%%%% $Id: pst-optic.tex 716 2023-05-07 18:37:07Z herbert $ %% This is file `pst-optic.tex', %% %% IMPORTANT NOTICE: %% %% Package `pst-optic.tex' %% %% Manuel Luque (France) %% Herbert Voss (Germany) %% %% 2023-05-07 %% %% 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, pst-plot, pst-grad, pst-3d, % pst-math, pst-xkey, multido packages \ifx\PSTricksLoaded\endinput\else \input pstricks.tex\fi \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\PSTGradLoaded\endinput\else \input pst-grad.tex\fi \ifx\PSTmathLoaded\endinput\else \input pst-math.tex\fi \ifx\PSTMultidoLoaded\endinput\else\input multido.tex\fi \ifx\PSTXKeyLoaded\endinput\else \input pst-xkey\fi % \def\fileversion{1.02a} \def\filedate{2023/05/07} \message{`PST-Optic' v\fileversion, \filedate\space (Manuel Luque and Herbert Voss)} % \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 ----------------- % \define@boolkey[psset]{pst-optic}[Pst@]{lensTwo}[false]{} % is a second lens present? \define@boolkey[psset]{pst-optic}[Pst@]{lensGlass}[true]{}% draw a _real_ lens? \define@boolkey[psset]{pst-optic}[Pst@]{onlyrays}[true]{}% draw only the rays? \define@boolkey[psset]{pst-optic}[Pst@]{drawing}[true]{} % draw the nodes and rays? \define@boolkey[psset]{pst-optic}[Pst@]{rightRay}[false]{}% a ray on the right side? % \psset[pst-optic]{lensGlass,drawing,lensTwo,rightRay,onlyrays=false} % % ------- the global definitions for the pspicture frame ------ % \define@key[psset]{pst-optic}{xLeft}[-7.5]{\def\psk@optic@xLeft{#1}} \define@key[psset]{pst-optic}{xRight}[7.5]{\def\psk@optic@xRight{#1}} \define@key[psset]{pst-optic}{yBottom}[-3.0]{\def\psk@optic@yBottom{#1}} \define@key[psset]{pst-optic}{yTop}[3.0]{\def\psk@optic@yTop{#1}} \psset[pst-optic]{xLeft=-7.5,xRight=7.5,yBottom=-3.0,yTop=3.0} % % ---------------- the lenses ----------------- % \define@key[psset]{pst-optic}{lensType}[CVG]{\def\psk@optic@lensType{#1}}% CVG|DVG|PCVG|PDVG \define@key[psset]{pst-optic}{lensColor}[lightgray]{\def\psk@optic@lensColor{#1}} \define@key[psset]{pst-optic}{lensWidth}[0.5]{\def\psk@optic@lensWidth{#1}}% the thichness of the lens \define@key[psset]{pst-optic}{lensDepth}[1]{\def\psk@optic@lensDepth{#1}} \define@key[psset]{pst-optic}{lensHeight}[5]{\def\psk@optic@lensHeight{#1}}% the TOTAL height of the lens \define@key[psset]{pst-optic}{lensScale}[1]{\def\psk@optic@lensScale{#1}}% more or less obsolete \define@key[psset]{pst-optic}{lensArrowSize}[0.2]{\def\psk@optic@lensArrowSize{#1}}% for the AB,... Arrows \define@key[psset]{pst-optic}{lensArrowInset}[0.5]{\def\psk@optic@lensArrowInset{#1}} \def\lensTypeCVG{CVG} \def\lensTypeDVG{DVG} \def\lensTypePCVG{PCVG} \def\lensTypePDVG{PDVG} \psset[pst-optic]{lensType=CVG,lensColor=lightgray,lensWidth=0.5,lensDepth=1, lensHeight=5,lensScale=1,lensArrowSize=0.2,lensArrowInset=0.5} % % ---------------- the mirrors ----------------- % \define@key[psset]{pst-optic}{mirrorType}[CVG]{\def\psk@optic@mirrorType{#1}}% PLAN|PARAbolic|SPHerical \define@key[psset]{pst-optic}{mirrorDepth}[1]{\def\psk@optic@mirrorDepth{#1}} \define@key[psset]{pst-optic}{mirrorHeight}[5]{\def\psk@optic@mirrorHeight{#1}}% it's the TOTAL height \define@key[psset]{pst-optic}{mirrorWidth}[0.25]{\def\psk@optic@mirrorWidth{#1}} \define@key[psset]{pst-optic}{mirrorColor}[lightgray]{\def\psk@optic@mirrorColor{#1}} \define@key[psset]{pst-optic}{mirrorFocus}[8]{\def\psk@optic@mirrorFocus{#1}} \define@key[psset]{pst-optic}{posMirrorTwo}[6]{\def\psk@optic@posMirrorTwo{#1}}% a sencond mirror? (telescope) \define@key[psset]{pst-optic}{mirrorTwoAngle}[45]{\def\psk@optic@mirrorTwoAngle{#1}}% the angle for the 2. plan mirror (telescope) \def\mirrorType{CVG} \psset[pst-optic]{mirrorType=CVG,mirrorDepth=1,mirrorHeight=5,mirrorWidth=0.25, mirrorFocus=8,mirrorTwoAngle=45,posMirrorTwo=6,mirrorColor=lightgray} % % -------------- the refrectionnumbers ------------- % \define@key[psset]{pst-optic}{refractA}[1]{\def\psk@optic@refractA{#1}} \define@key[psset]{pst-optic}{refractB}[1.41]{\def\psk@optic@refractB{#1}} \psset[pst-optic]{refractA=1,refractB=1.41} % % -------------- the length and node definitions ------------- % \define@key[psset]{pst-optic}{XO}[0]{\def\psk@optic@XO{#1}}% the X-offset \define@key[psset]{pst-optic}{YO}[0]{\def\psk@optic@YO{#1}}% the y-offset \define@key[psset]{pst-optic}{posStart}[0]{\def\psk@optic@posStart{#1}}% where the arrows start \define@key[psset]{pst-optic}{length}[2]{\def\psk@optic@length{#1}}% the length of the before|outlines \define@key[psset]{pst-optic}{focus}[2]{\def\psk@optic@focus{#1}}% for lenses/mirrors with a fixed focus \define@key[psset]{pst-optic}{AB}[1]{\def\psk@optic@AB{#1}}% the length of the object arrow \define@key[psset]{pst-optic}{OA}[-3]{\def\psk@optic@OA{#1}}% the xcoordinate of the object arrow \define@key[psset]{pst-optic}{arrowOffset}[0]{\def\psk@optic@arrowOffset{#1}}%offset for \arrowLine % \psset[pst-optic]{XO=0,YO=0,OA=-3,posStart=0,length=2,focus=2,AB=1,arrowOffset=0} % \define@key[psset]{pst-optic}{nameA}[A]{\def\psk@optic@nameA{#1}}% start of the object arrow \define@key[psset]{pst-optic}{spotA}[270]{\def\psk@optic@spotA{#1}}% where to draw the label \define@key[psset]{pst-optic}{nameB}[B]{\def\psk@optic@nameB{#1}} \define@key[psset]{pst-optic}{spotB}[90]{\def\psk@optic@spotB{#1}} \define@key[psset]{pst-optic}{nameF}[F]{\def\psk@optic@nameF{#1}} \define@key[psset]{pst-optic}{spotF}[270]{\def\psk@optic@spotF{#1}} \define@key[psset]{pst-optic}{nameO}[O]{\def\psk@optic@nameO{#1}} \define@key[psset]{pst-optic}{spotO}[225]{\def\psk@optic@spotO{#1}} \define@key[psset]{pst-optic}{nameAi}[A']{\def\psk@optic@nameAi{#1}} \define@key[psset]{pst-optic}{spotAi}[90]{\def\psk@optic@spotAi{#1}} \define@key[psset]{pst-optic}{nameBi}[B']{\def\psk@optic@nameBi{#1}} \define@key[psset]{pst-optic}{spotBi}[270]{\def\psk@optic@spotBi{#1}} \define@key[psset]{pst-optic}{nameFi}[F']{\def\psk@optic@nameFi{#1}} \define@key[psset]{pst-optic}{spotFi}[270]{\def\psk@optic@spotFi{#1}} % \psset[pst-optic]{nameA=A,spotA=270,nameB=B,spotB=90,nameF=F,spotF=270, nameO=O,spotO=225,nameAi=A',spotAi=90,nameBi=B',spotBi=270, nameFi=F',spotFi=270} % % -------------------- colors/fillstyles ------------------- % \definecolor{BleuVerre}{cmyk}{0.2,0,0,0} \definecolor{JauneVert}{cmyk}{0.3,0,1,0} \newpsstyle{rayuresJaunes}{fillstyle=hlines,hatchsep=2\pslinewidth,hatchcolor=JauneVert} \define@key[psset]{pst-optic}{rayColor}[red]{\pst@getcolor{#1}\psk@optic@rayColor} \psset[pst-optic]{rayColor=red} \define@key[psset]{pst-optic}{rayWidth}[1.5\pslinewidth]{\def\psk@optic@rayWidth{#1}} \psset[pst-optic]{rayWidth=1.5\pslinewidth} % \newpsstyle{opticalAxis}{linewidth=0.5pt,linecolor=black,linestyle=solid} % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 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)% }\ignorespaces} % % 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)% }\ignorespaces} % % 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) }\ignorespaces} % % #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 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} }\ignorespaces} % \def\rotateTriangle{\pst@rotateTriangle} \def\pst@rotateTriangle(#1)(#2)(#3)#4{{% \rotateNode(#1){#4} \rotateNode(#2){#4} \rotateNode(#3){#4} }\ignorespaces} % \def\rotateFrame{\pst@rotateFrame} \def\pst@rotateFrame(#1)(#2)(#3)(#4)#5{{% \rotateNode(#1){#5} \rotateNode(#2){#5} \rotateNode(#3){#5} \rotateNode(#4){#5} }\ignorespaces} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % 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[pst-optic]{lensType=CVG,OA=-7,% lensHeight=6,% lensWidth=1.5,% refractB=2} \ifx\relax#1\relax \else\psset[pst-optic,pstricks]{#1}\fi \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\lensTypeCVG% 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\lensTypeCVG% 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[style=opticalAxis](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\lensTypeCVG % 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*}% }\ignorespaces} % % 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[pst-optic,pstricks]{#1} \ifx\psk@optic@lensType\lensTypeCVG% 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\lensTypeCVG% 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''} }\ignorespaces} % % 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\lensTypeCVG% 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} } % \def\pst@drawDVGRays{% %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){$\mathrm{\psk@optic@nameO}$}% } \def\pst@drawCVGRays{% % 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){$\mathrm{\psk@optic@nameO}$} } %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[pst-optic]{xLeft=-7.5,xRight=7.5,yBottom=-3,yTop=3}% \psset[pst-optic,pstricks]{#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% \ifPst@onlyrays\else \begingroup% \ifPst@lensGlass \rput(! XO YO){% \ifx\psk@optic@lensType\lensTypeCVG\lensCVG% \else\ifx\psk@optic@lensType\lensTypePCVG\lensCVG \else\lensDVG\fi\fi}% \else% \ifx\psk@optic@lensType\lensTypeDVG\psset{arrows=>-<}\else \ifx\psk@optic@lensType\lensTypePDVG\psset{arrows=>-<}\else\psset{arrows=<->} \fi\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 \fi \ifPst@drawing % axe optique \psline[style=opticalAxis](! \psk@optic@xLeft\space YO)(! \psk@optic@xRight\space YO) \ifx\psk@optic@lensType\lensTypeDVG\pst@drawDVGRays\else \ifx\psk@optic@lensType\lensTypePDVG\pst@drawDVGRays\else \pst@drawCVGRays\fi\fi \fi \end{pspicture*}% }\ignorespaces} % % 25 december 2002 Herbert % 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}% \ifx\psk@optic@lensType\lensTypeDVG\addto@pscode{\pslensDVG@ii}% \else\addto@pscode{\pslensPDVG@ii}\fi% \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\pslensPDVG@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 0 h moveto wHalbe 0 rlineto x y Radius 180 angleA add 180 angleB add arc % x neg y Radius angleA angleB arc wHalbe neg 0 rlineto 0 h dup add rlineto } % \def\pslensCVG{\pst@object{pslensCVG}} \def\pslensCVG@i#1#2{% \begin@OpenObj \pssetlength\pst@dima{#1}% \pssetlength\pst@dimb{#2}% \ifx\psk@optic@lensType\lensTypeCVG\addto@pscode{\pslensCVG@ii}% \else\addto@pscode{\pslensPCVG@ii}\fi% \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 } \def\pslensPCVG@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 neg moveto 0 h dup add rlineto 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{% \psscalebox{\psk@optic@lensScale}{% \pscustom[linewidth=0.75\pslinewidth]{% \pslensCVG{\psk@optic@lensWidth}{\psk@optic@lensHeight} \fill[fillstyle=solid,fillcolor=BleuVerre] }% }% } % \def\lensDVG{% \psscalebox{\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[{\pst@mirrorCVGRay}{\pst@mirrorCVGRay[]}}% Herbert 2003/01/05 \def\pst@mirrorCVGRay[#1](#2)(#3)#4{{% \ifx\relax#1\relax \else\psset[pst-optic,pstricks]{#1}\fi% \ifx\psk@optic@mirrorType\mirrorType % CVG %\typeout{====>\mirrorType} %\typeout{====>\psk@optic@mirrorType} \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'} \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 ----------------- %\typeout{====>\mirrorType} %\typeout{====>\psk@optic@mirrorType} \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[pst-optic]{mirrorType=CVG}% restore \fi \ifPst@drawing \psline[#1](#2)(#4) \psline[#1](#4)(#4') \psline[#1](#4')(#4'') \fi }\ignorespaces} % % \def\mirrorCVG{\@ifnextchar[{\pst@mirrorCVG}{\pst@mirrorCVG[]}}% Herbert Voss 2003/01/05 \def\pst@mirrorCVG[#1]{{% \psset[pst-optic]{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}% \ifx\relax#1\relax \else\psset[pst-optic,pstricks]{#1}\fi% \def\mirrorType{CVG}% \begin{pspicture}(\psk@optic@xLeft,\psk@optic@yBottom)(\psk@optic@xRight,\psk@optic@yTop) \pnode(\psk@optic@xLeft, 0){xLeft} \pnode(\psk@optic@xRight, 0){xRight} \pstVerb{ /Height \psk@optic@mirrorHeight\space 2.0 div def /Depth \psk@optic@mirrorDepth\space def /Width \psk@optic@mirrorWidth\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 /radius Height dup mul Depth dup mul add 2 div Depth div def } \pnode(! OA XO add YO){A} \pnode(! OA XO add AB YO add){B} \pnode(! XO YO){O} \ifx\psk@optic@mirrorType\mirrorType % CVG \pnode(! \psk@optic@mirrorHeight\space dup mul 16 div \psk@optic@mirrorDepth\space div XO add YO){Focus} \else % SPH \pnode(! 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 % CVG or SPH \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 % CVG or SPH \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[style=opticalAxis](O)(xRight) \ifx\psk@optic@mirrorType\mirrorType\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[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[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[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}% }\ignorespaces} % % \def\mirrorDVG{\@ifnextchar[{% Herbert Voss 2003/01/05 \pst@mirrorDVG}{\pst@mirrorDVG[]}} \def\pst@mirrorDVG[#1]{{% \psset[pst-optic]{% 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,mirrorType=DVG}% \def\mirrorType{DVG}% \psset[pst-optic,pstricks]{#1}% \pstVerb{ /Height \psk@optic@mirrorHeight\space 2 div def /Depth \psk@optic@mirrorDepth\space def /Width \psk@optic@mirrorWidth\space def /radius Height dup mul Depth dup mul add 2 div Depth div 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 } \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(! OA XO add YO){A} \pnode(! OA XO add AB YO add){B} \pnode(! XO YO){O} \ifx\psk@optic@mirrorType\mirrorType % DVG \pnode(! Height dup mul 4 div Depth div XO add YO){Focus} \else % SPH \pnode(! 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[style=opticalAxis](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[drawing=false](B)(0,\psk@optic@AB){PR} % 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[drawing=false](B)(! 0 0){MR} % mirrorType=\psk@optic@mirrorType,% \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[drawing=false](B)(Focus){FR} % mirrorType=\psk@optic@mirrorType,% \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}% }\ignorespaces} % \def\mirrorDVGRay{\@ifnextchar[{\pst@mirrorDVGRay}{\pst@mirrorDVGRay[]}}% Herbert Voss 2003/01/05 \def\pst@mirrorDVGRay[#1](#2)(#3)#4{{% \psset[pst-optic,pstricks]{#1}% \pnode(!% \psk@optic@mirrorHeight\space dup mul 16 div \psk@optic@mirrorDepth\space div neg 0){Focus} \ifx\psk@optic@mirrorType\mirrorType % DVG or Spherical \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 }\ignorespaces} % % HEadlight Herbert 2003/01/23 % \def\beamLight{\@ifnextchar[{\pst@beamLight}{\pst@beamLight[]}} \def\pst@beamLight[#1]{{% \psset[pst-optic]{xLeft=-5,xRight=5,yBottom=-5,yTop=5,% drawing=false}% the defaults \psset[pst-optic,pstricks]{#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*}% }\ignorespaces} % % %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[pst-optic]{xLeft=-0.5,xRight=11,yBottom=-6,yTop=2}% the default \def\@tempa{#1}% \ifx\@tempa\@empty\else\psset[pst-optic,pstricks]{#1}\fi% \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){% \psscalebox{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){\psscalebox{0.6}{\eye}} \end{pspicture*}% }\ignorespaces} % %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} }\ignorespaces} % % 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@3Ddict begin TMChange end }% \box\pst@hbox \pst@Verb{ tx@3Ddict begin TMRestore end }}% }\ignorespaces} % % psrefractionRay[options](A)(B)(C)(D){rNoA}{rNoB}{E} % (A)(B) the ray nodes #2 #3 % (C)(D) the nodes of the other material #4 #5 % {rNoA}{rNoB} the refraction numbers (n1=#6, n2=#7) % {E} the intermediate node of the ray and the material (E=#8) % {E'} the end node of the ray (internal) % % Herbert Voss 2003-01-26 % \def\refractionRay{\@ifnextchar[{\pst@refractionRay}{\pst@refractionRay[]}} \def\pst@refractionRay[#1](#2)(#3)(#4)(#5)#6#7#8{{% \psset[pst-optic,pstricks]{#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} }\ignorespaces} % % Herbert Voss 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[pst-optic,pstricks]{#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 }\ignorespaces} % % Prism stuff initiated by Manuel 2006-07-26 % \define@key[psset]{pst-optic}{AnglePrism}{\edef\psk@Prism@AnglePrism{#1}} \define@key[psset]{pst-optic}{AnglePlan1}{\edef\psk@Prism@AnglePlanOne{#1}} \define@key[psset]{pst-optic}{AnglePlan2}{\edef\psk@Prism@AnglePlanTwo{#1}} \define@key[psset]{pst-optic}{lambda}{\edef\psk@Prism@Lambda{#1}} \define@key[psset]{pst-optic}{k}{\edef\psk@Prism@k{#1}} \define@boolkey[psset]{pst-optic}[Pst@Prism@]{notations}[true]{} % \psset[pst-optic]{AnglePrism=60,AnglePlan1=25,AnglePlan2=55,k=1,lambda=632.8,notations=true} % \def\psprism{\pst@object{psprism}} \def\psprism@i{% \begin@SpecialObj \ifPst@Prism@notations \psline{->}(0,8) \uput[90](0,8){$y$} \psline{->}(-6,0)(6,0) \uput[0](6,0){$x$} \fi \pnode(0,0){O} \pnode(! /AnglePrism \psk@Prism@AnglePrism\space 2 div def /AnglePlan1 \psk@Prism@AnglePlanOne\space def /AnglePlan2 \psk@Prism@AnglePlanTwo\space def /lambda \psk@Prism@Lambda\space def % le point C1 sur la droite 1 /C1x -6 def /C1y 6 def % le point C2 sur la droite 2 /C2x 7 def /C2y 5 def % donne la distance C1E /k \psk@Prism@k\space def % /g1x AnglePrism sin neg def % -sin(A/2) /g1y AnglePrism cos def % cos(A/2) /u1x AnglePlan1 sin neg def /u1y AnglePlan1 cos neg def % le point E émetteur /E1x C1x k u1x mul add def /E1y C1y k u1y mul add def % /n1x AnglePlan1 cos def /n1y AnglePlan1 sin neg def /Lambda {E1x g1y mul E1y g1x mul neg add n1y g1x mul neg n1x g1y mul add div neg} bind def % point I1 /i1x {E1x Lambda n1x mul add} bind def /i1y {E1y Lambda n1y mul add} bind def 0 0){Stockage_parametres_prism} \pspolygon[fillstyle=gradient,gradbegin=cyan,gradend=white,gradangle=60,gradmidpoint=0.5](O)% (! 7 90 AnglePrism add cos mul 7 90 AnglePrism add sin mul) (! 7 90 AnglePrism sub cos mul 7 90 AnglePrism sub sin mul) \pnode(! % Les datas % Sellmeier's % glass sf15 : verre flint % n=Sqrt(1+B1*L^2/(l^2-C1)+B2*L^2/(l^2-C2)+B3*L^2/(l^2-C3)) % Cauchy : /N {1.606 6545 1 mul lambda dup mul div add} bind def /L2 {lambda 1e-3 mul dup mul} bind def % en micromètres /N {1 1.539259 L2 mul L2 0.011931 sub div add 0.247621 L2 mul L2 0.055608 sub div add 1.038164 L2 mul L2 116.416755 sub div add Sqrt} bind def /alpha1 AnglePlan1 AnglePrism add def /sinB1 alpha1 sin N div def /B1 sinB1 arcsin def /Delta1 AnglePrism B1 sub def %%% /g2x AnglePrism sin def /g2y AnglePrism cos def /d12x Delta1 cos def % d12x /d12y Delta1 sin def % d12y /Lambda2 {i1x g2y mul i1y g2x mul sub d12y g2x mul d12x g2y mul sub div} bind def % point I2 /i2x {i1x Lambda2 d12x mul add} bind def /i2y {i1y Lambda2 d12y mul add} bind def % /B2 AnglePrism 2 mul B1 sub def /sinA2 N B2 sin mul def /alpha2 sinA2 asin def /u2x AnglePlan2 sin def /u2y AnglePlan2 cos neg def /Delta2 alpha2 AnglePrism sub def /d2x Delta2 cos def /d2y Delta2 sin def /DELTA u2x d2y mul neg u2y d2x mul add def /DELTA_X i2x C2x sub d2y mul neg i2y C2y sub d2x mul add def /DELTA_Y u2x i2y C2y sub mul neg u2y i2x C2x sub mul add def /MU DELTA_X DELTA div def /LAMBDA3 DELTA_Y DELTA div def % le point R2 /r2x C2x MU u2x mul add def /r2y C2y MU u2y mul add def /a_i {AnglePlan1 neg} bind def /a_r {alpha2 AnglePrism sub} bind def /tan_i {a_i tan} bind def /tan_r {a_r tan} bind def 0 0){factice} \pnode(! C1x C1y){C1} \pnode(! C2x C2y){C2} \pnode(! E1x E1y){E1} \pnode(! i1x i1y){P1} \pnode(! i2x i2y){I2} \pnode(! r2x r2y){R2} \pnode(! /bQ {i1y i1x AnglePrism tan mul sub} bind def /bQ' {i2y i2x AnglePrism tan mul add} bind def /xQ {bQ' bQ sub 2 div AnglePrism tan div} bind def /yQ {bQ bQ' add 2 div} bind def xQ yQ){Q} \pnode(! /bI {i1y i1x tan_i mul sub} bind def /bI'{i2y i2x tan_r mul sub} bind def /xI {bI bI' sub tan_r tan_i sub div} bind def /yI {xI tan_i mul bI add} bind def xI yI){I} \pcline[linestyle=dashed,nodesepB=-2](P1)(I) \pcline[linestyle=dashed,nodesepB=-2](I2)(I) \pcline[linestyle=dashed,nodesepB=-1,nodesepA=-2](P1)(Q) \pcline[linestyle=dashed,nodesepB=-1,nodesepA=-2](I2)(Q) \rput(P1){% \rput{30}(0,0){\psframe*(0,0)(0.2,0.2)} \psarc{<-}(0,0){0.8}{!180 AnglePrism add alpha1 sub}{!180 AnglePrism add} \uput{1}[! 180 AnglePrism add alpha1 2 div sub](0,0){$i_1$} \psarc[linecolor=blue]{<-}(0,0){1}{!AnglePrism B1 sub}{!AnglePrism} \uput{1.2}[! AnglePrism B1 2 div sub](0,0){$r_1$} \uput{0.4}[90](0,0){$I_1$}} \rput(I2){% \rput{60}(0,0){\psframe*(0,0)(0.2,0.2)} \psarc[linecolor=blue]{->}(0,0){0.8}{! AnglePrism neg 180 add}{!AnglePrism neg 180 add B2 add} \uput{1}[!AnglePrism neg 180 add B2 2 div add](0,0){$r_2$} \psarc{->}(0,0){1}{! AnglePrism neg}{!alpha2 AnglePrism sub} \uput{1.2}[!alpha2 2 div AnglePrism sub](0,0){$i_2$} \uput{0.4}[90](0,0){$I_2$}} \psline[linewidth=\psk@optic@rayWidth,linecolor={[wave]{\psk@Prism@Lambda}},arrowscale=2]{->}(P1)(I2)(R2) \psline[linewidth=\psk@optic@rayWidth,linecolor={[wave]{\psk@Prism@Lambda}}](E1)(P1) \psline[linewidth=\psk@optic@rayWidth,linecolor={[wave]{\psk@Prism@Lambda}},arrowscale=2]{->}(E1)(!i1x E1x add 2 div i1y E1y add 2 div) \psarc(0,0){0.8}{!90 AnglePrism sub}{!90 AnglePrism add} \uput[90](0,0.8){$\widehat{A}$} \psdot[dotstyle=o](O) \psdot[dotstyle=o](I) \psdot[dotstyle=o](Q) \rput(I){\psarc{->}(0,0){1}{!a_i}{!a_r} \uput{1.1}[!a_i a_r add 2 div](0,0){$\widehat{D}$}} \ifPst@Prism@notations \pcline[nodesepB=-2,nodesepA=-2](C1)(E1) \uput[180](C1){$C_1$} \uput[180](E1){$E_1$} % \pcline[nodesepB=-2,nodesepA=-2](C2)(R2) \uput[-90](C2){$C_2$} \uput[180](R2){$R_2$} \rput(C1){\psline(0,2) \psarc(0,0){1}{! 90 AnglePlan1 sub}{90} \uput{1.1}[!90 AnglePlan1 2 div sub](0,0){$\rho_1$} \psline[arrowinset=0,linewidth=2\pslinewidth]{->}(! 90 AnglePlan1 sub cos neg 90 AnglePlan1 sub sin neg) \uput[0](! 90 AnglePlan1 sub cos neg 90 AnglePlan1 sub sin neg){$\overrightarrow{u}_1$} \psline[arrowinset=0,linewidth=2\pslinewidth]{->}(! AnglePlan1 neg cos AnglePlan1 neg sin) \uput[90](! AnglePlan1 neg cos AnglePlan1 neg sin){$\overrightarrow{n}_1$}} \rput(C2){\psline(0,2) \psarc(0,0){1}{90}{! 90 AnglePlan2 add} \uput{1.1}[!90 AnglePlan2 2 div add](0,0){$\rho_2$} \psline[arrowinset=0,linewidth=2\pslinewidth]{->}(! AnglePlan2 cos AnglePlan2 sin) \uput[! AnglePlan2](! AnglePlan2 cos AnglePlan2 sin){$\overrightarrow{n}_2$} \psline[arrowinset=0,linewidth=2\pslinewidth]{->}(! 90 AnglePlan2 add cos 90 AnglePlan2 add sin) \uput[-90](! 90 AnglePlan2 add cos 90 AnglePlan2 add sin){$\overrightarrow{u}_2$}} \psdot[dotstyle=o](C1) \psdot[dotstyle=o,linecolor={[wave]{\psk@Prism@Lambda}}](E1) \psdot[dotstyle=o](C2) \psdot[dotstyle=o](R2) \fi% \end@SpecialObj% } % %% Commande \psprismColor \def\psprismColor{\pst@object{psprismColor}} \def\psprismColor@i{% \begin@SpecialObj \pnode(0,0){O} \pnode(! /AnglePrism \psk@Prism@AnglePrism\space 2 div def /AnglePlan1 \psk@Prism@AnglePlanOne\space def /AnglePlan2 \psk@Prism@AnglePlanTwo\space def % le point C1 sur la droite 1 /C1x -8 def /C1y 7 def % le point C2 sur la droite 2 /C2x 11 def /C2y 5 def % donne la distance C1E1 /k \psk@Prism@k\space def % /g1x AnglePrism sin neg def % -sin(A/2) /g1y AnglePrism cos def % cos(A/2) /u1x AnglePlan1 sin neg def /u1y AnglePlan1 cos neg def % le point E émetteur /E1x C1x k u1x mul add def /E1y C1y k u1y mul add def % /n1x AnglePlan1 cos def /n1y AnglePlan1 sin neg def /Lambda {E1x g1y mul E1y g1x mul neg add n1y g1x mul neg n1x g1y mul add div neg} bind def % point I1 /i1x {E1x Lambda n1x mul add} bind def /i1y {E1y Lambda n1y mul add} bind def 0 0){Stockage_parametres_prism} \pspolygon[fillstyle=gradient,gradbegin=cyan,gradend=white,gradangle=60,gradmidpoint=0.5](O)% (! 7 90 AnglePrism add cos mul 7 90 AnglePrism add sin mul) (! 7 90 AnglePrism sub cos mul 7 90 AnglePrism sub sin mul) \multido{\iLAMBDA=400+5}{80}{% \pstVerb{/lambda \iLAMBDA\space def}% \definecolor{prism}{wave}{\iLAMBDA}% \pnode(! % Les datas % Sellmeier's % glass sf15 : verre flint lourd % n=Sqrt(1+B1*L^2/(l^2-C1)+B2*L^2/(l^2-C2)+B3*L^2/(l^2-C3)) % Cauchy : /N {1.606 6545 1 mul lambda dup mul div add} bind def /L2 {lambda 1e-3 mul dup mul} bind def /N {1 1.539259 L2 mul L2 0.011931 sub div add 0.247621 L2 mul L2 0.055608 sub div add 1.038164 L2 mul L2 116.416755 sub div add Sqrt} bind def /alpha1 AnglePlan1 AnglePrism add def /sinB1 alpha1 sin N div def /B1 sinB1 asin def /Delta1 AnglePrism B1 sub def %%% /g2x AnglePrism sin def /g2y AnglePrism cos def /d12x Delta1 cos def % d12x /d12y Delta1 sin def % d12y /Lambda2 {i1x g2y mul i1y g2x mul sub d12y g2x mul d12x g2y mul sub div} bind def % point I2 /i2x {i1x Lambda2 d12x mul add} bind def /i2y {i1y Lambda2 d12y mul add} bind def % /B2 AnglePrism 2 mul B1 sub def /sinA2 N B2 sin mul def /alpha2 sinA2 asin def /u2x AnglePlan2 sin def /u2y AnglePlan2 cos neg def /Delta2 alpha2 AnglePrism sub def /d2x Delta2 cos def /d2y Delta2 sin def /s2x i2x C2x sub def /s2y i2y C2y sub def /dA d2x u2y mul d2y u2x mul sub def /dM d2x s2y mul d2y s2x mul sub def % le point R2 /r2x C2x dM dA div u2x mul add def /r2y C2y dM dA div u2y mul add def 0 0){factice} \pnode(! C1x C1y){C1} \pnode(! C2x C2y){C2} \pnode(! E1x E1y){E1} \pnode(! i1x i1y){I1} \pnode(! i2x i2y){I2} \pnode(! r2x r2y){R2} \psline[linewidth=\psk@optic@rayWidth,linecolor=prism](I1)(I2)(R2)} \psline[linewidth=\psk@optic@rayWidth,linecolor=\psk@optic@rayColor,linewidth=0.5mm](E1)(I1) \psline[linewidth=\psk@optic@rayWidth,linecolor=\psk@optic@rayColor,linewidth=0.5mm,arrowscale=2]{->}(E1)(!i1x E1x add 2 div i1y E1y add 2 div) \end@SpecialObj% } % % \def\resetOpticOptions{% hv 2006-07-20 \newpsstyle{opticalAxis}{linewidth=0.5pt,linecolor=black,linestyle=solid} \psset[pst-optic]{% lensGlass=false,drawing=true,,lensTwo,rightRay,onlyrays=false, xLeft=-7.5,xRight=7.5,yBottom=-3.0,yTop=3.0, lensType=CVG,lensColor=lightgray,lensWidth=0.5,lensDepth=1, lensHeight=5,lensScale=1,lensArrowSize=0.2,lensArrowInset=0.5, mirrorType=CVG,mirrorDepth=1,mirrorHeight=5,mirrorWidth=0.25, mirrorFocus=8,mirrorTwoAngle=45,posMirrorTwo=6,mirrorColor=lightgray, refractA=1,refractB=1.41, XO=0,YO=0,OA=-3,posStart=0,length=2,focus=2,AB=1,arrowOffset=0, nameO=O,spotO=225,nameAi=A',spotAi=90,nameBi=B',spotBi=270, nameFi=F',spotFi=270, rayColor=red,% AnglePrism=60,AnglePlan1=25,AnglePlan2=55,k=1,lambda=632.8,notations=true, rayWidth=\pslinewidth}% % \gdef\mirrorType{CVG}% % \gdef\lensTypeCVG{CVG}% } \catcode`\@=\PstAtCode\relax % %% END: pst-optic.tex \endinput