
+\newcommand{\PS}{PostScript}
+\newcommand\CMD[1]{\texttt{\textbackslash#1}}
+\psset{subgriddiv=0,gridlabels=7pt,griddots=5}
+\usepackage[vtex]{hyperref}
+
+\begin{document}
+\author{Manuel Luque\thanks{Mluque5130@aol.com} \and Herbert Voß\thanks{voss@perce.de}}
+\date{\today}
+\title{Lenses and Mirrors: PST-optic v0.9\\Examples}
+\maketitle
+
+
+\tableofcontents
+
+\clearpage
+
+\section*{Introduction}
+
+\verb|pstricks| writes pure PostScript\cite{PostScript} code, so it is not possible to run \TeX{} files with pdf\LaTeX{} when there are pstricks macros in the document. If you still need a PDF output use the package \verb|pdftricks.sty|\cite{pdftricks} or the for Linux free available program \verb|vlatex| (\url{http://www.micropress-inc.com/linux/}) or build the PDF with \verb|ps2pdf| (\verb|dvi|$\rightarrow$\verb|ps|$\rightarrow$\verb|pdf|).
+\par
+If you need package \verb|graphicx.sty| load it before any \verb|pstricks| package. You do not need to load \verb|pstricks.sty|, it will be done by \verb|pst-optic| by default.
+\par
+For more informations have a look into the documentations.
+
+\par
+\vspace{\fill}
+This PDF file was created with the \textbf{vlatex} program from the free available \textit{VTeX/Lnx v7.530 - the VTeX distribution for Linux (x86)}.
+
+
+\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}
+
+\resizebox{\textwidth}{!}{%
+\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}%extrémité supérieure de la lentille
+\pnode(!XO -2.5){L2}%extrémité inférieure de la lentille
+\psOutLine[length=2](L1)(B'){END}
+\psBeforeLine[length=2](B')(L2){START}
+\pspolygon[style=rayuresJaunes,linestyle=none](B)(L1)(END)(START)(L2)
+% pour bien distinguer le tracé des rayons.
+ \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}}
+
+\begin{lstlisting}
+\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}%extrémité supérieure de la lentille
+\pnode(!XO -2.5){L2}%extrémité inférieure de la lentille
+\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{lstlisting}
+
+
+\section{A Magnifier}
+
+\resizebox{\textwidth}{!}{%
+\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}% extrémité supérieure de la lentille
+ \pnode(!XO -2.5){L2}% extrémité inférieure de la lentille
+ \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)
+ \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}%
+}
+
+\begin{lstlisting}
+\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}% extrémité supérieure de la lentille
+ \pnode(!XO -2.5){L2}% extrémité inférieure de la lentille
+ \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)
+ \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{lstlisting}
+
+
+\section{Two Lenses}
+
+This is a simple system with two lenses, where the \verb|\lens| macro is used only once. The second lense (the left one) is drawn by the \verb|\psline| macro.
+
+\resizebox{\textwidth}{!}{%
+\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 intermédiaire 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}%extrémité sup de L1
+ \pnode(-6,-2.5){E2L1}%extrémité inf de L1
+ \pnode(4,0){A1}
+ \pnode(4,-1){B1}
+%intersection de O1 avec la lentille L2
+ \rayInterLens(O1)(B1){5}{Inter1L2}
+%rayon venant de l'infini jusqu'à la lentille L2
+ \pcline[nodesepB=-2](Inter1L2)(O1)
+%rayon parallèle au précédent et passant par E1L1
+ \Parallel(B1)(O1)(E1L1){B1infty}
+%rayon parallèle au précédent et passant par E2L2
+ \Parallel(B1)(O1)(E2L1){B2infty}
+%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}
+%lentille 1
+ \psline[%
+ linewidth=2\pslinewidth,%
+ linecolor=blue,%
+ arrowsize=0.2,arrowinset=0.5]{<->}(-6,-2.5)(-6,2.5)
+\end{pspicture}%
+}
+
+
+\begin{lstlisting}
+\begin{pspicture}(-8,-3)(8,3)
+%on place l'oculaire dès le début
+ \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 intermédiaire 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}%extrémité sup de L1
+ \pnode(-6,-2.5){E2L1}%extrémité inf de L1
+ \pnode(4,0){A1}
+ \pnode(4,-1){B1}
+%intersection de O1 avec la lentille L2
+ \rayInterLens(O1)(B1){5}{Inter1L2}
+%rayon venant de l'infini jusqu'à la lentille L2
+ \pcline[nodesepB=-2](Inter1L2)(O1)
+%rayon parallèle au précédent et passant par E1L1
+ \Parallel(B1)(O1)(E1L1){B1infty}
+%rayon parallèle au précédent et passant par E2L2
+ \Parallel(B1)(O1)(E2L1){B2infty}
+%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}
+%lentille 1
+ \psline[%
+ linewidth=2\pslinewidth,%
+ linecolor=blue,%
+ arrowsize=0.2,arrowinset=0.5]{<->}(-6,-2.5)(-6,2.5)
+\end{pspicture}
+\end{lstlisting}
+
+
+
+\section{Real Image}
+
+\resizebox{\textwidth}{!}{
+\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)
+ }
+ \psOutLine[length=7](B')(I){END}
+%pour prolonger au-delà de B' permet de définir END
+ \psBeforeLine[length=7](I')(B'){START}% permet de définir START
+ \pspolygon[style=rayuresJaunes,linestyle=none](B)(I)(END)(START)(I')
+ \psline(B)(I)(END)
+ \psline(B)(I')(START)
+\end{pspicture}%
+}
+
+\begin{lstlisting}
+\begin{pspicture}*(-7.5,-3)(7.5,3)
+\rput(0,0){%
+ \lens[lensGlass=true,lensType=DVG,lensWidth=0.5,%
+ XO=0,AB=2,OA=-4,focus=-6,spotAi=270,spotBi=90]%
+}
+\psOutLine[length=7](B')(I){END}
+% pour prolonger au-delà de B' permet de définir END
+\psBeforeLine[length=7](I')(B'){START}
+% permet de définir START
+\pspolygon[style=rayuresJaunes,linestyle=none](B)(I)(END)(START)(I')
+\psline(B)(I)(END)
+\psline(B)(I')(START)
+\end{pspicture}
+\end{lstlisting}
+
+
+\section{Virtual Image}
+
+\resizebox{\textwidth}{!}{%
+\begin{pspicture}*(-7.5,-6.5)(7.5,7.5)
+ \rput(0,0){%
+ \lens[lensType=DVG,lensWidth=0.75,lensHeight=8,focus=-2,%
+ OA=1.5,AB=1,XO=-1,lensGlass=true,%
+ rayColor=red,yBottom=-5,yTop=5,drawing=false]%
+ \psline[linewidth=1pt](xLeft)(xRight)
+ }
+ \pnode(!XO 2.5){L1}%extrémité de la lentille sup
+ \pnode(!XO -2.5){L2}%extrémité de la lentille inf
+ {%
+ \psset{linecolor=red,linestyle=dashed}
+ \psline(L1)(B)
+ \psline(L2)(B)%
+ }{%
+ \psset{length=4,linestyle=none}
+ \psOutLine(B)(L1){A1}
+ \psOutLine(B)(L2){A4}
+ \psOutLine(L1)(B'){A2}
+ \psOutLine(L2)(B'){A3}
+ \pspolygon[style=rayuresJaunes](A1)(L1)(A2)(A3)(L2)(A4)
+ }
+ \psline[linestyle=dashed]{->}(A)(B)
+ \psline{->}(A')(B')
+ \uput[90](B){B}
+ \uput[90](B'){$\mathrm{B'}$}
+ \uput[270](A){A}
+ \uput[270](A'){$\mathrm{A'}$}
+ {%
+ \psset{linecolor=red}
+ \psline(A1)(L1)(A2)
+ \psline(A4)(L2)(A3)}
+\end{pspicture}
+}
+
+\begin{lstlisting}
+\begin{pspicture}*(-7.5,-6.5)(7.5,7.5)
+ \rput(0,0){%
+ \lens[lensType=DVG,lensWidth=0.75,lensHeight=8,%
+ focus=-2,OA=1.5,AB=1,XO=-1,lensGlass=true,%
+ rayColor=red,yBottom=-5,yTop=5,drawing=false]%
+ \psline[linewidth=1pt](xLeft)(xRight)
+ }
+ \pnode(!XO 2.5){L1}%extrémité de la lentille sup
+ \pnode(!XO -2.5){L2}%extrémité de la lentille inf
+ {%
+ \psset{linecolor=red,linestyle=dashed}
+ \psline(L1)(B)
+ \psline(L2)(B)%
+ }{%
+ \psset{length=4,linestyle=none}
+ \psOutLine(B)(L1){A1}
+ \psOutLine(B)(L2){A4}
+ \psOutLine(L1)(B'){A2}
+ \psOutLine(L2)(B'){A3}
+ \pspolygon[style=rayuresJaunes]%
+ (A1)(L1)(A2)(A3)(L2)(A4)
+ }
+ \psline[linestyle=dashed]{->}(A)(B)
+ \psline{->}(A')(B')
+ \uput[90](B){B}
+ \uput[90](B'){$\mathrm{B'}$}
+ \uput[270](A){A}
+ \uput[270](A'){$\mathrm{A'}$}
+ {%
+ \psset{linecolor=red}
+ \psline(A1)(L1)(A2)
+ \psline(A4)(L2)(A3)}
+\end{pspicture}
+\end{lstlisting}
+
+\section{A Microscope}
+
+\resizebox{\textwidth}{!}{
+\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}%
+}
+
+\begin{lstlisting}
+\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{lstlisting}
+
+
+\clearpage
+\section{Telescope}
+
+\begin{center}
+\telescope[mirrorFocus=10,posMirrorTwo=8,yBottom=-8]
+\end{center}
+
+\begin{lstlisting}
+\telescope[mirrorFocus=10,posMirrorTwo=8,yBottom=-8]
+\end{lstlisting}
+
+
+\begin{center}
+\telescope[mirrorFocus=6,posMirrorTwo=5,yBottom=-5]
+\end{center}
+
+\begin{lstlisting}
+\telescope[mirrorFocus=6,posMirrorTwo=5,yBottom=-5]
+\end{lstlisting}
+
+
+\section{Lightspeed measured by Foucault}
+1849 Foucault (1819-1868) determines with the following configuration the speed of the light.
+
+\begin{pspicture}(-8,-5)(7,6)
+ \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}
+
+Sp chink; \\
+D rotating mirror;\\
+L collecting lens;\\
+E end mirror;\\
+S half diaphanous mirror;\\
+M scale
+
+\begin{lstlisting}
+\begin{pspicture}(-8,-5)(7,6)
+ \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{lstlisting}
+
+
+
+\part{Mirrors}
+
+\section{High Beam Light\label{beamlight}}
+\begin{pspicture}(-1.5,-5.5)(10,5.5)
+% \psgrid[subgriddiv=0,griddots=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}
+
+
+\begin{lstlisting}
+\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{lstlisting}
+
+\section{Low Beam Light}
+\begin{pspicture}(-1.5,-5)(10,5)
+% \psgrid[subgriddiv=0,griddots=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}
+
+\begin{lstlisting}
+\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{lstlisting}
+
+
+
+
+\part{Refraction}
+
+\section{Vertical Medium}
+
+Refrectionnumbers are $n_1=1$ and $n_2=1.5$:
+
+\bigskip
+
+
+\begin{pspicture}(-5,-3)(5,3)
+ \psgrid
+ \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}
+\bigskip
+
+
+\begin{lstlisting}
+\begin{pspicture}(-5,-3)(5,3)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \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{lstlisting}
+
+\section{Horizontal Medium}
+Refrectionnumbers are $n_1=1$ and $n_2=1.5$:
+\bigskip
+
+
+\begin{pspicture}(-5,-4)(5,3)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \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}
+
+
+\begin{lstlisting}
+\begin{pspicture}(-5,-4)(5,3)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \pnode(-2.5,-1){A}
+ \pnode(2.5,-1){B}
+ \pnode(2.5,1){C}
+ \pnode(-2.5,1){D}
+ \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{lstlisting}
+
+\section{Parallel Rays and a sloping medium}
+Refrectionnumbers are $n_1=1$ and $n_2=1.5$:
+\bigskip
+
+
+\begin{pspicture}(-7,-1)(5,6)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \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}
+\begin{lstlisting}
+\begin{pspicture}(-7,-1)(5,6)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \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[-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=3.0+-0.3}{8}{%
+ \refractionRay(-7,\r)(-4,\r)(D)(A){1}{1.25}{END}
+ \arrowLine(-7,\r)(END){2}
+ \ABinterCD(END)(END')(C)(B){Out}
+ \arrowLine(END)(Out){1}
+ \refractionRay(END)(Out)(C)(B){1.25}{1}{Q}
+ \psline(Q)(Q')
+ \psOutLine[length=3](Q)(Q'){End}%
+ }
+\end{pspicture}
+\end{lstlisting}
+
+\section{A Prisma}
+Refrectionnumbers are $n_1=1$ and $n_2=1.5$:
+\bigskip
+
+
+\begin{pspicture}(-7,0)(5,6)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \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}
+\bigskip
+
+\begin{lstlisting}
+\begin{pspicture}(-7,0)(5,6)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \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{lstlisting}
+
+
+\begin{landscape}
+\section{A Prisma for Dispersion}
+The following figure shows the lioght dispersion with realistic values for the refractions numbers of the different light colors.
+\bigskip
+
+\begin{tabular}{l|l}
+ Color & Refraction number $n$ for glass\\\hline
+ dark blue & $1.528$ \\
+ bluegreen & $1.523$ \\
+ yellow & $1.517$ \\
+ red & $1.514$ \\
+ darkred & $1.511$ \\
+\end{tabular}
+
+\bigskip
+\begin{pspicture}(-7,0)(14,6)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \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{landscape}
+
+
+\begin{lstlisting}
+\begin{pspicture}(-7,0)(14,6)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \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{lstlisting}
+
+
+\clearpage
+\section{Refration with different Angles}
+Refrectionnumbers are $n_1=1$ and $n_2=1.5$:
+\bigskip
+
+\begin{pspicture}(-6,-5)(6,5)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \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}
+
+\bigskip
+
+\begin{lstlisting}
+\begin{pspicture}(-6,-5)(6,5)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \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{lstlisting}
+
+\clearpage
+\section{Great difference in the Refractionsnumbers}
+
+Refrectionnumbers are $n_1=1$ and $n_2=4$:
+
+
+\bigskip
+
+\begin{pspicture}(-5,-1)(2,6)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \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}
+
+
+\begin{lstlisting}
+\begin{pspicture}(-5,-1)(2,6)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \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)(D)(A){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{lstlisting}
+
+
+\clearpage
+
+\section{Total Reflection}
+
+Refrectionnumbers are $n_1=2$ and $n_2=1$:
+\bigskip
+
+\begin{pspicture}(-8,-3)(8,6)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \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}
+
+
+\bigskip
+
+
+\begin{lstlisting}
+\begin{pspicture}(-8,-3)(8,6)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \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}{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{lstlisting}
+
+\clearpage
+
+
+\section{Total Reflection with a sloping medium}
+
+Refrectionnumbers are $n_1=2$ and $n_2=1$:
+
+
+\begin{pspicture}(-8,-6)(8,6)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \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}
+
+\par
+\bigskip
+
+\begin{lstlisting}
+\begin{pspicture}(-8,-6)(8,6)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \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{lstlisting}
+
+
+\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{pspicture*}(-10,-4)(3,4)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \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*}
+
+
+\bigskip
+
+
+\begin{lstlisting}
+\begin{pspicture}*(-10,-4)(3,4)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \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(-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{lstlisting}
+
+
+\subsection[Height of an Image]{Construction for determining the height of an image formed by refraction at a sperical surface}
+
+\begin{pspicture}*(-13,-3)(3,5)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \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}
+
+\bigskip
+\begin{lstlisting}
+\begin{pspicture}*(-13,-3)(3,5)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \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{lstlisting}
+
+
+\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.
+
+\psset{xunit=0.75cm}
+\begin{pspicture}(-10,-4)(10,4)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \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}
+
+\bigskip
+\begin{lstlisting}
+\psset{xunit=0.75cm}
+\begin{pspicture}(-10,-4)(10,4)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \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{lstlisting}
+
+\clearpage
+
+
+
+\section{Thick Convergent Lenses}
+
+There is no real image possible.
+
+\begin{pspicture}(-10,-4)(10,4)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \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}
+
+
+\bigskip
+\begin{lstlisting}
+\begin{pspicture}(-10,-4)(10,4)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \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{lstlisting}
+
+\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.
+
+\bigskip
+\begin{pspicture*}(-6,-3)(6,3)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \rput(0,0){\lensSPH[%
+ lensType=DVG,%
+ lensWidth=0.1,%
+ lensDepth=0.2,%
+ AB=1,OA=-5,%
+ drawing=true,%
+ rayColor=red]}
+\end{pspicture*}
+
+\bigskip
+\begin{lstlisting}
+\begin{pspicture*}(-6,-3)(6,3)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \rput(0,0){\lensSPH[%
+ lensType=DVG,%
+ lensWidth=0.1,%
+ lensDepth=0.2,%
+ AB=1,OA=-5,%
+ drawing=true,%
+ rayColor=red]}
+\end{pspicture*}
+\end{lstlisting}
+
+
+\clearpage
+
+\section{Thick Divergent Lenses}
+
+There is no real image possible.
+
+\bigskip
+\begin{pspicture*}(-6,-3)(6,3)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \rput(0,0){\lensSPH[%
+ lensType=DVG,%
+ lensWidth=1,%
+ lensDepth=1,%
+ AB=1,OA=-5,%
+ drawing=true,%
+ rayColor=red]}
+\end{pspicture*}
+
+
+\bigskip
+\begin{lstlisting}
+\begin{pspicture*}(-6,-3)(6,3)
+ \psgrid[subgriddiv=0,griddots=5,gridlabels=7pt]
+ \rput(0,0){\lensSPH[%
+ lensType=DVG,%
+ lensWidth=1,%
+ lensDepth=1,%
+ AB=1,OA=-5,%
+ drawing=true,%
+ rayColor=red]}
+\end{pspicture*}
+\end{lstlisting}
+
+\clearpage
+\section{\CMD{mirrorCVG}}
+
+
+\begin{pspicture*}(-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}
+ }
+ \psgrid
+\end{pspicture*}
+
+
+
+\bigskip
+
+\begin{lstlisting}
+\begin{pspicture*}(-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](8,\rA)(4,\rA){E}
+ \psOutLine[linecolor=red,length=4](E')(E''){EEnd}
+ }
+ \multido{\rA=-2.25+0.25}{19}{%
+ \ABinterSPHLens(8,\rA)(4,\rA)(Center){Ptemp}
+ \reflectionRay[mirrorType=CVG-SPH](5,\rA)(Ptemp){E}
+ \psline[linecolor=red](8,\rA)(Ptemp)(E)
+ \psOutLine[linecolor=red,length=6](Ptemp)(E){EEnd}
+ }
+ \multido{\rA=2.50+0.25}{5}{%
+ \mirrorCVGRay[mirrorType=SPH,linecolor=red](8,\rA)(4,\rA){E}
+ \psOutLine[linecolor=red,length=4](E')(E''){EEnd}
+ }
+ \psgrid
+\end{pspicture*}
+\end{lstlisting}
+
+
+
+
+\section{\CMD{mirrorDVG}}
+
+
+\begin{pspicture*}(-5,-5)(8,5)
+ \psgrid
+ \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*}
+
+\par
+
+\begin{lstlisting}
+\begin{pspicture*}(-5,-5)(8,5)
+ \psgrid
+ \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{lstlisting}
+
+
+
+\end{document}
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