path: root/Master/texmf-dist/tex/generic/pst-optic/pst-optic.tex

%%
%% This is file `pst-optic.tex',
%% 
%% IMPORTANT NOTICE:
%% 
%% Package `pst-optic.tex'
%%
%% Manuel Luque <Mluque5130@aol.com> (France)
%% Herbert Voss <voss@perce.de> (Germany)
%%
%% February 16, 2003
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%% DESCRIPTION:
%%   `pst-optic' is a PSTricks package to define lenses and mirrors
%%
\csname PSTopticLoaded\endcsname
\let\PSTopticLoaded\endinput
% Requires PSTricks, pst-node, pstcol, pst-plot, pst-3d, multido packages
\ifx\PSTnodesLoaded\endinput\else\input pst-node.tex\fi
\ifx\PSTplotLoaded\endinput\else\input pst-plot.tex\fi  % parametric-plot
\ifx\PSTthreeDLoaded\endinput\else\input pst-3d.tex\fi	% symplan
\ifx\PSTMultidoLoaded\endinput\else\input multido.tex\fi
\ifx\PSTXKeyLoaded\endinput\else\input pst-xkey \fi
%
\def\fileversion{0.92}
\def\filedate{2004/11/09}
\message{`PST-Optic' v\fileversion, \filedate\space (Manuel Luque and Herbert Voss)}
%
% DPC interface to the `keyval' package (until keyval based version of PSTricks)
%
\edef\PstAtCode{\the\catcode`\@} \catcode`\@=11\relax
\pst@addfams{pst-optic}
\SpecialCoor
%
%%%%%%%%%%%%%%%%%% Macrolist %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%% \def\Arrows[#1](#2)(#3)
%% \def\psOutLine[#1](#2)(#3)#4
%% \def\psBeforeLine[#1](#2)(#3)#4
%% \def\ABinterCD(#1)(#2)(#3)(#4)#5
%% \def\Parallel[#1](#2)(#3)(#4)#5
%% \def\arrowLine[#1](#2)(#3)#4
%% \def\nodeBetween(#1)(#2)#3
%% \def\rotateNode(#1)#2
%% \def\rotateTriangle(#1)(#2)(#3)#4
%% \def\rotateFrame(#1)(#2)(#3)(#4)#5
%% \def\lensSPH[#1]
%% \def\lensSPHRay[#1](#2)(#3)#4#5#6
%% \def\ABinterSPHLens(#1)(#2)(#3)#4
%% \def\lens[#1]
%% \def\pslensDVG
%% \def\pslensDVG@i#1#2
%% \def\pslensDVG@ii
%% \def\pslensCVG
%% \def\pslensCVG@ii
%% \def\lensCVG
%% \def\lensDVG
%% \def\Transform
%% \def\rayInterLens(#1)(#2)#3#4
%% \def\mirrorCVGRay[#1](#2)(#3)#4
%% \def\mirrorCVG[#1]
%% \def\mirrorDVG[#1]
%% \def\mirrorDVGRay[#1](#2)(#3)#4
%% \def\beamLight[#1]
%% \def\mirrorTwo
%% \def\telescope[#1]
%% \def\planMirrorRay(#1)(#2)(#3)#4
%% \def\symPlan(#1)(#2)
%% \def\refractionRay[#1](#2)(#3)(#4)(#5)#6#7#8
%% \def\reflectionRay[#1](#2)(#3)#4
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% ---------------- the if's -----------------
%
\newif\ifPst@lensTwo%			is a second lens present?
\define@key[psset]{pst-optic}{lensTwo}[false]{\@nameuse{Pst@lensTwo#1}%
}
\newif\ifPst@lensGlass%			draw a _real_ lens?
\define@key[psset]{pst-optic}{lensGlass}[true]{\@nameuse{Pst@lensGlass#1}%
}
\newif\ifPst@drawing%			draw the nodes and rays?
\define@key[psset]{pst-optic}{drawing}[true]{\@nameuse{Pst@drawing#1}%
}
\newif\ifPst@rightRay%			a ray on the right side?
\define@key[psset]{pst-optic}{rightRay}[false]{\@nameuse{Pst@rightRay#1}%
}
%
\psset{lensGlass=false}
\psset{drawing=true}
%
% ------- the global definitions for the pspicture frame ------
%
\define@key[psset]{pst-optic}{xLeft}{\edef\psk@optic@xLeft{#1}}
\define@key[psset]{pst-optic}{xRight}{\edef\psk@optic@xRight{#1}}
\define@key[psset]{pst-optic}{yBottom}{\edef\psk@optic@yBottom{#1}}
\define@key[psset]{pst-optic}{yTop}{\edef\psk@optic@yTop{#1}}
\psset{xLeft=-7.5,xRight=7.5,yBottom=-3.0,yTop=3.0}
%
% ---------------- the lenses -----------------
%
\define@key[psset]{pst-optic}{lensType}{%		CVG|DVG
	\edef\psk@optic@lensType{#1}%
}
\define@key[psset]{pst-optic}{lensColor}{%
	\edef\psk@optic@lensColor{#1}%
}
\define@key[psset]{pst-optic}{lensWidth}{%		the thichness of the lens
	\edef\psk@optic@lensWidth{#1}%
}
\define@key[psset]{pst-optic}{lensDepth}{%
	\edef\psk@optic@lensDepth{#1}%
}
\define@key[psset]{pst-optic}{lensHeight}{%	the TOTAL height of the lens
	\edef\psk@optic@lensHeight{#1}%
}
\define@key[psset]{pst-optic}{lensScale}{%		more or less obsolete
	\edef\psk@optic@lensScale{#1}%
}
\define@key[psset]{pst-optic}{lensArrowSize}{%	for the AB,... Arrows
	\edef\psk@optic@lensArrowSize{#1}%
}
\define@key[psset]{pst-optic}{lensArrowInset}{%
	\edef\psk@optic@lensArrowInset{#1}%
}
\psset{lensType=CVG}
\def\Type{CVG}
\psset{lensColor=lightgray}
\psset{lensWidth=0.5}
\psset{lensDepth=1}
\psset{lensHeight=5}
\psset{lensScale=1}
\psset{lensArrowSize=0.2}
\psset{lensArrowInset=0.5}
%
% ---------------- the mirrors -----------------
%
\define@key[psset]{pst-optic}{mirrorType}{%	PLAN|PARAbolic|SPHerical
	\edef\psk@optic@mirrorType{#1}%
}
\define@key[psset]{pst-optic}{mirrorDepth}{%
	\edef\psk@optic@mirrorDepth{#1}%
}
\define@key[psset]{pst-optic}{mirrorHeight}{%	it's the TOTAL height
	\edef\psk@optic@mirrorHeight{#1}%
}
\define@key[psset]{pst-optic}{mirrorWidth}{%
	\edef\psk@optic@mirrorWidth{#1}%
}
\define@key[psset]{pst-optic}{mirrorColor}{%
	\edef\psk@optic@mirrorColor{#1}%
}
\define@key[psset]{pst-optic}{mirrorFocus}{%
	\edef\psk@optic@mirrorFocus{#1}%	
}
\define@key[psset]{pst-optic}{posMirrorTwo}{%	a sencond mirror? (telescope)
	\edef\psk@optic@posMirrorTwo{#1}%
}
\define@key[psset]{pst-optic}{mirrorTwoAngle}{%	the angle for the 2. plan mirror (telescope)
	\edef\psk@optic@mirrorTwoAngle{#1}%
}
\psset{mirrorType=CVG}% possible CVG|DVG
\def\mirrorType{CVG}
\psset{mirrorDepth=1}
\psset{mirrorHeight=5}
\psset{mirrorWidth=0.25}
\psset{mirrorFocus=8}% only for LensTwo option
\psset{mirrorTwoAngle=45}
\psset{posMirrorTwo=6}
\psset{mirrorColor=lightgray}
%
% -------------- the refrectionnumbers -------------
%
\define@key[psset]{pst-optic}{refractA}{%
	\edef\psk@optic@refractA{#1}%
}
\define@key[psset]{pst-optic}{refractB}{%
	\edef\psk@optic@refractB{#1}%
}
\psset{refractA=1}
\psset{refractB=1.41}
%
% -------------- the length and node definitions -------------
%
\define@key[psset]{pst-optic}{XO}{%			the X-offset
	\edef\psk@optic@XO{#1}%
}
\define@key[psset]{pst-optic}{YO}{%			the y-offset
	\edef\psk@optic@YO{#1}%
}
\define@key[psset]{pst-optic}{posStart}{%		where the arrows start
	\edef\psk@optic@posStart{#1}%
}
\define@key[psset]{pst-optic}{length}{%		the length of the before|outlines
	\edef\psk@optic@length{#1}%
}
\define@key[psset]{pst-optic}{focus}{%		for lenses/mirrors with a fixed focus
	\edef\psk@optic@focus{#1}%
}
\define@key[psset]{pst-optic}{AB}{%			the length of the object arrow
	\edef\psk@optic@AB{#1}%
}
\define@key[psset]{pst-optic}{OA}{%			the xcoordinate of the object arrow
	\edef\psk@optic@OA{#1}%
}
\define@key[psset]{pst-optic}{arrowOffset}{%	offset for \arrowLine
	\edef\psk@optic@arrowOffset{#1}%
}
%
\psset{XO=0,YO=0}
\psset{OA=-3}
\psset{posStart=0,length=2}
\psset{focus=2}
\psset{AB=1}
\psset{arrowOffset=0}
%
\define@key[psset]{pst-optic}{nameA}{%		start of the object arrow
	\edef\psk@optic@nameA{#1}%
}
\define@key[psset]{pst-optic}{spotA}{%		where to draw the label
	\edef\psk@optic@spotA{#1}%
}
\define@key[psset]{pst-optic}{nameB}{%
	\edef\psk@optic@nameB{#1}%
}
\define@key[psset]{pst-optic}{spotB}{%
	\edef\psk@optic@spotB{#1}%
}
\define@key[psset]{pst-optic}{nameF}{%
	\edef\psk@optic@nameF{#1}%
}
\define@key[psset]{pst-optic}{spotF}{%
	\edef\psk@optic@spotF{#1}%
}
\define@key[psset]{pst-optic}{nameO}{%
	\edef\psk@optic@nameO{#1}%
}
\define@key[psset]{pst-optic}{spotO}{%
	\edef\psk@optic@spotO{#1}%
}
\define@key[psset]{pst-optic}{nameAi}{%
	\edef\psk@optic@nameAi{#1}%
}
\define@key[psset]{pst-optic}{spotAi}{%
	\edef\psk@optic@spotAi{#1}%
}
\define@key[psset]{pst-optic}{nameBi}{%
	\edef\psk@optic@nameBi{#1}%
}
\define@key[psset]{pst-optic}{spotBi}{%
	\edef\psk@optic@spotBi{#1}%
}
\define@key[psset]{pst-optic}{nameFi}{%
	\edef\psk@optic@nameFi{#1}%
}
\define@key[psset]{pst-optic}{spotFi}{%
	\edef\psk@optic@spotFi{#1}%
}
%
\psset{nameA=A}
\psset{spotA=270}
\psset{nameB=B}
\psset{spotB=90}
\psset{nameF=F}
\psset{spotF=270}
\psset{nameO=O}
\psset{spotO=225}
\psset{nameAi=A'}
\psset{spotAi=90}
\psset{nameBi=B'}
\psset{spotBi=270}
\psset{nameFi=F'}
\psset{spotFi=270}
%
% -------------------- colors/fillstyles -------------------
%
\definecolor{BleuVerre}{cmyk}{0.2,0,0,0}
\definecolor{JauneVert}{rgb}{0.7,1,0}
\newpsstyle{rayuresJaunes}{%
	fillstyle=hlines,hatchsep=2\pslinewidth,hatchcolor=JauneVert%
}
\define@key[psset]{pst-optic}{rayColor}{%
	\edef\psk@optic@rayColor{#1}%
}
\psset{rayColor=red}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
% Utility stuff
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% posStart=Starting point
% length=  Arrow length.
\def\Arrows{\@ifnextchar[{\pst@Arrows}{\pst@Arrows[]}}
\def\pst@Arrows[#1](#2)(#3){{%
	\psset{#1}%
	\pst@getcoor{#2}\pst@tempa
	\pst@getcoor{#3}\pst@tempb
	\pnode(!%
		/StartArrow \psk@optic@posStart\space def
		/LengthArrow \psk@optic@length\space def
		\pst@tempa /YA exch \pst@number\psyunit div def
		/XA exch \pst@number\psxunit div def
		\pst@tempb /YB exch \pst@number\psyunit div def
		/XB exch \pst@number\psxunit div def
		/denominateur XB XA sub def
		/numerateur YB YA sub def
		/angleDirectionAB numerateur denominateur Atan def
		/XD StartArrow angleDirectionAB cos mul XA add def
		/YD StartArrow angleDirectionAB sin mul YA add def
		/XF XD LengthArrow angleDirectionAB cos mul add def
		/YF YD LengthArrow angleDirectionAB sin mul add def
		XD YD ){ArrowStart}
	\pnode(! XF YF){ArrowEnd}
	\psset{arrows=->}
	\psline[#1](ArrowStart)(ArrowEnd)%
}}
%
% draw a line (===) outside: #2-----#3=======#4
%
\def\psOutLine{\@ifnextchar[{\pst@ToDrawOut}{\pst@ToDrawOut[]}}
\def\pst@ToDrawOut[#1](#2)(#3)#4{{%
	\psset{#1}%
	\pst@getcoor{#2}\pst@tempa
	\pst@getcoor{#3}\pst@tempb
	\pnode(!%
		/LengthArrow \psk@optic@length\space def
		\pst@tempa /YA exch \pst@number\psyunit div def
		/XA exch \pst@number\psxunit div def
		\pst@tempb /YB exch \pst@number\psyunit div def
		/XB exch \pst@number\psxunit div def
		/denominateur XB XA sub def
		/numerateur YB YA sub def
		/angleDirectionAB numerateur denominateur Atan def
		/Xend XB LengthArrow angleDirectionAB cos mul add def
		/Yend YB LengthArrow angleDirectionAB sin mul add def
		Xend Yend){#4}
	\psline[#1](#3)(#4)
}}
%
% draw a line (===) before: #4========#2-----#3
%
\def\psBeforeLine{\@ifnextchar[{\pst@BeforeLine}{\pst@BeforeLine[]}}
\def\pst@BeforeLine[#1](#2)(#3)#4{{%
	\psset{#1}%
	\pst@getcoor{#2}\pst@tempa
	\pst@getcoor{#3}\pst@tempb
	\pnode(!%
		/LengthArrow \psk@optic@length\space def
		\pst@tempa /YA exch \pst@number\psyunit div def
		/XA exch \pst@number\psxunit div def
		\pst@tempb /YB exch \pst@number\psyunit div def
		/XB exch \pst@number\psxunit div def
		/denominateur XB XA sub def
		/numerateur YB YA sub def
		/angleDirectionAB numerateur denominateur Atan def
		/Xstart XA LengthArrow angleDirectionAB cos mul sub def
		/Ystart YA LengthArrow angleDirectionAB sin mul sub def
		Xstart Ystart){#4}
	\psline[#1](#4)(#2)%
}}
%
% intersection de deux droites
% 2 juillet 2001/ rewritten 2003-01-27 Herbert
%
\def\ABinterCD(#1)(#2)(#3)(#4)#5{%
    \pst@getcoor{#1}\pst@tempa
    \pst@getcoor{#2}\pst@tempb
    \pst@getcoor{#3}\pst@tempc
    \pst@getcoor{#4}\pst@tempd
\pnode(!%
    /YA \pst@tempa exch pop \pst@number\psyunit div def
    /XA \pst@tempa pop \pst@number\psxunit div def
    /YB \pst@tempb exch pop \pst@number\psyunit div def
    /XB \pst@tempb pop \pst@number\psxunit div def
    /YC \pst@tempc exch pop \pst@number\psyunit div def
    /XC \pst@tempc pop \pst@number\psxunit div def
    /YD \pst@tempd exch pop \pst@number\psyunit div def
    /XD \pst@tempd pop \pst@number\psxunit div def
    /dY1 YB YA sub def
    /dX1 XB XA sub def
    /dY2 YD YC sub def
    /dX2 XD XC sub def
    dX1 abs 0.01 lt {
	/m2 dY2 dX2 div def
	XA dup XC sub m2 mul YC add 
    }{
	dX2 abs 0.01 lt {
	    /m1 dY1 dX1 div def
	    XC dup XA sub m1 mul YA add 
	}{%
	    /m1 dY1 dX1 div def
	    /m2 dY2 dX2 div def
	    m1 XA mul m2 XC mul sub YA sub YC add m1 m2 sub div dup
	    XA sub m1 mul YA add 
	} ifelse
    } ifelse ){#5}
}
%
% draw a parallel line
%     #2---------#3
%         #4----------#5(new)  
\def\Parallel{\@ifnextchar[{\pst@Parallel}{\pst@Parallel[]}}
\def\pst@Parallel[#1](#2)(#3)(#4)#5{{%
	\psset{#1}%
	\pst@getcoor{#2}\pst@tempa
	\pst@getcoor{#3}\pst@tempb
	\pst@getcoor{#4}\pst@tempc
	\pnode(!%
		/LengthArrow \psk@optic@length\space def
		\pst@tempa /YA exch \pst@number\psyunit div def
		/XA exch \pst@number\psxunit div def
		\pst@tempb /YB exch \pst@number\psyunit div def
		/XB exch \pst@number\psxunit div def
		\pst@tempc /YC exch \pst@number\psyunit div def
		/XC exch \pst@number\psxunit div def
		/denominateur XB XA sub def
		/numerateur YB YA sub def
		/angleDirectionAB numerateur denominateur Atan def
		/XstartParallel XC LengthArrow angleDirectionAB cos mul add def
		/YstartParallel YC LengthArrow angleDirectionAB sin mul add def
		XstartParallel YstartParallel){#5}
	\psline[#1](#4)(#5)
}}
%
% arrowLine[options](A)(B){n}
% #2---->---->---->---->----#3  #4-arrows inside
\def\arrowLine{\@ifnextchar[{\pst@arrowLine}{\pst@arrowLine[]}}
\def\pst@arrowLine[#1](#2)(#3)#4{{%
	\psset{arrowsize=4pt,arrows=->}% the defaults
	\psset{#1}%
	\def\pst@optic@n{#4}
	\pst@getcoor{#2}\pst@tempa
	\pst@getcoor{#3}\pst@tempb
	\pnode(!%
	    	/YA \pst@tempa exch pop \pst@number\psyunit div def
		/XA \pst@tempa pop \pst@number\psxunit div def
		/YB \pst@tempb exch pop \pst@number\psyunit div def
		/XB \pst@tempb pop \pst@number\psxunit div def
		/dY YB YA sub \pst@optic@n\space 1 add div def
		/dX XB XA sub \pst@optic@n\space 1 add div def
		/Alpha dY dX atan def
		/dYOffset \psk@optic@arrowOffset\space Alpha sin mul def
		/dXOffset \psk@optic@arrowOffset\space Alpha cos mul def
		XA YA ){tempArrowC}
	\multido{\i=1+1}{#4}{%
		\pnode(!%
			XA dX \i\space mul add dXOffset add
			YA dY \i\space mul add dYOffset add){tempArrowB}
		\psline(tempArrowC)(tempArrowB)
		\pnode(tempArrowB){tempArrowC}
    	}
	\psline[arrows=-](tempArrowB)(#3)
}}
%
%   #1------#3------#2
\def\nodeBetween(#1)(#2)#3{%    Herbert 2003/01/05
    \pst@getcoor{#1}\pst@tempa
    \pst@getcoor{#2}\pst@tempb
    \pnode(!%
	/XA \pst@tempa pop \pst@number\psxunit div def
	/YA \pst@tempa exch pop \pst@number\psyunit div def
	/XB \pst@tempb pop \pst@number\psxunit div def
	/YB \pst@tempb exch pop \pst@number\psyunit div def
	XB XA add 2 div YB YA add 2 div){#3}
}
%
% rotateNode(A)
% (A) the node
% #2  the angle
% Herbert Voss <voss@perce.de> 2003-01-26
\def\rotateNode{\pst@rotateNode}
\def\pst@rotateNode(#1)#2{{%
    \pst@getcoor{#1}\pst@tempa
    \def\pst@optic@angle{#2}	% the rotating angle
    \pnode(!%
    	/YA \pst@tempa exch pop \pst@number\psyunit div def
	/XA \pst@tempa pop \pst@number\psxunit div def
	YA 0 eq XA 0 eq and {0 0}{
	    /r XA dup mul YA dup mul add sqrt def
	    /AlphaOld YA XA atan def
	    /AlphaNew AlphaOld \pst@optic@angle\space add def
	    r AlphaNew cos mul r AlphaNew sin mul
	} ifelse ){temp}
    \pnode(temp){#1}
}}
%
\def\rotateTriangle{\pst@rotateTriangle}
\def\pst@rotateTriangle(#1)(#2)(#3)#4{{%
    \rotateNode(#1){#4}
    \rotateNode(#2){#4}
    \rotateNode(#3){#4}
}}
%
\def\rotateFrame{\pst@rotateFrame}
\def\pst@rotateFrame(#1)(#2)(#3)(#4)#5{{%
    \rotateNode(#1){#5}
    \rotateNode(#2){#5}
    \rotateNode(#3){#5}
    \rotateNode(#4){#5}
}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                              %
%                        L E N S E S	                          %
%                                                              %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% A spherical lens is drawn only with a spherical bow
%
\def\lensSPH{\@ifnextchar[{\pst@lensSPH}{\pst@lensSPH[]}}
\def\pst@lensSPH[#1]{{%
	\psset{lensType=CVG,OA=-7,%
		lensHeight=6,%
		lensWidth=1.5,%
		refractB=2}
	\psset{#1}
	\begin{pspicture*}(\psk@optic@xLeft ,\psk@optic@yBottom )
			(\psk@optic@xRight ,\psk@optic@yTop)
	\pnode(! \psk@optic@xLeft\space 0){xLeft}
	\pnode(! \psk@optic@xRight\space 0){xRight}
	\pstVerb{%
		/Height \psk@optic@lensHeight\space 2.0 div def
		/Depth \psk@optic@lensDepth\space def
		/Width \psk@optic@lensWidth\space def
		/Width2 Width 2.0 div def
	}
	\ifx\psk@optic@lensType\Type%	CVG ?
		\pnode(!%
			/radius Width2 dup mul Height dup mul add Width2 div 2 div def
			/XM Width2 radius sub def
			/YM 0 def
			XM YM){Center}
	\else%					DVG ?
		\pnode(!%
        /radius Depth dup mul Height dup mul add Depth div 2.0 div def
        /XM Width2 radius add neg def
        /YM 0 def
        XM YM){Center}
	\fi
% and vice versa
	\pnode(! XM neg 0){Center'}
	\pnode(!%
		/AB \psk@optic@AB\space def
		/OA \psk@optic@OA\space def
		/XO \psk@optic@XO\space def
		/YO \psk@optic@YO\space def
		OA XO add YO){A}
	\pnode(! OA XO add AB YO add){B}
	\pnode(! XO YO){O}
	\pnode(! XO AB YO add){I}
	\begingroup% for the fill option
	\psset{fillstyle=solid,%
		fillcolor=\psk@optic@lensColor,%
		linecolor=\psk@optic@lensColor%
	}
	\rput(! XO YO){%
		\ifx\psk@optic@lensType\Type% CVG
		\pscustom{%
              \parametricplot{\psk@optic@lensHeight}{-\psk@optic@lensHeight}{%
                  /arg t radius 2.0 mul div def 
                  arg 1 arg dup mul sub sqrt atan 
                  cos 1 sub radius mul neg Width2 sub
                  t 2.0 div
		   }
              \parametricplot{-\psk@optic@lensHeight}{\psk@optic@lensHeight}{%
                  /arg t radius 2.0 mul div def 
                  arg 1 arg dup mul sub sqrt atan 
                  cos 1 sub radius mul neg Width2 sub neg
                  t 2.0 div
		   }
	        \fill
		 }%
        \else 
           \pscustom{%
	        % (d+w/2,h/2)->(d-w,h/2)
	        \psline(! Depth Width2 add Height)(! Depth Width2 add neg Height)
	        % (-d-w/2,h/2)->(-d-w/2,-h/2)
	        \parametricplot{\psk@optic@lensHeight}{-\psk@optic@lensHeight}{%
                  /arg t 2.0 div radius div def 
                  arg 1 arg dup mul sub sqrt atan cos 1 sub radius mul Width2 sub 
                  t 2.0 div
	        }
	        % (-d-w/2,-h/2)(d+w/2,-h/2)
	        \psline(! Depth Width2 add neg Height neg)(! Depth Width2 add Height neg)
	        % (d+w/2,-h/2)->(d+w/2,h/2)
	        \parametricplot{-\psk@optic@lensHeight}{\psk@optic@lensHeight}{%
                  /arg t 2.0 div radius div def 
                  1 arg 1 arg dup mul sub sqrt atan cos sub radius mul Width2 add 
                  t 2.0 div
	        }
	        \fill
           }
         \fi%
       }%
	\endgroup
  \ifPst@drawing
    % optical axes
    \psline[linewidth=0.5pt](xLeft)(xRight)
    \psset{dotstyle=|}
    \psdots(Center')
    \uput[-90](Center'){Center'}
    \psdots(Center)
    \uput[-90](Center){Center}
    \psset{linecolor=\psk@optic@rayColor}
    \psline[linewidth=1.5\pslinewidth,arrowinset=0]{->}(A)(B)
    \ifx\psk@optic@lensType\Type
      % the parallel ray
      \lensSPHRay[lensType=CVG]%
         (B)(I){\psk@optic@refractA}{\psk@optic@refractB}{PSPH}
      \ABinterCD(PSPH')(PSPH'')(O)(xRight){F'}
      \pst@getcoor{F'}\pst@tempf
      \pnode(!%
        /XF \pst@tempf pop \pst@number\psxunit div neg def
        /YF \pst@tempf exch pop \pst@number\psyunit div def
	   XF YF){F}
      \psline(B)(PSPH)(PSPH')(F')
      \psOutLine[length=5](PSPH')(F'){PEnd}
      % the center ray
      \lensSPHRay[lensType=CVG]%
        (B)(O){\psk@optic@refractA}{\psk@optic@refractB}{OSPH}
      \ABinterCD(PSPH')(PSPH'')(OSPH')(OSPH''){B'}
      \pnode(B'|0,0){A'}
      \psOutLine[length=5](OSPH')(OSPH''){OEnd}
      \psline(B)(OSPH)(OSPH')(OEnd)
      % the focus ray
      \lensSPHRay[lensType=CVG]%
         (B)(F){\psk@optic@refractA}{\psk@optic@refractB}{FSPH}
      \psOutLine[length=10](FSPH')(FSPH''){FEnd}
      \psline(B)(FSPH)(FSPH')(FEnd)
    \else % the DVG part
      % the parallel ray
      \lensSPHRay[lensType=DVG]%
         (B)(I){\psk@optic@refractA}{\psk@optic@refractB}{PSPH}
      \ABinterCD(PSPH')(PSPH'')(O)(xRight){F}
      \pst@getcoor{F}\pst@tempf
      \pnode(!%
        /XF \pst@tempf pop \pst@number\psxunit div def
        /YF \pst@tempf exch pop \pst@number\psyunit div def
   	   XF neg YF){F'}
      \psOutLine[linestyle=dashed,length=5](F)(PSPH'){PEnd'}
      \psOutLine[linestyle=dashed,length=5](PEnd')(PSPH'){PEnd}
      \psline(B)(PSPH)(PSPH')
      % the center ray
      \lensSPHRay[lensType=DVG]%
          (B)(O){\psk@optic@refractA}{\psk@optic@refractB}{OSPH}
      \ABinterCD(PSPH')(PSPH'')(OSPH')(OSPH''){B'}
      \pnode(B'|0,0){A'}
      \psOutLine(PSPH')(B'){PEnd}
      \psline(B)(OSPH)(OSPH')
      \psOutLine[linestyle=dashed,length=5](OSPH)(OSPH'){OEnd}
      % the focus ray
      \lensSPHRay[lensType=DVG]%
         (B)(F'){\psk@optic@refractA}{\psk@optic@refractB}{FSPH}
      \psline(B)(FSPH)(FSPH')(FSPH'')
      \psOutLine[length=5](FSPH')(FSPH''){FEnd}
      \psOutLine[linestyle=dashed,length=5](FSPH'')(FSPH'){FEnd'}
      \psline[linestyle=dashed](FSPH')(F')
    \fi
    \psdots(F')
    \uput[\psk@optic@spotFi](F'){$\mathrm{\psk@optic@nameFi}$}
    \uput[\psk@optic@spotF](F){$\mathrm{\psk@optic@nameF}$}
    \psline[linewidth=1.5\pslinewidth,arrowinset=0]{->}(A')(B')
    \uput[\psk@optic@spotA](A){$\mathrm{\psk@optic@nameA}$}
    \uput[\psk@optic@spotB](B){$\mathrm{\psk@optic@nameB}$}
    \uput[\psk@optic@spotAi](A'){$\mathrm{\psk@optic@nameAi}$}
    \uput[\psk@optic@spotBi](B'){$\mathrm{\psk@optic@nameBi}$}
    \uput[\psk@optic@spotO](O){$\mathrm{\psk@optic@nameO}$}
  \fi% ifdrawing
\end{pspicture*}
}}
%
% Herbert Voss 2003/02/02
% [#1]    : lensType=CVG/DVG
% (#2)(#3): the ray coordinates
% #4 #5:    the refraction numbers IN and OUT
% #6:       the intersection point
%
\def\lensSPHRay{\@ifnextchar[{\pst@lensSPHRay}{\pst@lensSPHRay[]}}
\def\pst@lensSPHRay[#1](#2)(#3)#4#5#6{{%
  \psset{#1}
  \ifx\psk@optic@lensType\Type% CVG
    \ifPst@rightRay
      \ABinterSPHLens(#2)(#3)(Center){#6}
    \else
      \ABinterSPHLens(#2)(#3)(Center'){#6}
    \fi
  \else
    \ABinterSPHLens(#2)(#3)(Center){#6}
  \fi
%  \psline(! Y mT sub X 1 sub neg)(! Y mT add X 1 add neg)
  \refractionRay(#2)(#6)(! Y mT sub X 1 sub neg)(! Y mT add X 1 add neg){#4}{#5}{tempSPHRay}
  \ifx\psk@optic@lensType\Type% CVG
    \ifPst@rightRay
      \ABinterSPHLens(#6)(tempSPHRay')(Center'){#6'}
    \else
      \ABinterSPHLens(#6)(tempSPHRay')(Center){#6'}
    \fi
  \else
    \ABinterSPHLens(#6)(tempSPHRay')(Center'){#6'}
  \fi
%  \psline(! Y mT sub X 1 sub neg)(! Y mT add X 1 add neg)
  \refractionRay(#6)(#6')(! Y mT sub X 1 sub neg)%
                (! Y mT add X 1 add neg){#5}{#4}{tempSPHRay}
  \pnode(tempSPHRay'){#6''}
}}
%
% Intersection Point of ray and sperical lense
% 2003-02-03 Herbert
% (#1)(#2): the ray coordinates
% (#3):     The center of the sperical
% #4:       the intersection point
%
\def\ABinterSPHLens(#1)(#2)(#3)#4{%
  \pst@getcoor{#1}\pst@tempa
  \pst@getcoor{#2}\pst@tempb
  \pst@getcoor{#3}\pst@tempm
  % calculate the intersection point. we change the coordinates
  \ifx\psk@optic@lensType\Type% CVG
    \pnode(!%
      /YA \pst@tempa pop \pst@number\psxunit div def
      /XA \pst@tempa exch pop \pst@number\psyunit div neg def
      /YB \pst@tempb pop \pst@number\psxunit div def
      /XB \pst@tempb exch pop \pst@number\psyunit div neg def
      /YM \pst@tempm pop \pst@number\psxunit div def
      /XM \pst@tempm exch pop \pst@number\psyunit div neg def
%     /radius YM abs Width2 add def
      /dX XB XA sub def
      dX abs 0.01 lt {
% a horizontal line 
        /Y YM radius dup mul XA dup mul sub sqrt YM 0 gt {sub}{add}ifelse def
        /YSecond YM radius dup mul XA dup mul sub sqrt YM 0 gt {add}{sub}ifelse def
        /X XA def
        /XSecond XA def
        /mT XA radius dup mul XA dup mul sub sqrt div YM 0 lt {neg}if def
        Y X neg
      }{
        /dY YB YA sub def
        /m dY dX div def
        /m21 m dup mul 1 add def
        /klammer YM m XA mul add YA sub def
        /p2neg klammer m mul m21 div def
        /q klammer dup mul radius dup mul sub m21 div def
        /root p2neg dup mul q sub sqrt def
        /X p2neg root YM m mul 0 gt {sub}{add}ifelse def
        /XSecond p2neg root YM m mul 0 gt {add}{sub}ifelse def
        /Y m X XA sub mul YA add def
        /YSecond m XSecond XA sub mul YA add def
        /mT X radius dup mul X dup mul sub sqrt div YM 0 lt {neg}if def
        Y X neg
      } ifelse){#4}
  \else% DVG
    \pnode(!%
      /YA \pst@tempa pop \pst@number\psxunit div def
      /XA \pst@tempa exch pop \pst@number\psyunit div neg def
      /YB \pst@tempb pop \pst@number\psxunit div def
      /XB \pst@tempb exch pop \pst@number\psyunit div neg def
      /YM \pst@tempm pop \pst@number\psxunit div def
      /XM \pst@tempm exch pop \pst@number\psyunit div neg def
%     /radius YM abs Width2 add def
      /dX XB XA sub def
      dX abs 0.01 lt {
% a horizontal line 
        /Y YM radius dup mul XA dup mul sub sqrt YM 0 gt {sub}{add}ifelse def
        /YSecond YM radius dup mul XA dup mul sub sqrt YM 0 gt {add}{sub}ifelse def
        /X XA def
        /mT XA radius dup mul XA dup mul sub sqrt div YM 0 lt {neg}if def
        /XSecond XA def
        Y X neg
      }{
        /dY YB YA sub def
        /m dY dX div def
        /m21 m dup mul 1 add def
        /klammer YM m XA mul add YA sub def
        /p2neg klammer m mul m21 div def
        /q klammer dup mul radius dup mul sub m21 div def
        /root p2neg dup mul q sub sqrt def
        /X p2neg root YM m mul 0 gt {sub}{add}ifelse def
        /XSecond p2neg root YM m mul 0 gt {add}{sub}ifelse def
        /Y m X XA sub mul YA add def
        /YSecond m XSecond XA sub mul YA add def
        /mT X radius dup mul X dup mul sub sqrt div YM 0 lt {neg}if def
        Y X neg
      } ifelse){#4}
  \fi
  \pnode(! YSecond XSecond neg){#4'}
%\arrowLine[linecolor=blue,arrows=->](#4)(#4'){2}
}
%
%fin 26 juin 2001
%Lentille convergente : CVG
%(#2) est l'abscisse du centre optique
\def\lens{\@ifnextchar[{\pst@lens}{\pst@lens[]}}
\def\pst@lens[#1]{{%
  \psset{xLeft=-7.5,xRight=7.5,yBottom=-3,yTop=3}%
  \psset{#1}%
  \pst@killglue
%
% trace les rayons
% calcule la position de l'image
  \begin{pspicture*}(\psk@optic@xLeft,\psk@optic@yBottom)(\psk@optic@xRight,\psk@optic@yTop)
    \pnode(! \psk@optic@xLeft\space 0){xLeft}
    \pnode(! \psk@optic@xRight\space 0){xRight}
    \ifPst@lensTwo
      \pnode(!%
        /OF' \psk@optic@focus\space def
        %/AB \psk@optic@AB\space def
	   /AB A'1B'1 def
        %/OA \psk@optic@OA\space def
        /XO \psk@optic@XO\space def
        /YO \psk@optic@YO\space def
        /OA XO neg XO1 add O1A1' add def
        /TesT OA OF' add def
        TesT 0 eq {/OA OF' neg 0.001 add def} if
        /OA' OA OF' mul OA OF' add div def
        /Gamma OA' OA div def
        /A'B' Gamma AB mul def
        OA' XO add YO){A'}
      \pnode(! OA XO add YO){A}
      \pnode(! OA XO add AB YO add){B}
      \pnode(! OF' XO add YO){F'}
      \pnode(! OF' neg XO add YO){F}
      \pnode(! OA' XO add A'B' YO add){B'}
      \pnode(! XO YO){O}
      \pnode(! XO AB YO add){I}
      \pnode(! XO A'B' YO add){I'}
      \pnode(! \psk@optic@xRight\space A'B' YO add){I1}
      \pnode(! \psk@optic@xRight\space neg A'B' YO add){I2}
    \else
      \pnode(!%
	   /OF' \psk@optic@focus\space def
	   /AB \psk@optic@AB\space def
	   /OA \psk@optic@OA\space def
	   /XO \psk@optic@XO\space def
	   /YO \psk@optic@YO\space def
	   /TesT OA OF' add def
	   TesT 0 eq {/OA OF' neg 0.001 add def} if
	   /OA' OA OF' mul OA OF' add div def
	   /Gamma OA' OA div def
	   /A'B' Gamma AB mul def
	   OA' XO add YO){A'}
      \pnode(! OA XO add YO){A}
      \pnode(! OA XO add AB YO add){B}
      \pnode(! OF' XO add YO){F'}
      \pnode(! OF' neg XO add YO){F}
      \pnode(! OA' XO add A'B' YO add){B'}
      \pnode(! XO YO){O}
      \pnode(! XO AB YO add){I}
      \pnode(! XO A'B' YO add){I'}
      \pnode(! \psk@optic@xRight\space A'B' YO add){I1}
      \pnode(! \psk@optic@xRight\space neg A'B' YO add){I2}
    \fi
    \begingroup
      \ifPst@lensGlass
        \rput(! XO YO){\ifx\psk@optic@lensType\Type\lensCVG\else\lensDVG\fi}%
      \else
        \ifx\psk@optic@lensType\Type
          \psset{arrows=<->}
        \else
          \psset{arrows=>-<}
        \fi
        \psline[linecolor=\psk@optic@lensColor,
          linewidth=\psk@optic@lensWidth,arrowsize=\psk@optic@lensArrowSize,
          arrowinset=\psk@optic@lensArrowInset]%
          (! XO -0.5 \psk@optic@lensHeight\space mul 
             \psk@optic@lensScale\space mul YO add)%
          (! XO 0.5 \psk@optic@lensHeight\space mul 
             \psk@optic@lensScale\space mul YO add)
	 \fi
    \endgroup%
\ifPst@drawing
% axe optique
    \psline(! \psk@optic@xLeft\space YO)(! \psk@optic@xRight\space YO)
    \ifx\psk@optic@lensType\Type
% Position des foyers
	\psdots[dotstyle=|](F')
	\uput[\psk@optic@spotFi](F'){$\mathrm{\psk@optic@nameFi}$}
	\psdots[dotstyle=|](F)
	\uput[\psk@optic@spotF](F){$\mathrm{\psk@optic@nameF}$}
%dessin de l'objet
        \psline[linewidth=1.5\pslinewidth,arrowinset=0]{->}(A)(B)
% dessin de l'image
        \psline[linewidth=1.5\pslinewidth,arrowinset=0]{->}(A')(B')
%dessin des rayons
        \psset{linecolor=\psk@optic@rayColor}
        \pcline(B)(B')
        \Arrows[length=16,arrows=-](B)(O)
        \Arrows(B)(I)
        \psline(B)(I)
        \Arrows[length=10,posStart=0,arrows=-](I)(F')
        \Arrows[posStart=1,arrows=->](I)(F')
        \Arrows[arrows=->>](B)(I')
        \psline(B)(I')(B')
        \Arrows[length=10,arrows=-](I')(B')
        \Arrows[length=2,posStart=0.5,arrows=->>](I')(B')
        %\uput[-45](I'){I'}
        %\uput[45](I){I}
        \uput[\psk@optic@spotA](A){$\mathrm{\psk@optic@nameA}$}
        \uput[\psk@optic@spotB](B){$\mathrm{\psk@optic@nameB}$}
        \uput[\psk@optic@spotAi](A'){$\mathrm{\psk@optic@nameAi}$}
        \uput[\psk@optic@spotBi](B'){$\mathrm{\psk@optic@nameBi}$}
        \uput[\psk@optic@spotO](O){$\mathrm{\psk@optic@nameO}$}
    \else
        %dessin de l'objet
        \psline[linewidth=1.5\pslinewidth,arrowinset=0]{->}(A)(B)
% dessin de l'image
        \psline[linewidth=1.5\pslinewidth,arrowinset=0,linestyle=dashed]{->}(A')(B')
%dessin des rayons
        \psset{linecolor=\psk@optic@rayColor}
        \Arrows[length=16,arrows=-](B)(O)
        \Arrows(B)(I)
        \psline(B)(I)
        \psOutLine[arrows=->,length=1](B')(I){END1}
        \psOutLine[length=5](B')(I){END2}
        \psline[linestyle=dashed](F')(I)
        \Arrows[arrows=->>](B)(I')
        \psline(B)(I')
        \psOutLine[arrows=->>,length=2](B')(I'){END3}
        \psOutLine[length=10](B')(I'){END4}
        \psline[linestyle=dashed](B')(I')
        %\uput[45](I'){I'}
        %\uput[45](I){I}
        \uput[\psk@optic@spotA](A){$\mathrm{\psk@optic@nameA}$}
        \uput[\psk@optic@spotB](B){$\mathrm{\psk@optic@nameB}$}
        \uput[\psk@optic@spotAi](A'){$\mathrm{\psk@optic@nameAi}$}
        \uput[\psk@optic@spotBi](B'){$\mathrm{\psk@optic@nameBi}$}
        \uput[\psk@optic@spotO](O){$\mathrm{\psk@optic@nameO}$}
    \fi
\fi
\end{pspicture*}
}\ignorespaces}
%
% 25 december 2002 Herbert <voss@perce.de>
% make the lenses dynamical to width _and_ height
% \pslens calculates the radius and the angles from the given values
% of lensWidth and lensHeight and draws the lens with it's origin (0,0)
% 
\def\pslensDVG{\pst@object{pslensDVG}}
\def\pslensDVG@i#1#2{%
	\begin@OpenObj
		\pssetlength\pst@dima{#1}%
		\pssetlength\pst@dimb{#2}%
		\addto@pscode{\pslensDVG@ii}%
	\end@OpenObj%
}
\def\pslensDVG@ii{%
	/w \pst@number\pst@dima def% lensWidth
	/wHalbe w 2 div def% half of the width
	/h \pst@number\pst@dimb 2 div def% the half of the height
	/Radius wHalbe 2 div dup mul h dup mul add wHalbe div def
	/x Radius wHalbe 2 div add def
	/y 0 def
	/angleA h x wHalbe sub atan neg def
	/angleB angleA neg def
	wHalbe h moveto
	x y Radius 180 angleA add 180 angleB add arc
	x neg y Radius angleA angleB arc
	wHalbe h lineto
}
%
\def\pslensCVG{\pst@object{pslensCVG}}
\def\pslensCVG@i#1#2{%
	\begin@OpenObj
		\pssetlength\pst@dima{#1}%
		\pssetlength\pst@dimb{#2}%
		\addto@pscode{\pslensCVG@ii}%
	\end@OpenObj%
}
%
\def\pslensCVG@ii{%
	/w \pst@number\pst@dima def% lensWidth
	/wHalbe w 2 div def% half of the width
	/h \pst@number\pst@dimb 2 div def% the half of the height
	/Radius wHalbe dup mul h dup mul add w div def
	/x Radius wHalbe sub def
	/y 0 def
	/angleA h x atan neg def
	/angleB angleA neg def
	0 h moveto
	x y Radius 180 angleA add 180 angleB add arc
	x neg y Radius angleA angleB arc
}
%
%22 juin 2001 / 25 december 2002
%Choisir la forme et la taille de la lentille
%Le dessin de la lentille
%
\def\lensCVG{%
    \scalebox{\psk@optic@lensScale}{%
	\pscustom[linewidth=0.75\pslinewidth]{%
	    \pslensCVG{\psk@optic@lensWidth}{\psk@optic@lensHeight}
    	    \fill[fillstyle=solid,fillcolor=BleuVerre]
	}%
    }%
}
%
\def\lensDVG{%
	\scalebox{\psk@optic@lensScale}{%
		\pscustom[linewidth=0.75\pslinewidth]{%
			\pslensDVG{\psk@optic@lensWidth}{\psk@optic@lensHeight}
			\fill[fillstyle=solid,fillcolor=BleuVerre]%
		}%
	}%
}
%Sauvegarde des points pour le cas d'un
%système à deux lentilles (26 juin 2001)
\def\Transform{%
    \pnode(A){A1}
    \pnode(B){B1}
    \pnode(A'){A'1}
    \pnode(B'){B'1}
    \pnode(O){O1}
    \pnode(F){F1}
    \pnode(F'){F'1}
    \pnode(I){I11}
    \pnode(I'){I'1}
    \pnode(!%
        /XO1 XO def
        /YO1 YO def
        /O1A1' OA' def
        /A'1B'1 A'B' def
        XO1 YO1){factice}
}
%
%intersection d'un rayon avec une lentille
\def\rayInterLens(#1)(#2)#3#4{{%
    \pst@getcoor{#1}\pst@tempa
    \pst@getcoor{#2}\pst@tempb
    \pnode(!%
	/LengthArrow \psk@optic@length\space def
	\pst@tempa /YE1 exch \pst@number\psyunit div def
	/XE1 exch \pst@number\psxunit div def
	\pst@tempb /YB1 exch \pst@number\psyunit div def
	/XB1 exch \pst@number\psxunit div def
	/XO2 #3 def
	/YO2 YB1 YE1 sub
	XB1 XE1 sub div
	XO2 XE1 sub
	mul
	YE1 add
	def
	XO2 YO2){#4}
}}
%
%eye du philatéliste
\def\eye{%
    \psarc[linewidth=2pt](0,2.5){2.5}{215}{270}%
    \psarc[linewidth=2pt](0,-2.5){2.5}{90}{140}%
    \psarc(-2.5,0){1}{-30}{30}%
    \psarc(0,0){1.75}{160}{200}
    \psclip{%
	\pscircle[linestyle=none](0,0){1.75}}
    \pscircle[fillstyle=solid,fillcolor=lightgray](-2.5,0){0.9}
    \endpsclip%
}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                              %
%                    M I R R O R S                             %
%                                                              %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\mirrorCVGRay{\@ifnextchar[{% Herbert 2003/01/05
    \pst@mirrorCVGRay}{\pst@mirrorCVGRay[]}}
\def\pst@mirrorCVGRay[#1](#2)(#3)#4{{%
    \psset{#1}%
%
    \ifx\psk@optic@mirrorType\mirrorType% PARA
      \pst@getcoor{#2}\pst@tempa
      \pst@getcoor{#3}\pst@tempb
      \pnode(!%
	  \psk@optic@mirrorHeight\space dup mul 16 div 
	  \psk@optic@mirrorDepth\space div XO add YO){Focus}
      \pnode(!%
	  /Xmax \psk@optic@mirrorHeight\space 2 div def
	  /Ymax \psk@optic@mirrorDepth\space def
	  /A 2 \psk@optic@mirrorHeight\space div dup mul Ymax mul def
	  /XA \pst@tempa exch pop \pst@number\psyunit div neg def
	  /YA \pst@tempa pop \pst@number\psxunit div def
	  /XB \pst@tempb exch pop \pst@number\psyunit div neg def
	  /YB \pst@tempb pop \pst@number\psxunit div def
	  XB XA sub abs 0.01 lt {A XA dup mul mul XA neg}{
	    /m YB YA sub XB XA sub div def
	    /m2a m A div 2 div def
	    /Root m2a dup mul m XA mul YA sub A div sub sqrt def
	    /Xp m2a Root add XA sub def
	    /Xn m2a Root sub XA sub def
	    /YSp m Xp mul YA add def
	    /XSp Xp XA add neg def
	    /YSn m Xn mul YA add def
	    /XSn Xn XA add neg def
	    YA 0 eq {0 0}{XB XA lt {YSn XSn}{YSp XSp} ifelse} ifelse} ifelse) {#4}
    \pst@getcoor{#2}\pst@tempc% the starting point
    \pst@getcoor{#4}\pst@tempa% the point on the mirror
        \pnode(!%
	/XA \pst@tempa exch pop \pst@number\psyunit div neg def
	/YA \pst@tempa pop \pst@number\psxunit div def
	/XC \pst@tempc exch pop \pst@number\psyunit div neg def
	/YC \pst@tempc pop \pst@number\psxunit div def
% Mittelpunktsstrahl?
	XA abs 0.01 lt YA abs 0.01 lt and {%
	    /NoMoreReflection true def 
	    YC XC
	}{%
	    /DY YA YC sub def
	    /DX XA XC sub def
% Steigung der Tangente im Punkt (XA|YA) y'=2ax
	    /mRay A XA mul 2 mul def
% zugehoeriger Steigungswinkel alpha=arctan y'
	    /Alpha mRay 2 div 0.5 atan def
% das dazugehoerige Lot
	    /AlphaPerp 1.0 neg mRay atan def
% Winkel des einfallenden Strahls
	    /Beta DY DX atan def
% Winkel des ausfallenden Strahls
	    /BetaStrich AlphaPerp 2 mul Beta sub def 
% senkrechte Steigung? cos BetaStrich = 0 
	    BetaStrich cos abs 0.1 lt {%
		/NoMoreReflection true def 
		Ymax 2 mul XA neg
	    }{%
% Steigung
		/m BetaStrich sin BetaStrich cos div def
% Steigung, ab der kein Schnittpunkt mehr stattfindet
		/mMax 2 A mul Xmax mul def
		m abs mMax gt {
% no more second reflection
		    /NoMoreReflection true def 
		    Ymax 2 mul dup YA sub m div XA add neg
		}{
% moegliche 2. Reflektion
		    /NoMoreReflection false def 
% pq Formel anwenden
		    /m2a m A div 2 div def
		    /Root m2a dup mul m XA mul YA sub A div sub sqrt def
		    /X1 m2a Root add def
		    /X2 m2a Root sub def
% be sure, that we get the right point
		    /X XA X1 sub abs 0.01 gt {X1}{X2} ifelse def
		    /Y A X dup mul mul def
    		    Y X neg
		} ifelse 
	    } ifelse
	} ifelse){#4'}
%{\psset{linecolor=cyan}
%\qdisk(#4'){3pt}}
    \pst@getcoor{#2}\pst@tempa
    \pst@getcoor{#4'}\pst@tempb
    \pst@getcoor{#4}\pst@tempc
    \pnode(!%
	/XB \pst@tempb exch pop \pst@number\psyunit div neg def
	/YB \pst@tempb pop \pst@number\psxunit div def
	NoMoreReflection
	    {YB XB neg}{%
	    /XC \pst@tempc exch pop \pst@number\psyunit div neg def
	    /YC \pst@tempc pop \pst@number\psxunit div def
	    /XAtemp \pst@tempa exch pop \pst@number\psyunit div neg def
	    /YAtemp \pst@tempa pop \pst@number\psxunit div def
	    /m1 2 A mul XB mul def
	    /Alpha2 m1 abs 0.01 lt {90}{1 neg m1 atan} ifelse def
	    /Beta XB XC sub abs 0.01 gt 
		{YC YB sub XC XB sub atan}
		{90} ifelse def
	    /Gamma Alpha2 Beta sub def
	    /Delta Alpha2 Gamma add def
	    Delta cos abs 0.01 gt {%
		/mDelta Delta sin Delta cos div def
		/X YAtemp YB sub mDelta div XB add neg def}{%
		/X XB neg def} ifelse
	    m1 abs 0.01 lt {YAtemp XAtemp}{YAtemp X} ifelse 
	} ifelse ){#4''}
    \else
%--------------- A Spherical Mirror -----------------
      \ABinterSPHLens(#2)(#3)(Center){tempRef0}
    	 \pst@getcoor{tempRef0}\pst@tempa
    	 \pst@getcoor{tempRef0'}\pst@tempb
      \pnode(!%
        \pst@tempa /Y1 exch \pst@number\psyunit div def
        /X1 exch \pst@number\psxunit div def
        \pst@tempb /Y2 exch \pst@number\psyunit div def
        /X2 exch \pst@number\psxunit div def
        X1 X2 lt {X1 Y1}{X2 Y2}ifelse ){#4}
      \reflectionRay[#1](#2)(#4){tempRef1}
% we try if we have another intermediate point
      \ABinterSPHLens(#4)(tempRef1)(Center){tempRef2}
    	 \pst@getcoor{#4}\pst@tempa
    	 \pst@getcoor{tempRef2}\pst@tempb
    	 \pst@getcoor{tempRef2'}\pst@tempc
      \pnode(!%
        \pst@tempa /YP exch \pst@number\psyunit div def
        /XP exch \pst@number\psxunit div def
        \pst@tempb /Y1 exch \pst@number\psyunit div def
        /X1 exch \pst@number\psxunit div def
        \pst@tempc /Y2 exch \pst@number\psyunit div def
        /X2 exch \pst@number\psxunit div def
          XP X1 sub abs 0.01 gt {X1 Y1}{X2 Y2}ifelse
      ){#4'}
      \reflectionRay[#1](tempRef1)(#4'){#4''}
    \psset{mirrorType=CVG}% restore
    \fi
    \ifPst@drawing
	\psline[#1](#2)(#4)
	\psline[#1](#4)(#4')
	\psline[#1](#4')(#4'')
    \fi
}}
%
%
\def\mirrorCVG{\@ifnextchar[{%  Herbert Voss 2003/01/05
    \pst@mirrorCVG}{\pst@mirrorCVG[]}}
\def\pst@mirrorCVG[#1]{{%
    \psset{%
		mirrorType=CVG,%
		AB=1.25,OA=4.5,%
		XO=0,YO=0,xLeft=-5,xRight=5,yBottom=-3,yTop=3,%
		mirrorHeight=5,mirrorDepth=1,mirrorWidth=0.2}
    \psset{#1}
    \begin{pspicture}(\psk@optic@xLeft,\psk@optic@yBottom)(\psk@optic@xRight,\psk@optic@yTop)
		\pnode(! \psk@optic@xLeft\space 0){xLeft}
		\pnode(! \psk@optic@xRight\space 0){xRight}
		\pstVerb{%
			/Height \psk@optic@mirrorHeight\space 2.0 div def
			/Depth \psk@optic@mirrorDepth\space def
			/Width \psk@optic@mirrorWidth\space def
		}
		\pnode(!%
			/AB \psk@optic@AB\space def
			/OA \psk@optic@OA\space def
			/XO \psk@optic@XO\space def
			/YO \psk@optic@YO\space def
			OA XO add YO){A}
		\pnode(! OA XO add AB YO add){B}
		\pnode(! XO YO){O}
		\ifx\psk@optic@mirrorType\mirrorType
			 \pnode(!%
				\psk@optic@mirrorHeight\space dup mul 16 div 
				\psk@optic@mirrorDepth\space div XO add YO){Focus}
		\else
			\pnode(!%
				/radius \psk@optic@mirrorHeight\space dup mul 4 div 
				\psk@optic@mirrorDepth\space dup mul add 
				2 div \psk@optic@mirrorDepth\space div def
				radius XO add YO){Center}
			\pnode(! radius 2 div XO add YO){Focus}
		\fi
		\pscustom[fillstyle=solid,%
			fillcolor=\psk@optic@mirrorColor,%
			linecolor=\psk@optic@mirrorColor]{%
			% (d,h/2)->(d-w,h/2)
				\psline(!%
       \psk@optic@mirrorDepth\space \psk@optic@mirrorHeight\space 2 div)(!%
       \psk@optic@mirrorDepth\space \psk@optic@mirrorWidth\space sub 
       \psk@optic@mirrorHeight\space 2 div)
	% (-w/2,h/2)->(-w/2,-h/2)
    \ifx\psk@optic@mirrorType\mirrorType
	\parametricplot{\psk@optic@mirrorHeight}{-\psk@optic@mirrorHeight}{%
	    2 \psk@optic@mirrorHeight\space div dup mul \psk@optic@mirrorDepth\space mul 
	    t 2 exp 4 div mul \psk@optic@mirrorWidth\space sub t 2 div
	}
    \else
	\parametricplot{\psk@optic@mirrorHeight}{-\psk@optic@mirrorHeight}{%
       /radD radius \psk@optic@mirrorWidth\space add def
       radius \psk@optic@mirrorWidth\space sub radD dup mul t 2 div dup mul sub sqrt sub 
       t 2 div 
      }
    \fi
	% (d-w,-h/2)(d,-h/2)
	\psline(!%
       \psk@optic@mirrorDepth\space \psk@optic@mirrorWidth\space sub
       \psk@optic@mirrorHeight\space 2 div neg)(!%
       \psk@optic@mirrorDepth\space \psk@optic@mirrorHeight\space 2 div neg)
	% (w/2,-h/2)->(w/2,h/2)
     \ifx\psk@optic@mirrorType\mirrorType
       \parametricplot{-\psk@optic@mirrorHeight}{\psk@optic@mirrorHeight}{%
	    2 \psk@optic@mirrorHeight\space div dup mul \psk@optic@mirrorDepth\space mul 
	    t 2 exp 4 div mul t 2 div
	}
     \else
	\parametricplot{-\psk@optic@mirrorHeight}{\psk@optic@mirrorHeight}{%
       radius dup dup mul t 2 div dup mul sub sqrt sub 
       t 2 div 
      }
     \fi
	\fill
    }
    \ifPst@drawing
      \psline[linewidth=0.5pt,linecolor=black](O)(xRight)
      \ifx\psk@optic@mirrorType\mirrorType
      \else
        \qdisk(Center){1.5pt}\uput{0.2}[-90](Center){Center}
      \fi
      \qdisk(Focus){2pt}\uput[0](Focus){F}
      \psline[linewidth=3\pslinewidth]{->}(A)(B)
      \psset{%
	    linewidth=\pslinewidth,%
	    linecolor=\psk@optic@rayColor,%
	    arrows=>}
      \uput[0](A){A}
      \uput[0](B){B}
      \pnode(! 1 \psk@optic@AB\space){Dummy}
      \mirrorCVGRay[mirrorType=\psk@optic@mirrorType,drawing=false](B)(Dummy){PR}
     \psOutLine[length=\psk@optic@OA](PR)(PR'){PR''}
	\nodeBetween(B)(PR){Dummy}
	\psline(B)(Dummy)
	\psline(Dummy)(PR)
	\nodeBetween(PR)(PR''){Dummy}
	\psline(PR)(Dummy)
	\psline(Dummy)(PR'')
%
	\mirrorCVGRay[mirrorType=\psk@optic@mirrorType,drawing=false](B)(! 0 0){MR}
     \psOutLine[length=\psk@optic@OA](MR)(MR'){MR''}
	\nodeBetween(B)(MR){Dummy}
	\psline(B)(Dummy)
	\psline(Dummy)(MR)
	\nodeBetween(MR)(MR'){Dummy}
	\psline(MR)(Dummy)
	\psline(Dummy)(MR')
%
	\mirrorCVGRay[mirrorType=\psk@optic@mirrorType,drawing=false](B)(Focus){FR}
     \psOutLine[length=\psk@optic@OA](FR)(FR'){FR''}
	\nodeBetween(B)(FR){Dummy}
	\psline(B)(Dummy)
	\psline(Dummy)(FR)
	\nodeBetween(FR)(FR'){Dummy}
	\psline(FR)(Dummy)
	\psline(Dummy)(FR')
%
     \ABinterCD(PR)(PR')(FR)(FR'){B'}
     \pnode( B'|0,0 ){A'}
     \psline[linecolor=black,linewidth=3\pslinewidth,arrows=->](A')(B')
     \uput[45](A'){A'}
     \uput[-45](B'){B'}
    \fi
    \end{pspicture}
}}
%
%
\def\mirrorDVG{\@ifnextchar[{%  Herbert Voss 2003/01/05
    \pst@mirrorDVG}{\pst@mirrorDVG[]}}
\def\pst@mirrorDVG[#1]{{%
	\psset{%	the defaults
		AB=1.25,OA=4,XO=0,YO=0,%
		xLeft=-5,xRight=5,yBottom=-3,yTop=3,%
		mirrorHeight=5,mirrorDepth=1,mirrorWidth=0.2}
	\psset{#1}%
	\pstVerb{%
		/Height \psk@optic@mirrorHeight\space 2 div def
		/Depth \psk@optic@mirrorDepth\space def
		/Width \psk@optic@mirrorWidth\space def
	}
	\begin{pspicture}(\psk@optic@xLeft,\psk@optic@yBottom)(\psk@optic@xRight,\psk@optic@yTop)
	\pnode(! \psk@optic@xLeft\space 0){xLeft}
	\pnode(! \psk@optic@xRight\space 0){xRight}
	\pnode(!%
		/AB \psk@optic@AB\space def
		/OA \psk@optic@OA\space def
		/XO \psk@optic@XO\space def
		/YO \psk@optic@YO\space def
		OA XO add YO){A}
	\pnode(! OA XO add AB YO add){B}
	\pnode(! XO YO){O}
	\ifx\psk@optic@mirrorType\mirrorType
		\pnode(! Height dup mul 4 div Depth div XO add YO){Focus}
	\else
		\pnode(!%
			/radius Height dup mul Depth dup mul add 2 div Depth div def
			radius neg XO add YO){Center}
		\pnode(! radius 2 div XO add YO){Focus}
	\fi
	\pscustom[fillstyle=solid,%
		fillcolor=\psk@optic@mirrorColor,%
		linecolor=\psk@optic@mirrorColor]{%
		% (d,h/2)->(d-w,h/2)
		\psline(! Depth neg Height)(! Depth Width add neg Height)
		% (-w/2,h/2)->(-w/2,-h/2)
		\ifx\psk@optic@mirrorType\mirrorType
			\parametricplot{\psk@optic@mirrorHeight}{-\psk@optic@mirrorHeight}{%
	    			Depth Height dup mul div t 2 exp 4 div mul neg 
				t 2 div
			}
		\else
			\parametricplot{\psk@optic@mirrorHeight}{-\psk@optic@mirrorHeight}{%
				radius dup mul t 2 div dup mul sub sqrt radius sub 
				t 2 div 
      		}
		\fi
		% (d-w,-h/2)(d,-h/2)
		\psline(! Depth Width add neg Height neg)(! Depth neg Height neg)%
		% (w/2,-h/2)->(w/2,h/2)
		\ifx\psk@optic@mirrorType\mirrorType
			\parametricplot{-\psk@optic@mirrorHeight}{\psk@optic@mirrorHeight}{%
	    			Depth Height dup mul div t 2 exp 4 div mul neg Width sub 
				t 2 div
			}
		\else
			\parametricplot{-\psk@optic@mirrorHeight}{\psk@optic@mirrorHeight}{%
				radius Width sub dup mul t 2 div dup mul sub sqrt radius sub
				t 2 div 
			}
		\fi
	\fill
    }
	\ifPst@drawing
		\psline[linecolor=black,linewidth=0.5pt](xLeft)(xRight)
		\qdisk(Center){2pt}\uput[-90](Center){C}
		\qdisk(Focus){2pt}\uput{0.25}[-90](Focus){F}
		\psline[linewidth=3\pslinewidth,arrowinset=0]{->}(A)(B)
		\psset{%
			linewidth=1.5\pslinewidth,%
			linecolor=\psk@optic@rayColor,%
			arrows=->%
		}
		\uput{0.15}[0](A){A}
		\uput{0.15}[0](B){B}
%
		\mirrorDVGRay[%
			mirrorType=\psk@optic@mirrorType,%
			drawing=false](B)(! 0 \psk@optic@AB){PR}
		\qdisk(PR){1.5pt}\uput{0.2}[180](PR){PR}
		\qdisk(PR'){1.5pt}\uput{0.2}[0](PR'){PR'}
		\nodeBetween(B)(PR){PDummy}
		\psline(B)(PDummy)
		\psline(PDummy)(PR)
		\psline[arrows=-, linestyle=dotted](Focus)(PR)
		\psOutLine[arrows=-,linestyle=dotted](P)(Focus){PBegin}
		\psline(PR)(PR')
%
		\mirrorDVGRay[%
			mirrorType=\psk@optic@mirrorType,%
			drawing=false](B)(! 0 0){MR}
		\qdisk(MR){1.5pt}\uput{0.2}[180](MR){MR}
		\qdisk(MR'){1.5pt}\uput{0.2}[0](MR'){MR'}
		\nodeBetween(B)(! 0 0){MDummy}
		\psline(B)(MDummy)
		\psline(MDummy)(! 0 0)
		\psline(MR)(MR')
%
		\mirrorDVGRay[%
			mirrorType=\psk@optic@mirrorType,%
			drawing=false](B)(Focus){FR}
		\qdisk(FR){1.5pt}\uput{0.2}[180](FR){FR}
		\qdisk(FR'){1.5pt}\uput{0.2}[0](FR'){FR'}
		\nodeBetween(B)(FR){Dummy}
		\psline(B)(Dummy)
		\psline(Dummy)(FR)
		\psline(FR)(FR')
		\psline[arrows=-,linestyle=dotted](Focus)(FR)
		\psOutLine[arrows=-, linestyle=dotted](FR)(Focus){PBegin}
    \fi
    \end{pspicture}
}}
%
\def\mirrorDVGRay{\@ifnextchar[{%  Herbert Voss 2003/01/05
    \pst@mirrorDVGRay}{\pst@mirrorDVGRay[]}}
\def\pst@mirrorDVGRay[#1](#2)(#3)#4{{%
	\psset{#1}%
	\pnode(!%
		\psk@optic@mirrorHeight\space dup mul 16 div 
		\psk@optic@mirrorDepth\space div neg 0){Focus}
	\ifx\psk@optic@mirrorType\mirrorType
		\pst@getcoor{#2}\pst@tempa
		\pst@getcoor{#3}\pst@tempb
		\pnode(!%
		/A 2 \psk@optic@mirrorHeight\space div dup mul \psk@optic@mirrorDepth\space mul neg def
		/XA \pst@tempa exch pop \pst@number\psyunit div neg def
		/YA \pst@tempa pop \pst@number\psxunit div def
		/XB \pst@tempb exch pop \pst@number\psyunit div neg def
		/YB \pst@tempb pop \pst@number\psxunit div def
		XB abs 0.001 lt YB abs 0.001 lt and 
	    		{ 0 0 }{
	    XB XA sub abs 0.01 lt 
		{A XA dup mul mul XA neg}{
		/Xmax \psk@optic@mirrorHeight\space 2 div def
		/m YB YA sub XB XA sub div def
		/m2a m A div 2 div def
		/Root m2a dup mul m XA mul YA sub A div sub sqrt def
		/X1 m2a Root add def
		/X2 m2a Root sub def
		/X XB X1 sub abs XB X2 sub abs lt 
	    	    {X1}{X2} ifelse def
		/Y A X dup mul mul def
		X abs Xmax lt 
	    	    {Y X neg}
	    	    {A Xmax dup mul mul Xmax neg} ifelse
	    } ifelse
	} ifelse){#4}
    % #4 is the point on the mirror
    \pst@getcoor{#2}\pst@tempc% the starting point
    \pst@getcoor{#4}\pst@tempa% the point on the mirror
    \pst@getcoor{Focus}\pst@tempf% the point on the mirror
    \pnode(!
	/XA \pst@tempa exch pop \pst@number\psyunit div neg def
	/YA \pst@tempa pop \pst@number\psxunit div def
	/XC \pst@tempc exch pop \pst@number\psyunit div neg def
	/YC \pst@tempc pop \pst@number\psxunit div def
	XA abs 0.001 lt YA abs 0.001 lt and 
	    {YC XC}{
	    /YF \pst@tempf pop \pst@number\psxunit div def
	    /DY YA YC sub def
	    /DX XA XC sub def 
	    /Alpha A XA mul 0.5 atan def
	    /Delta 180 DY DX atan sub Alpha 2 mul add def 
	    Delta round cvi 90 mod 0 eq {YC XA neg}{
		/m DX abs 0.01 lt 
		    {YA YF sub XA div}
		    {Delta sin Delta cos div} ifelse def
		/X \psk@optic@length\space Delta cos mul neg XA add def
		/Y \psk@optic@length\space Delta sin mul neg YA add def
		Y X neg
	    } ifelse
	} ifelse){#4'}% second point on the mirror
    \else
%--------------- A Spherical Mirror -----------------
      \ABinterSPHLens(#2)(#3)(Center){tempRef0}
    	 \pst@getcoor{tempRef0}\pst@tempa
    	 \pst@getcoor{tempRef0'}\pst@tempb
      \pnode(!%
        \pst@tempa /Y1 exch \pst@number\psyunit div def
        /X1 exch \pst@number\psxunit div def
        \pst@tempb /Y2 exch \pst@number\psyunit div def
        /X2 exch \pst@number\psxunit div def
        X1 X2 gt {X1 Y1}{X2 Y2}ifelse ){#4}
      \reflectionRay[mirrorType=SPH](#2)(#4){tempRef1}
	\pnode(tempRef1){#4'}
    \fi
    \ifPst@drawing
	\psline[#1](#2)(#4)(#4')
    \fi
}}
%
% HEadlight Herbert <voss@perce.de> 2003/01/23
%
\def\beamLight{\@ifnextchar[{\pst@beamLight}{\pst@beamLight[]}}
\def\pst@beamLight[#1]{{%
	\psset{xLeft=-5,xRight=5,yBottom=-5,yTop=5,%
		drawing=false}% 	the defaults
	\psset{#1}%
\begin{pspicture*}(\psk@optic@xLeft,\psk@optic@yBottom)(\psk@optic@xRight,\psk@optic@yTop)
	\rput(0,0){%
		\mirrorCVG[#1]%
	}
	\psline[linewidth=0.1cm]%
		(!\psk@optic@mirrorDepth\space \psk@optic@mirrorHeight\space 2 div neg)%
		(!\psk@optic@mirrorDepth\space \psk@optic@mirrorHeight\space 2 div)
	\psset{linewidth=0.75mm,fillstyle=solid}
	\psline(-1.1,1)(0.2,1)
	\psline(-1.1,-1)(0.2,-1)
	\pscurve(0.2,0.75)(1.6,1.5)(3,1)(3.5,0)(3,-1)(1.6,-1.5)(0.2,-0.75)
	\psframe(-1.1,-0.85)(0.2,0.85)
	\psframe(0.2,-0.3)(0.5,0.3)
	\psline(-1.1,-0.85)(-1.4,-0.6)(-1.4,0.6)(-1.1,0.85)
	\psline(0,0)(2.9,0)(2.9,0.5)(0.9,0.5)(0.9,0)%
	\psline(3.0,0)(3.0,-0.3)(2.5,-0.3)(2.2,0.15)(2,-0.15)%
		(1.8,0.15)(1.6,-0.15)(1.4,0.15)(1.2,-0.15)(1,0.15)%
	\psline[linecolor=black,linewidth=0.5pt,linestyle=dashed](-1.75,0)(10,0)
\end{pspicture*}
}}
%
%
%Telescope
%2 juillet 2001
%
\def\mirrorTwo{%
	\psframe[linestyle=none,%
		fillstyle=vlines,%
		hatchwidth=0.5\pslinewidth,%
		hatchsep=3\pslinewidth](-1,0)(1,0.2)
    \psline[linewidth=1.5\pslinewidth](-1,0)(1,0)%
}
%
\def\telescope{\@ifnextchar[{\pst@telescope}{\pst@telescope[]}}
\def\pst@telescope[#1]{{%
    \psset{xLeft=-0.5,xRight=11,yBottom=-6,yTop=2}% the default
    \psset{#1}%
    \pstVerb{%
	/mirrorFocus \psk@optic@mirrorFocus\space def
	/Coeff mirrorFocus 4 mul def
	/mirrorTwoAngle \psk@optic@mirrorTwoAngle\space def
	/posMirrorTwo \psk@optic@posMirrorTwo\space def
    }%
%
\begin{pspicture}*(\psk@optic@xLeft,\psk@optic@yBottom)(\psk@optic@xRight,\psk@optic@yTop)
	\rput(0,0){%
	    \mirrorCVG[%
		mirrorHeight=4,%
		mirrorWidth=0.25,%
		mirrorDepth=0.25,%
		drawing=false]%
	}
	\pnode(! \psk@optic@xLeft\space 0){xLeft}
	\pnode(! \psk@optic@xRight\space 0){xRight}
	\psline[linewidth=0.5\pslinewidth](11,0)
	\pnode(! 1.5 dup mul Coeff div 1.5){P1}
	\pnode(! 1.5 dup mul Coeff div 1.5 neg){P2}
	\pnode(! mirrorFocus 0){mirrorFocusNode}
	\pnode(! posMirrorTwo 1 mirrorTwoAngle cos mul sub
		1 mirrorTwoAngle sin mul){UpMirror2}
	\pnode(! posMirrorTwo 1 mirrorTwoAngle cos mul add
		1 mirrorTwoAngle sin mul neg){DownMirror2}
	\ABinterCD(P1)(mirrorFocusNode)(UpMirror2)(DownMirror2){Inter1}
	\ABinterCD(P2)(mirrorFocusNode)(UpMirror2)(DownMirror2){Inter2}
	\pnode(!%
		 \psk@optic@posMirrorTwo\space posMirrorTwo mirrorFocus sub){ocularFocusNode}
	{%
	    \psset{linecolor=red}
	    \Arrows[arrows=->,arrowsize=0.2](11,1.5)(P1)
	    \Arrows[arrows=->,arrowsize=0.2](P1)(Inter1)
%
	    \Arrows[arrows=->>,arrowsize=0.2](11,-1.5)(P2)
	    \Arrows[arrows=->>,arrowsize=0.2](P2)(Inter2)
	    \psline[linestyle=dashed](Inter2)(mirrorFocusNode)
	    \pnode(! 5 \psk@optic@posMirrorTwo\space 2 sub neg){ocularLeft}
	    \pnode(! 7 \psk@optic@posMirrorTwo\space 2 sub neg){ocularRight}
	    \ABinterCD(Inter1)(ocularFocusNode)(ocularLeft)(ocularRight){FO1}
	    \ABinterCD(Inter2)(ocularFocusNode)(ocularLeft)(ocularRight){FO2}
	    \Arrows[arrows=->>,arrowsize=0.2,length=1](Inter2)(FO2)
	    \psline(11,-1.5)(P2)(Inter2)(FO2)
	    \Arrows[arrows=->,arrowsize=0.2](Inter1)(ocularFocusNode)
	    \psline[linestyle=dashed](Inter1)(mirrorFocusNode)
	    \psline(11,1.5)(P1)(Inter1)(FO1)
	}
	\rput{-\psk@optic@mirrorTwoAngle}(\psk@optic@posMirrorTwo,0){\mirrorTwo}
	\uput[90](mirrorFocusNode){$\mathrm{F_1}$}
	\uput[180](ocularFocusNode){$\mathrm{F_2}$}
	\rput{90}(!%
	    \psk@optic@posMirrorTwo\space 
	    \psk@optic@posMirrorTwo\space 2 sub neg){%
		\scalebox{0.5 0.4}{\lens[lensWidth=0.4,lensGlass=true,drawing=false]}}
	\pnode(0,2){Aux1}
	\pnode(0,-2){Aux2}
	\Parallel[length=1](Aux1)(Aux2)(FO1){Eye1}
	\Parallel[length=1](Aux1)(Aux2)(FO2){Eye2}
	{%
	    \psset{linecolor=red,arrowsize=0.2,length=0.7}
	    \psline[linecolor=red](FO1)(Eye1)
	    \psline[linecolor=red](FO2)(Eye2)
	    \Arrows[arrows=->](FO1)(Eye1)
	    \Arrows[arrows=->>](FO2)(Eye2)%
	}
	\rput{-90}(!%
	    \psk@optic@posMirrorTwo\space 
	    \psk@optic@posMirrorTwo\space neg){\scalebox{0.6}{\eye}}
    \end{pspicture}
}}
%
%Images et réflexions sur un miroir plan
%(#1) coordonnées du point objet (XA,YA)
%(#2) coordonnées d'une extrémité du miroir (X1,Y1)
%(#3) coordonnées de l'autre extrémité du miroir (X2,Y2)
%{#4} nom de l'image A'
%
\def\planMirrorRay(#1)(#2)(#3)#4{{%
\pst@getcoor{#1}\pst@tempa
\pst@getcoor{#2}\pst@tempb
\pst@getcoor{#3}\pst@tempc
\pnode(!%
    \pst@tempa /YA exch \pst@number\psyunit div def
    /XA exch \pst@number\psxunit div def
    \pst@tempb /Y1 exch \pst@number\psyunit div def
    /X1 exch \pst@number\psxunit div def
    \pst@tempc /Y2 exch \pst@number\psyunit div def
    /X2 exch \pst@number\psxunit div def
    /Dx X2 X1 sub def
    /Dy Y2 Y1 sub def
    /xH XA Dx Dx mul mul
        X1 Dy Dy mul mul
        add
        YA Y1 sub Dx Dy mul mul
        add
        Dx Dx mul Dy Dy mul add
        div
    def
    /yH YA Dy Dy mul mul
        Y1 Dx Dx mul mul
        add
        XA X1 sub Dx Dy mul mul
        add
        Dx dup mul Dy dup mul add
        div
    def
    /xA' 2 xH mul XA sub def
    /yA' 2 yH mul YA sub def
    /D12 Dx Dx mul Dy Dy mul add sqrt def
    xA' yA' moveto
    xH yH rlineto
    xA' yA'){#4}
}}
%
% 2002/12/27
%
\def\symPlan(#1)(#2){\pst@killglue\pst@makebox{\symPlan@(#1)(#2)}}%
\def\symPlan@(#1)(#2){{%
    \pst@getcoor{#1}\pst@tempa%
    \pst@getcoor{#2}\pst@tempb%
    \leavevmode
    \hbox{%
	\pnode(!%
	    \pst@tempa /Y1 exch def
	    /X1 exch def
	    \pst@tempb /Y2 exch def
	    /X2 exch def
	    /DX X2 X1 sub def
	    /DY Y2 Y1 sub def
	    /D12 DX dup mul DY dup mul add def
	    /ax 2 DX dup mul mul D12 div 1 sub def
	    /by 2 DX DY mul mul D12 div def
	    /cx by def
	    /dy 2 DY dup mul mul D12 div 1 sub def
	    /tx X1 DY dup mul mul
	    Y1 DX DY mul mul sub
	    2 mul
	    D12 div
	    def
	    /ty Y1 DX dup mul mul
	    X1 DX DY mul mul sub
	    2 mul
	    D12 div
	    def
	    X1 Y1){Factice}%
	\pst@Verb{%
	    { [ax by cx dy tx ty] concat
	    } \tx@TMChange}%
	\box\pst@hbox
	\pst@Verb{\tx@TMRestore}}%
}}
%
% refractionRay[options](A)(B)(C)(D){rNoA}{rNoB}{E}
% (A)(B) the ray nodes
% (C)(D) the nodes of the other material
% {rNoA}{rNoB} the refraction numbers
% {E} the intermediate node of the ray and the material
% {E'} the end node of the ray
%
% Herbert Voss <voss@perce.de> 2003-01-26
%
\def\refractionRay{\@ifnextchar[{\pst@refractionRay}{\pst@refractionRay[]}}
\def\pst@refractionRay[#1](#2)(#3)(#4)(#5)#6#7#8{{%
    \psset{#1}
    \pst@getcoor{#2}\pst@tempa
    \pst@getcoor{#3}\pst@tempb
    \pst@getcoor{#4}\pst@tempc
    \pst@getcoor{#5}\pst@tempd
    \ABinterCD(#2)(#3)(#4)(#5){#8}
%\psset{linecolor=black}
%\qdisk(#8){2pt}
% #8 is the point on the material
    \pst@getcoor{#8}\pst@tempp
    \def\pst@optic@cIn{#6}	% refraction number 1
    \def\pst@optic@cOut{#7}	% refraction number 2
    \pnode(!%
    	/YA \pst@tempa exch pop \pst@number\psyunit div def
	/XA \pst@tempa pop \pst@number\psxunit div def
	/YB \pst@tempb exch pop \pst@number\psyunit div def
	/XB \pst@tempb pop \pst@number\psxunit div def
    	/YC \pst@tempc exch pop \pst@number\psyunit div def
	/XC \pst@tempc pop \pst@number\psxunit div def
	/YD \pst@tempd exch pop \pst@number\psyunit div def
	/XD \pst@tempd pop \pst@number\psxunit div def
	/YP \pst@tempp exch pop \pst@number\psyunit div def
	/XP \pst@tempp pop \pst@number\psxunit div def
	/dY1 YP YA sub def
	/dX1 XP XA sub def
	/dY2 YD YC sub def
	/dX2 XD XC sub def
% the gradient of the material (if negativ then it must be the nominator)
	/Gamma dY2 dX2 mul 0 lt {dY2 abs neg dX2 abs}{dY2 dX2} ifelse atan def
% the perpendicular line is: 90°-Gamma
	/GammaStrich 90 Gamma sub def
% the angle of the incoming ray
	/AlphaStrich dY1 dX1 atan def
% the same relative to the material
	/Alpha 90 AlphaStrich sub Gamma add def
% the angle of the outgoing ray relative to the material
% the law of Snell: sin(Alpha)/sin(Beta) = n2/n1
% sin(Beta)>1 is a total reflection instead of a refraction
	/sinBeta \pst@optic@cIn\space \pst@optic@cOut\space div Alpha sin mul def
	sinBeta abs 1 le{
		/Root 1 sinBeta dup mul sub sqrt def
		/Beta sinBeta Root atan def
	}{
		/Beta 180 Alpha sub def
	} ifelse
% the same absolute
	/BetaStrich 90 Gamma sub Beta add def 
% Determine the intermediate point
	XP BetaStrich cos sub
	YP BetaStrich sin add ){#8'}
%\qdisk(#8){5pt}
}}
%
% Herbert Voss <voss@perce.de> 2003-02-10
%
% reflectionRay[options](A)(B){C}
% options: the type of
% (A)(B) the ray nodes
% {C} the intermediate node of the ray and the material
% {C'} the end node of the reflected ray
%
\def\reflectionRay{\@ifnextchar[{\pst@reflectionRay}{\pst@reflectionRay[]}}
\def\pst@reflectionRay[#1](#2)(#3)#4{{%
	\psset{#1}
	\pst@getcoor{#2}\pst@tempa% the starting point
	\pst@getcoor{#3}\pst@tempp% the point on the mirror
	\pst@getcoor{Center}\pst@tempc% the center/focus of the mirror
	\ifx\psk@optic@mirrorType\mirrorType%  Parabolic
	\else% Spherical
  \pnode(!%
        /XA \pst@tempa exch pop \pst@number\psyunit div neg def
        /YA \pst@tempa pop \pst@number\psxunit div def
        /XC \pst@tempc exch pop \pst@number\psyunit div neg def
        /YC \pst@tempc pop \pst@number\psxunit div def
        /XP \pst@tempp exch pop \pst@number\psyunit div neg def
        /YP \pst@tempp pop \pst@number\psxunit div def
        /dY1 YA YP sub def
        /dX1 XA XP sub def
	   /signum YP 0 lt {-1}{1}ifelse def
% the gradient of the point. radius must be defined
        /root radius dup mul XP dup mul sub sqrt def
        /Gamma XP signum mul root atan 180 sub def
% the angle of the incoming ray
        /AlphaStrich dY1 dX1 atan 180 sub def
% the same relative to the material
        /Alpha 90 AlphaStrich sub Gamma add def
% the angle of the outgoing ray absolute
%       /BetaStrich Alpha 2 mul AlphaStrich sub def
        /BetaStrich Gamma Alpha add 90 sub def
% Determine the intermediate point
        YP BetaStrich sin add XP BetaStrich cos add neg){#4}
	\fi
}}
%
\catcode`\@=\PstAtCode\relax
%
%% END: pst-optic.tex
\endinput