Ce document regroupe les codes TIKZ des figures utilisées pour le cours "Les miroirs" situé à la page: http://femto-physique.fr/optique_geometrique/opt_C2.php
% !TEX encoding = UTF-8 Unicode
% J.Roussel
% Ce document regroupe les codes TIKZ des figures utilisées pour le cours "Les miroirs" situé à la page http://femto-physique.fr/optique_geometrique/opt_C2.php
%-------------------------------------------
\documentclass[11pt]{article}
\input{styles_optique}
\title{Figures TikZ du cours "les miroirs"}
\author{J.Roussel}
\begin{document}
% =========================================================
% Quelques exemples de sources ponctuelles
% =========================================================
\begin{tikzpicture}[decoration={markings,mark=at position 1cm with {\arrow[red]{stealth};}}]
\coordinate (O) at (0,0);
\begin{scope}
\foreach \alphaM in {180,160,...,-160}
\draw[red,->,postaction={decorate}] (O)--(\alphaM:2);
\draw (O) node{$\bullet$};
\draw (0,-2) node[below,text width=3cm]{\small Source ponctuelle isotrope};
\end{scope}
\begin{scope}[shift={(4,0)}]
\coordinate (O) at (0,0);
\foreach \alphaM in {90,80,...,-90}
\draw[red,->,postaction={decorate},opacity={cos(\alphaM)^3}] (O)--(\alphaM:2);
\draw (O) node{$\bullet$};
\draw (0,-2) node[below right,text width=3cm]{\small Source ponctuelle anisotrope};
\end{scope}
\begin{scope}[shift={(8,0)}]
\coordinate (O) at (0,0);
\foreach \y in {1,0.7,...,-1}
\draw[red,->,postaction={decorate}] (0,\y)--++(3,0);
\draw (0,-2) node[below right,text width=3cm]{\small Source ponctuelle à l'infini};
\end{scope}
\end{tikzpicture}
%------ FIN FIGURE -------
% =========================================================
% Formation de l'image d'un objet ponctuel réel par un système optique stigmatique
% =========================================================
\begin{tikzpicture}[scale=0.9,decoration={markings,mark=at position 1cm with {\arrow[red]{stealth};}}]
\begin{scope}
\coordinate (A) at (-3,0);%source ponctuelle
\coordinate (AA) at (3,0);%image ponctuelle
\foreach \incidence in {-30,-20,...,30}{
\draw[thick,red,->,postaction={decorate}](A)--(-1,{2*tan(\incidence)});
\draw[thick,red,->](1,{2*tan(\incidence)})--++({-\incidence}:3);}
\node[draw,rounded corners=3pt,minimum width=3cm,minimum height=3cm,fill=SkyBlue!20] (SO){};
\draw (0,-1.5) node[above] {\small Syst\`eme Optique};
\draw (-3,1)node{\small Objet r\'eel}++(6,0)node{\small Image r\'eelle};
\draw(A)node{$\bullet$} node[above=2pt]{A};
\draw(AA) node{$\bullet$} node[above=2pt]{A'};
\end{scope}
\begin{scope}[shift={(8,0)}]
\coordinate (A) at (-3,0);%source ponctuelle
\coordinate (AA) at (-1,0);%image ponctuelle
\foreach \incidence in {-30,-20,...,30}{
\draw[thick,red,->,postaction={decorate}](A)--(-1,{2*tan(\incidence)});
\draw[thick,red,->](AA)--++({\incidence}:4);
}
\node[draw,rounded corners=3pt,text width=2cm,text centered,minimum width=3cm,minimum height=3cm,fill=SkyBlue!20] (SO) at (0,0){};
\draw (-3,1)node{\small Objet r\'eel}++(3,0)node{\small Image virtuelle};
\foreach \incidence in {-30,-20,...,30}{
\draw[dashed,red](AA)--++({\incidence}:3);
}
\oeil[shift={(4,0)},rotate=180];
\draw (0,-1.5) node[above] {\small Syst\`eme Optique};
\draw(A)node{$\bullet$} node[above=2pt]{A};
\draw(AA) node{$\bullet$} node[above=2pt]{A'};
\end{scope}
\end{tikzpicture}
% =========================================================
% Formation de l'image d'un objet ponctuel virtuel par un système optique stigmatique.
% =========================================================
\begin{tikzpicture}[decoration={markings,mark=at position 1cm with {\arrow[red]{stealth};}}]
\begin{scope}
\coordinate (A) at (1,0);%source ponctuelle
\coordinate (AA) at (3,0);%image ponctuelle
\foreach \incidence in {-30,-20,...,30}{
\draw[thick,red,->,postaction={decorate}](-3,{3*tan(\incidence)})--(A);
\draw[thick,red,->](1,{2*tan(\incidence)})--++({-\incidence}:3);}
\node[draw,rounded corners=3pt,minimum width=3cm,minimum height=3cm,fill=SkyBlue!20] (SO) at (0,0){};
\draw (1,1)node{\small Objet virtuel}++(2.5,0)node{\small Image r\'eelle};
\foreach \incidence in {-30,-20,...,30}{
\draw[dashed,red](-3,{3*tan(\incidence)})--(A);}
\draw (0,-1.5) node[above] {\small Syst\`eme Optique};
\draw(A)node{$\bullet$} node[above=2pt]{A};
\draw(AA) node{$\bullet$} node[above=2pt]{A'};
\end{scope}
\begin{scope}[shift={(8,0)}]
\coordinate (A) at (1,0);%source ponctuelle
\coordinate (AA) at (-1,0);%image ponctuelle
\foreach \incidence in {-30,-20,-10,10,20,30}{
\draw[thick,red,->,postaction={decorate}](-3,{3*tan(\incidence)})--(A);
\draw[thick,red,->](AA)--++({\incidence}:4);}
\node[draw,rounded corners=3pt,minimum width=3cm,minimum height=3cm,fill=SkyBlue!20] (SO) at (0,0){};
\draw (-1,1)node{\small Objet virtuel}++(2.5,0)node{\small Image virtuelle};
\foreach \incidence in {-30,-20,-10,10,20,30}{
\draw[dashed,red](AA)--++({\incidence}:3);
\draw[dashed,red](-3,{3*tan(\incidence)})--(A);
}
\oeil[shift={(4,0)},rotate=180];
\draw (0,-1.5) node[above] {\small Syst\`eme Optique};
\draw(A)node{$\bullet$} node[above=2pt]{A};
\draw(AA) node{$\bullet$} node[above=2pt]{A'};
\end{scope}
\end{tikzpicture}
% =========================================================
% Exemples de stigmatisme rigoureux
% =========================================================
\begin{tikzpicture}[scale=0.7,decoration={markings,mark=at position 8mm with {\arrowreversed[red]{stealth};},mark=at position -15mm with {\arrowreversed[red]{stealth};}}]
\begin{scope}
\def \parametre {2.5};%parametre de l'ellipse
\def \excentric {0.6};%excentricitŽé
\def \alphaM {60};%angle correspondant au point M
\def \gdaxe {\parametre/(1-\excentric*\excentric)};
\def \focale {\excentric*\gdaxe};
\coordinate (O) at ({-\focale},0);
\coordinate (F) at (0,0);%foyer
\coordinate (FF) at ({-2*\focale},0);%foyer image
\coordinate (P) at ({\parametre/(1+\excentric)},0);%PŽérigéŽe
\clip (-7.25,-4) rectangle (2.56,4);
\shadedraw[very thin,outer color=white,inner color=gray] (O) circle(8);
\draw[fill=white,thick,variable=\t , domain=0:360,samples=200] plot ({\parametre*cos(\t)/(1+\excentric*cos(\t))},{\parametre*sin(\t)/(1+\excentric*cos(\t))});
\foreach \alphaM in {110,100,...,-120}{
\draw[red,postaction={decorate}] (F)--({\parametre*cos(\alphaM)/(1+\excentric*cos(\alphaM))},{\parametre*sin(\alphaM)/(1+\excentric*cos(\alphaM))})--(FF);
}
\draw[shift={(F)}] (0pt,2pt) -- (0pt,-2pt) node[below,fill=white] {F};
\draw[shift={(FF)}] (0pt,2pt) -- (0pt,-2pt) node[below,fill=white] {F'};
\draw[ultra thin,dashed] (O) --++({\gdaxe+1},0)--++({-2*\gdaxe-2},0);
\draw (2.56,-4) node[above left]{\small miroir elliptique};
\end{scope}
\begin{scope}[shift={(10,0)}]
\def \parametre {2.5};%parametre de la parabole
\def \focale {\parametre*0.5};
\coordinate (P) at ({\focale},0);
\coordinate (F) at (0,0);
\foreach \alphaM in {110,100,...,-110}{
\draw[red,postaction={decorate}] (F)--({\parametre*cos(\alphaM)/(1+cos(\alphaM))},{\parametre*sin(\alphaM)/(1+cos(\alphaM))})--(-5,{\parametre*sin(\alphaM)/(1+cos(\alphaM))});
}
\draw[shift={(F)}] (0pt,2pt) -- (0pt,-2pt) node[below,fill=white] {F};
\shadedraw[very thin,right color=lightgray,left color=white,variable=\t , domain=-115:115,samples=200] plot ({\parametre*cos(\t)/(1+cos(\t))},{\parametre*sin(\t)/(1+cos(\t))})--++(4,0)--++(0,{-2*tan(57.5)*\parametre})--cycle node[above left]{\small miroir parabolique};
\draw[dashed,->] (-5,0)--(\parametre,0);
\end{scope}
\end{tikzpicture}
% =========================================================
% déformation transversale
% =========================================================
\begin{tikzpicture}[scale=0.85,decoration={markings,mark=at position 7mm with {\arrow[red]{stealth};},mark=at position -7mm with {\arrow[red] {stealth};}}]
\coordinate (A) at (-3,0);%source ponctuelle
\coordinate (AA) at (3,0);%image ponctuelle
\coordinate (B) at (-2.5,0);%source ponctuelle
\coordinate (BB) at (4,0);%image ponctuelle
\foreach \incidence in {30,15}
\draw[thick,red,postaction={decorate}](A)--(-1,{2*tan(\incidence)})--(AA);
\foreach \incidence in {-30,-15}
\draw[thick,red,postaction={decorate}](B)--(-1,{2*tan(\incidence)})--(BB);
\node[draw,rounded corners=3pt,minimum width=3cm,minimum
height=3cm,fill=SkyBlue!20] (SO){};
\draw (0,-1.5) node[above] {\small Syst\`eme Optique};
\draw[->,ultra thick](A) node{$\bullet$}node[below=2pt]{A}--(B)
node[below=2pt]{B};
\draw[->,ultra thick](AA) node{$\bullet$}node[above=2pt]{A'}--(BB)
node[above=2pt]{B'};
\draw[->,thin](-3.5,0)--(4.5,0)node[above]{\tiny $+$};
\end{tikzpicture}
% =========================================================
% Déformations d'un système optique aplanétique
% =========================================================
\begin{tikzpicture}[scale=0.85,decoration={markings,mark=at position 7mm with {\arrow[red]{stealth};},mark=at position -7mm with {\arrow[red] {stealth};}}]
\coordinate (A) at (-3,0);%source ponctuelle
\coordinate (AA) at (3,0);%image ponctuelle
\coordinate (B) at (-3,1.5);%source ponctuelle
\coordinate (BB) at (3,-1);%image ponctuelle
\foreach \incidence in {-30,-15}
\draw[thick,red,postaction={decorate}](A)--(-1,{2*tan(\incidence)})--(AA);
\foreach \incidence in {30,15}
\draw[thick,red,postaction={decorate}](B)--(-1,{2*tan(\incidence)})--(BB);
\node[draw,rounded corners=3pt,minimum width=3cm,minimum
height=3cm,fill=SkyBlue!20] (SO){};
\draw (0,-1.5) node[above] {\small Syst\`eme Optique};
\draw[->,ultra thick](A) node{$\bullet$}node[below=2pt]{A}--(B)
node[above=2pt]{B};
\draw[->,ultra thick](AA) node{$\bullet$}node[above=2pt]{A'}--(BB)
node[below=2pt]{B'};
\draw[->,thin](-3.5,0)--(4,0)node[above]{\tiny $+$};
\draw[->,thin](3.5,0)--++(0,0.5) node[above]{\tiny $+$};
\end{tikzpicture}
% =========================================================
%
% =========================================================
\begin{tikzpicture}[scale=0.85,decoration={markings,mark=at position 1cm with {\arrow[red]{stealth};}}]
\def \ep{1}%épaisseur de la lame
\def \OA{-2}%distance algébrique OA
\def \indice{1.75}%indice de réfraction
%\def \incidence {20}% angle d'incidence
\coordinate (O) at (0,0);
\coordinate (A) at ({\OA},0);%source ponctuelle
\coordinate (AA) at ({-\OA},0);%image ponctuelle
\draw[->,shift={(2.1,-2)}] (0,0)--++(0.5,0)node[right]{\tiny $+$};
\draw[->,shift={(2.1,-2)}] (0,0)--++(0,0.5)node[above]{\tiny $+$};
\draw[ultra thick] (0,-2.1)--(0,2.1);
\shadedraw[white,right color=white,left color=gray] (0,-2.1)--++(0,4.2)--++({\ep},0)--++(0,-4.2)--cycle;
\draw[thin]({\OA-1},0)--({1-\OA},0);
\foreach \incidence in {-30,-20,-10,10,20,30}{
\draw[thick,red, ->,postaction={decorate}] (A)--(0,{(-\OA)*tan(\incidence)})--++({180-\incidence}:3);
\draw[dashed] (0,{(-\OA)*tan(\incidence)})--(AA);
}
\draw[shift={(A)}]node{$\bullet$}node[above=2pt]{A};
\draw[shift={(AA)}]node{$\bullet$}node[above=2pt]{A'};
\oeil[shift={(-4,2)},rotate=-20];
\end{tikzpicture}
% =========================================================
% Formation d'une image avec un miroir plan. L'image est inversée (gauche/droite) mais pas renversée (haut/bas).
% =========================================================
\begin{tikzpicture}[decoration={markings,mark=at position 1cm with {\arrow[red]{stealth};}}]
\def \OA{-2}%distance algébrique OA
\def \indice{1.75}%indice de réfraction
\coordinate (O) at (0,0);
\coordinate (A) at ({\OA},0);%source ponctuelle
\coordinate (B) at ({\OA},-1.25);%source ponctuelle
\coordinate (C) at ({\OA},0.25);%source ponctuelle
\coordinate (AA) at ({-\OA},0);%image ponctuelle
\coordinate (BB) at ({-\OA},-1.25);%source ponctuelle
\coordinate (CC) at ({-\OA},0.25);%source ponctuelle
\draw[ultra thick] (0,-2.1)--(0,2.1);
\shadedraw[white,right color=white,left color=gray] (0,-2.1)--++(0,4.2)--++(1,0)--++(0,-4.2)--cycle;
\foreach \incidence in {22,26}{
\draw[thick,red, ->,postaction={decorate}] (A)--(0,{(-\OA)*tan(\incidence)})--++({180-\incidence}:3);
\draw[dashed] (0,{(-\OA)*tan(\incidence)})--(AA);
}
\draw[thick] (C)node[above]{\small Gauche}--(B)node[below]{\small Droite} node[pos=0.5,right=-2pt]{$\triangleright$};
\draw[thick,gray] (CC)node[above]{\small Droite}--(BB)node[below]{\small Gauche} node[pos=0.5,left=-2pt]{$\triangleleft$};
\oeil[shift={(-3.5,2.4)},scale=0.75,rotate=-24];
\end{tikzpicture}
% =========================================================
% Formation d'une image avec un miroir plan. L'image est inversée (gauche/droite) mais pas renversée (haut/bas).
% =========================================================
\begin{tikzpicture}[decoration={markings,mark=at position 1cm with {\arrow[red]{stealth};}}]
\def \rayon {4}% angle d'incidence
\coordinate (S) at (0,0);
\coordinate (F) at ({(-0.5)*\rayon},0);%foyer
\coordinate (C) at ({-\rayon},0);%centre de courbure
\foreach \y in {1.5,1.3,...,0}{
\draw[red,postaction={decorate}] (-4,\y)--({sqrt(\rayon^2-\y^2)-\rayon},\y)--(F);
\draw[red,postaction={decorate}] (-4,-\y)--({sqrt(\rayon^2-\y^2)-\rayon},-\y)--(F);
}
\foreach \xtext in {F,C}
\draw[shift={(\xtext)}] (0pt,2pt) -- (0pt,-2pt) node[below,fill=white] {\xtext};
\shadedraw[very thin,right color=black,left color=lightgray] (S) arc(0:30:\rayon)--++(1,0)--++(0,{-\rayon})--++(-1,0) arc(-30:0:\rayon);
\draw[thin,->](-4.5,0)--++(5.5,0) node[above]{\tiny $+$};
\end{tikzpicture}
% =========================================================
%
% =========================================================
\begin{tikzpicture}[decoration={markings,mark=at position 1cm with {\arrow[red]{stealth};}}]
\def \rayon {4}% angle d'incidence
\coordinate (S) at (0,0);
\coordinate (F) at ({(0.5)*\rayon},0);%foyer
\coordinate (C) at ({\rayon},0);%centre de courbure
\foreach \y in {1.3,1.1,...,0}{
\draw[red,->,postaction={decorate}] (-2,\y)--({-sqrt(\rayon^2-\y^2)+\rayon},\y)--++({180-2*asin(\y/(\rayon))}:1);
\draw[red,->,postaction={decorate}] (-2,-\y)--({-sqrt(\rayon^2-\y^2)+\rayon},-\y)--++({2*asin(\y/(\rayon))-180}:1);
\draw[lightgray] ({-sqrt(\rayon^2-\y^2)+\rayon},\y)--(F)--({-sqrt(\rayon^2-\y^2)+\rayon},-\y);
;
}
\foreach \xtext in {F,C}
\draw[shift={(\xtext)}] (0pt,2pt) -- (0pt,-2pt) node[below,fill=white] {\xtext};
\shadedraw[very thin,right color=black,left color=lightgray] (S) arc(180:150:\rayon)--++(0,{-\rayon}) arc(-150:-180:\rayon);
\draw[thin,->](-2,0)--++(6.5,0)node[above]{\tiny $+$};
\end{tikzpicture}
% =========================================================
%
% =========================================================
\begin{tikzpicture}[decoration={markings,mark=at position 1cm with {\arrow[red]{stealth};}}]
\def \rayon {4}% angle d'incidence
\begin{scope}
\coordinate (S) at (0,0);
\coordinate (F) at ({(-0.5)*\rayon},0);%foyer
\coordinate (C) at ({-\rayon},0);%centre de courbure
\foreach \y in {2,1.85,...,0}{
\draw[red,postaction={decorate}] (-5,\y)--({sqrt(\rayon^2-\y^2)-\rayon},\y)--++({2*asin(\y/(\rayon))-180}:\rayon);
\draw[red,postaction={decorate}] (-5,-\y)--({sqrt(\rayon^2-\y^2)-\rayon},-\y)--++({2*asin(-\y/(\rayon))-180}:\rayon);
}
\foreach \xtext in {F,C}
\draw[shift={(\xtext)}] (0pt,2pt) -- (0pt,-2pt) node[below,fill=white] {\xtext};
\shadedraw[very thin,right color=black,left color=lightgray] (S) arc(0:30:\rayon)--++(1,0)--++(0,{-\rayon})--++(-1,0) arc(-30:0:\rayon);
\draw[thin,->](-5,0)--++(6,0);
\end{scope}
\begin{scope}[shift={(7,0)}]
\coordinate (S) at (0,0);
\coordinate (F) at ({(-0.5)*\rayon},0);%foyer
\coordinate (C) at ({-\rayon},0);%centre de courbure
\foreach \y in {0.7,0.55,...,0}{
\draw[red,postaction={decorate}] (-5,\y)--({sqrt(\rayon^2-\y^2)-\rayon},\y)--++({2*asin(\y/(\rayon))-180}:\rayon);
\draw[red,postaction={decorate}] (-5,-\y)--({sqrt(\rayon^2-\y^2)-\rayon},-\y)--++({2*asin(-\y/(\rayon))-180}:\rayon);
}
\foreach \xtext in {F,C}
\draw[shift={(\xtext)}] (0pt,2pt) -- (0pt,-2pt) node[below,fill=white] {\xtext};
\shadedraw[very thin,right color=black,left color=lightgray] (S) arc(0:30:\rayon)--++(1,0)--++(0,{-\rayon})--++(-1,0) arc(-30:0:\rayon);
\draw[thin,->](-5,0)--++(6,0);
\end{scope}
\end{tikzpicture}
% =========================================================
%
% =========================================================
\begin{tikzpicture}[decoration={markings,mark=at position 1cm with {\arrow[red]{stealth};}}]
\def \rayon {4};% rayon de courbure
\def \y{1}; %hauteur du rayon incident
\coordinate (S) at (0,0);
\coordinate (F') at ({(-0.5)*\rayon},0);%foyer
\coordinate (C) at ({-\rayon},0);%centre de courbure
\coordinate (I) at ({sqrt(\rayon^2-\y^2)-\rayon},\y);
\draw[red,->,postaction={decorate}] (-4.5,\y)--(I)--++({2*asin(\y/(\rayon))-180}:\rayon);
\draw[dashed] (C)--(I) node[above left]{I};
\shadedraw[very thin,right color=black,left color=lightgray] (S) arc(0:30:\rayon)--++(1,0)--++(0,{-\rayon})--++(-1,0) arc(-30:0:\rayon);
\draw[thin,->](-5,0)--++(6,0);
\draw[-] (C)++(1.2,0) arc(0:14.5:1.2);
\draw[-] (I)++(194.5:1.2) arc(194.5:209:1.2);
\draw (C)++(1.2,0) arc(0:7:1.2) node[right]{$\alpha$};
\foreach \xtext in {F',C,S}
\draw[shift={(\xtext)}] (0pt,2pt) -- (0pt,-2pt) node[below] {\xtext};
\draw[<->] (-4.2,0)--++(0,\y) node[pos=0.5,fill=white]{$y$};
\end{tikzpicture}
% =========================================================
% Construction d'image avec un miroir concave
% =========================================================
\begin{tikzpicture}[decoration={markings,mark=at position 1cm with {\arrow[red]{stealth};},mark=at position -1cm with {\arrow[red]{stealth};}}]
\def \rayon {4}% angle d'incidence
\def \xA{-6};%position de l'objet
\def \yB{2};%hauteur de l'objet
\def \f{-0.5*\rayon};%focale
\def \xAA {{(\f*\f)/(\xA-\f)+\f}};%position de l'image
\def \yBB {(\f*\yB)/(\f-\xA)};%hauteur de l'image
\coordinate (S) at (0,0);
\coordinate (F) at (\f,0);%foyer
\coordinate (C) at ({-\rayon},0);%centre de courbure
\coordinate (A) at (\xA,0);
\coordinate (B) at (\xA,\yB);
\coordinate (A') at ({\xAA},0);
\coordinate (B') at ({\xAA},{\yBB});
\draw[thin,->](-6.5,0)--++(7,0);
\draw[thick,->,>=latex] (A)node{$\bullet$}--(B);
\draw[thick,->,>=latex,gray] (A')node{$\bullet$}--(B');
\draw[thick,red,postaction={decorate}] (B)--(0,\yB)--(B');
\draw[thick,red,postaction={decorate}] (B)--(0,{\yBB})--(B');
\draw[thick,red,postaction={decorate}] (B)--(0,0)--(B');
\draw[ultra thick] (S)--++(0,2)--++(120:0.2);
\draw[ultra thick] (S)--++(0,-2)--++(-120:0.2);
\foreach \xtext in {A,C,F}
\draw[shift={(\xtext)}] (0pt,2pt) -- (0pt,-2pt) node[below] {\xtext};
\foreach \xtext in {A',B}
\draw[shift={(\xtext)}] node[above] {\xtext};
\draw[shift={(B')}] node[below] {B'};
\draw[shift={(S)}] node[below right] {S};
\end{tikzpicture}
\end{document}