\documentclass[12pt]{article}
\usepackage[T1]{fontenc}
\usepackage[latin1]{inputenc}
\usepackage{geometry}
\usepackage{graphicx}
\usepackage{subfigure}
\usepackage{pstricks}
\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{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}%	extrmitsuprieuredelalentille
\pnode(!XO -2.5){L2}%	extrmitinfrieuredelalentille
\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}
}

\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}%	extrmitsuprieuredelalentille
\pnode(!XO -2.5){L2}%	extrmitinfrieuredelalentille
\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{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)
  }
  \psline[linecolor=red,linestyle=dashed](I')(F)% Verlaengerung des Brennstrahls
  \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,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}
%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=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}%	extrmitdelalentillesup
\pnode(!XO -2.5){L2}%	extrmitdelalentilleinf
{%
  \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*}
}

\begin{lstlisting}
\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}%	extrmitdelalentillesup
\pnode(!XO -2.5){L2}%	extrmitdelalentilleinf
{%
  \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{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}