Ce document regroupe les codes TIKZ des figures utilisées pour le cours "Les lentilles minces" situé à la page: http://femto-physique.fr/optique_geometrique/opt_C3.php
% !TEX encoding = UTF-8 Unicode
% J.Roussel
% MAJ : 2014-06-03
% Ce document regroupe les codes TIKZ des figures utilisées pour le cours "Les lentilles minces" situé à la page http://femto-physique.fr/optique_geometrique/opt_C3.php
%-------------------------------------------
\documentclass[11pt]{article}
\input{styles_optique}
\title{Figures TikZ du cours "Les lentilles minces"}
\author{J.Roussel}
\begin{document}
% =========================================================
% Lentille optique
% =========================================================
\begin{tikzpicture}
\def \y {2};%demi hauteur de la lentille
\def \Ra {3};%rayon de la première face
\def \Rb {5};%rayon de la face de sortie
\def \anglea {asin(\y/\Ra)};
\def \angleb {asin(\y/\Rb)};
\def \ep {\Rb+\Ra-sqrt(\Rb*\Rb-\y*\y)-sqrt(\Ra*\Ra-\y*\y)};
\coordinate (O) at (0,0);
\coordinate (B) at (0,\y);
\coordinate (A) at (0,-\y);
\coordinate (C1) at ({sqrt(\Ra*\Ra-\y*\y)},0);
\coordinate (C2) at ({-sqrt(\Rb*\Rb-\y*\y)},0);
\coordinate (S1) at ({sqrt(\Ra*\Ra-\y*\y)-\Ra},0);
\coordinate (S2) at ({\Rb-sqrt(\Rb*\Rb-\y*\y)},0);
\draw (C2)--(B) node[midway,fill=white]{$R_{2}$}--(A)--(C1)node[midway,fill=white]{$R_{1}$};
\draw[verre] (A) arc({180+\anglea}:{180-\anglea}:\Ra) arc({\angleb}:{-\angleb}:\Rb);
\draw[thin,->] (-5,0)--++(8,0)node[above]{\small axe optique};
\foreach \x/\xtex in {C1/$\mathrm{C_{1}}$,C2/$\mathrm{C_{2}}$,S1/$\mathrm{S_{1}}$,S2/$\mathrm{S_{2}}$}
\draw[shift={(\x)}] (0pt,2pt) -- (0pt,-2pt) node[below] {\xtex};
\draw[shift={(S1)},|<->|] (0,20pt)--++({\ep},0) node[pos=0.5,above]{e};
\draw (0,-\y)node[above=20pt]{\small $n$};
\end{tikzpicture}
% =========================================================
% Les différentes formes de lentilles minces
% =========================================================
\begin{tikzpicture}[scale=0.9]
\begin{scope}
\draw[verre] (0,-2) to[bend left] (0,2) to [bend left] (0,-2);
\draw[verre,shift={(2,0)}] (0,-2) to[bend left] (0,2) --cycle;
\draw[verre,shift={(4,0)}] (0,-2) to[bend left] (0,2) to [bend right=15] (0,-2);
\draw[ultra thick,<->,>=latex,shift={(5,0)}] (0,-2) -- (0,2);
\draw (2,-2) node[below,text width=4cm]{\small Lentilles convergentes};
\draw (5,-2) node[below]{\small Symbole};
\end{scope}
\begin{scope}[shift={(8,0)}]
\draw[verre] (0,-2) -- (0,2) --++(0.7,0) to [bend right] (0.7,-2)--cycle;
\draw[verre,shift={(2,0)}] (0,-2) to[bend left=10] (0,2) --++(0.7,0) to[bend right=35] (0.7,-2)--cycle;
\draw[verre,shift={(4,0)}] (0,-2) to[bend right=15] (0,2) --++(0.7,0) to [bend right=15] (0.7,-2)--cycle;
\draw[ultra thick,>-<,>=latex,shift={(5.5,0)}] (0,-2) -- (0,2);
\draw (2,-2) node[below,text width=4cm]{\small Lentilles divergentes};
\draw (5.5,-2) node[below]{\small Symbole};
\end{scope}
\end{tikzpicture}
% =========================================================
% Aberrations géométriques : simulation du trajet de la lumière traversant deux lentilles convergentes plan-convexe de même rayon de courbure et d'épaisseur différente.
% =========================================================
\begin{tikzpicture}[scale=0.8,decoration={markings,mark=at position 1cm with {\arrow[red]{stealth};}}]
\begin{scope}
\def \indice {1.7};%indice du verre
\def \y {3};%demi hauteur de la lentille
\def \Rb {5};%rayon de la face de sortie
\def \angleb {asin(\y/\Rb)};
\coordinate (B) at (0,\y);
\coordinate (A) at (0,-\y);
\coordinate (C2) at ({-sqrt(\Rb*\Rb-\y*\y)},0);
\coordinate (S1) at (0,0);
\coordinate (S2) at ({\Rb-sqrt(\Rb*\Rb-\y*\y)},0);
\draw[thin,->] (-2,0)--++(12,0);
\draw (0,\y) node[above]{$\frac{e}{R_{2}}=20\%$};
\foreach \k in {2.7,2.65,...,0}{
\draw[->,red,postaction={decorate},opacity=0.5] (-2,\k)--({-sqrt(\Rb*\Rb-\y*\y)+sqrt(\Rb^2-\k^2)},\k)--++({asin(\k/\Rb)-asin(\indice*\k/\Rb)}:2*\Rb);
\draw[->,red,postaction={decorate},opacity=0.5] (-2,-\k)--({-sqrt(\Rb*\Rb-\y*\y)+sqrt(\Rb^2-\k^2)},-\k)--++({asin(\indice*\k/\Rb)-asin(\k/\Rb)}:2*\Rb);
}
\draw[verre] (A) --(B) arc({\angleb}:{-\angleb}:\Rb);
\end{scope}
\begin{scope}[shift={(0,-6)}]
\def \indice {1.7};%indice du verre
\def \y {1.2};%demi hauteur de la lentille
\def \Rb {5};%rayon de la face de sortie
\def \angleb {asin(\y/\Rb)};
\coordinate (B) at (0,\y);
\coordinate (A) at (0,-\y);
\coordinate (C2) at ({-sqrt(\Rb*\Rb-\y*\y)},0);
\coordinate (S1) at (0,0);
\coordinate (S2) at ({\Rb-sqrt(\Rb*\Rb-\y*\y)},0);
\draw[thin,->] (-2,0)--++(12,0);
\foreach \k in {1.1,1.05,...,0}{
\draw[->,red,postaction={decorate},opacity=0.5] (-2,\k)--({-sqrt(\Rb*\Rb-\y*\y)+sqrt(\Rb^2-\k^2)},\k)--++({asin(\k/\Rb)-asin(\indice*\k/\Rb)}:2*\Rb);
\draw[->,red,postaction={decorate},opacity=0.5] (-2,-\k)--({-sqrt(\Rb*\Rb-\y*\y)+sqrt(\Rb^2-\k^2)},-\k)--++({asin(\indice*\k/\Rb)-asin(\k/\Rb)}:2*\Rb);
}
\draw (0,\y) node[above]{$\frac{e}{R_{2}}=3\%$};
\draw[verre] (A) --(B) arc({\angleb}:{-\angleb}:\Rb);
\end{scope}
\end{tikzpicture}
% =========================================================
% Aberrations chromatiques : le trajet des rayons lumineux dépend de la longueur d'onde.
% =========================================================
\begin{tikzpicture}[decoration={markings,mark=at position 1cm with {\arrow[]{stealth};}}]
\def \y {2};%demi hauteur de la lentille
\def \Rb {5};%rayon de la face de sortie
\def \angleb {asin(\y/\Rb)};
\def \k {1};%éloignement du rayon par rapport à l'axe optique
\coordinate (B) at (0,\y);
\coordinate (A) at (0,-\y);
\node (P) at (0.1,1) {};
\node (S) at (3,1.5) {\small milieu dispersif};
\draw[verre] (A) --(B) arc({\angleb}:{-\angleb}:\Rb);
\draw[thin,->] (-2,0)--++(12,0);
\foreach \couleur/\indice in {red/1.7,green/1.8,blue/1.9}{
\draw[->,\couleur,postaction={decorate}] (-2,\k)--({-sqrt(\Rb*\Rb-\y*\y)+sqrt(\Rb^2-\k^2)},\k)--++({asin(\k/\Rb)-asin(\indice*\k/\Rb)}:8);
\draw[->,\couleur,postaction={decorate}] (-2,-\k)--({-sqrt(\Rb*\Rb-\y*\y)+sqrt(\Rb^2-\k^2)},-\k)--++({asin(\indice*\k/\Rb)-asin(\k/\Rb)}:8);
}
\draw[->] (S.west) to[bend right] (P);
\end{tikzpicture}
% =========================================================
%
% =========================================================
\begin{tikzpicture}[scale=0.9,decoration={markings,mark=at position 1cm with {\arrow[red]{stealth};}}]
\begin{scope}
\def \indice {2};%indice du verre
\def \y {2};%demi hauteur de la lentille
\def \Rb {5};%rayon de la face de sortie
\def \angleb {asin(\y/\Rb)};
\coordinate (B) at (0,\y);
\coordinate (A) at (0,-\y);
\coordinate (F') at ({\Rb/(\indice-1)},0);
\draw[verre] (A) --(B) arc({\angleb}:{-\angleb}:\Rb);
\draw[thin,->] (-2,0)--++(8,0);
\foreach \k in {1}{
\draw[->,red,postaction={decorate}] (-2,\k)--({-sqrt(\Rb*\Rb-\y*\y)+sqrt(\Rb^2-\k^2)},\k)--++({asin(\k/\Rb)-asin(\indice*\k/\Rb)}:6);
\draw[->,red,postaction={decorate}] (-2,-\k)--({-sqrt(\Rb*\Rb-\y*\y)+sqrt(\Rb^2-\k^2)},-\k)--++({asin(\indice*\k/\Rb)-asin(\k/\Rb)}:6);
}
\foreach \x in {F'}
\draw[shift={(\x)}] (0pt,2pt) -- (0pt,-2pt) node[below] {\x};
\draw (0,\y) node[above]{\small Lentille convergente};
\end{scope}
\begin{scope}[shift={(13,0)}]
\def \indice {2};%indice du verre
\def \y {2};%demi hauteur de la lentille
\def \ep {0.5}; %épaisseur de la lentille divergente
\def \Rb {5};%rayon de la face de sortie
\def \angleb {asin(\y/\Rb)};
\coordinate (B) at (0,\y);
\coordinate (A) at (0,-\y);
\coordinate (F') at ({-\Rb/(\indice-1)},0);
\draw[verre] (A) --(B)--++(\ep,0) arc({180-\angleb}:{180+\angleb}:\Rb);
\draw[thin,->] (-6,0)--++(8,0);
\foreach \k in {1}{
\draw[->,red,postaction={decorate}] (-5,\k)--({\ep+\Rb*cos(\angleb)-sqrt(\Rb^2-\k^2)},\k)--++({asin(\indice*\k/\Rb)-asin(\k/\Rb)}:2);
\draw[dashed] (F')--({\ep+\Rb*cos(\angleb)-sqrt(\Rb^2-\k^2)},\k);
\draw[->,red,postaction={decorate}] (-5,-\k)--({\ep+\Rb*cos(\angleb)-sqrt(\Rb^2-\k^2)},-\k)--++({asin(\k/\Rb)-asin(\indice*\k/\Rb)}:2);
\draw[dashed] (F')--({\ep+\Rb*cos(\angleb)-sqrt(\Rb^2-\k^2)},-\k);
}
\foreach \x in {F'}
\draw[shift={(\x)}] (0pt,2pt) -- (0pt,-2pt) node[below] {\x};
\draw (0,\y) node[above]{\small Lentille divergente};
\end{scope}
\end{tikzpicture}
% =========================================================
%
% =========================================================
\begin{tikzpicture}[decoration={markings,mark=at position 1cm with {\arrow[red]{stealth};}}]
\begin{scope}
\def \indice {2};%indice du verre
\def \y {2};%demi hauteur de la lentille
\def \Rb {5};%rayon de la face de sortie
\def \angleb {asin(\y/\Rb)};
\coordinate (B) at (0,\y);
\coordinate (A) at (0,-\y);
\coordinate (F) at ({-\Rb/(\indice-1)},0);
\draw[verre] (A) --(B) arc({\angleb}:{-\angleb}:\Rb);
\draw[thin,->] (-6,0)--++(8,0);
\foreach \k in {1}{
\draw[->,red,postaction={decorate}] (F)--(0,{\k-0.03})--({-sqrt(\Rb*\Rb-\y*\y)+sqrt(\Rb^2-\k^2)},\k)--++(2,0);
\draw[->,red,postaction={decorate}] (F)--(0,-\k+0.03)--({-sqrt(\Rb*\Rb-\y*\y)+sqrt(\Rb^2-\k^2)},-\k)--++(2,0);
}
\foreach \x in {F}
\draw[shift={(\x)}] (0pt,2pt) -- (0pt,-2pt) node[below] {\x};
\draw (0,\y) node[above]{\small Lentille convergente};
\end{scope}
\begin{scope}[shift={(5,0)}]
\def \indice {2};%indice du verre
\def \y {2};%demi hauteur de la lentille
\def \ep {0.5}; %épaisseur de la lentille divergente
\def \Rb {5};%rayon de la face de sortie
\def \angleb {asin(\y/\Rb)};
\coordinate (B) at (0,\y);
\coordinate (A) at (0,-\y);
\coordinate (F) at ({\Rb/(\indice-1)},0);
\draw[verre] (A) --(B)--++(\ep,0) arc({180-\angleb}:{180+\angleb}:\Rb);
\draw[thin,->] (-2,0)--++(8,0);
\foreach \k in {1}{
\draw[->,red,postaction={decorate},shift={(0,\k)}] ({180-atan(\k*(\indice-1)/\Rb)}:2)--(0,0)--++(3,0);
\draw[dashed,shift={(0,\k)}] (0,0)--(F);
\draw[->,red,postaction={decorate},shift={(0,-\k)}] ({180+atan(\k*(\indice-1)/\Rb)}:2)--(0,0)--++(3,0);
\draw[dashed,shift={(0,-\k)}] (0,0)--(F);
}
\foreach \x in {F}
\draw[shift={(\x)}] (0pt,2pt) -- (0pt,-2pt) node[below] {\x};
\draw (0,\y) node[above]{\small Lentille divergente};
\end{scope}
\end{tikzpicture}
% =========================================================
%
% =========================================================
\begin{tikzpicture}[scale=1,decoration={markings,mark=at position 1cm with {\arrow[]{stealth};}}]
\coordinate (O1) at (0,0);%centre optique de la première lentille
\coordinate (A) at (-5,0);%position de l'objet
\coordinate (B) at (-5,1);%sommet de l'objet
\def \focaleUn{2};%focale de la première lentille
\coordinate (A') at (3.33,0);%position de l'objet
\coordinate (B') at (3.33,-0.667);%sommet de l'objet
%\draw[help lines] (-7,-3) grid (7,3);
%\draw[very thin, lightgray, step=2mm] (-7,-3) grid (7,3);
\draw[thin,->](-6.5,0)--++(13,0)node[above right,fill=white]{\tiny +};
\draw[|->, thick] (A)node[below]{A}--(B)node[above]{B};
\draw[|->, thick,gray] (A')node[above]{A'}--(B')node[below]{B'};
\draw[shift={(O1)},ultra thick,<->,>=latex] (0,-2)--++(0,4) node[above]{$\mathcal{L}$};%lentille convergente
\draw[shift={(B)},red, postaction={decorate},->] (0,0)--++(5,0)--++({-atan(1/2)}:5);
\draw[shift={(B)},red, postaction={decorate},->] (0,0)--++({-atan(1/5)}:11);
\draw[shift={(B)},red, postaction={decorate},->] (0,0)--++({-atan(1/3)}:5.27)--++(5,0);
\foreach \x/\z in {O1/\focaleUn}{
\draw[shift={(\x)}] (0,0) node[below left] {O};
\draw[shift={(\x)}] (\z,2pt) --++ (0,-4pt) node[below] {F'};
\draw[shift={(\x)}] ({-\z},2pt) --++ (0,-4pt) node[below] {F};
}
\end{tikzpicture}
\end{document}