Tikz의 양면 오목 렌즈

Question

안녕하세요 여러분, 즐거운 크리스마스 보내세요(늦었지만 ㅋㅋㅋ). 아래와 같은 양면 오목 렌즈를 그리고 싶지만 실제로는 불가능합니다.

이렇게 글을 쓰긴 했지만, 제가 원하는 결과는 아닙니다.

\documentclass[tikz,border=3mm]{standalone}
\begin{document}
\begin{tikzpicture}[scale=0.9]
\pgfmathsetmacro{\lensRadius}{2.6}
\pgfmathsetmacro{\lensHeight}{1.8}
\pgfmathsetmacro{\startAngle}{-asin(\lensHeight/\lensRadius)}

\draw [fill=lightgray!50, very thick]  (0,\lensHeight)
arc[start angle=-\startAngle,delta 
angle=2*\startAngle,radius=\lensRadius]
--++ (0:2)
arc[start angle=-\startAngle,delta angle=2*\startAngle,radius=- 
\lensRadius]
-- cycle;
\end{tikzpicture}
\end{document}

Answer 1

이런 렌즈가 그려지네요. 반경을 다르게 선택할 수 있지만 물론 동일하게 설정할 수도 있습니다. 초점의 위치는 다음과 같이 계산됩니다.렌즈메이커 방정식. 매크로 대신 pgf 키가 사용됩니다. 매개변수는 높이 h, 두께 d, 굴절률 n, 반경 R1및 입니다 R2. 매개변수는 alpha청록색 파선의 기울기를 나타냅니다.

\documentclass[tikz,border=3mm]{standalone}
\begin{document}
 \begin{tikzpicture}[bullet/.style={circle,black,fill,inner sep=1.8pt},
   every label/.append style={black},
   declare function={lensf(\n,\d,\Rone,\Rtwo)=1/(
   (\n-1)*(1/\Rone-1/\Rtwo+(\n-1)*\d/(\n*\Rone*\Rtwo)));
   startangle(\h,\r)=asin(\h/\r);},
   lens/.cd,n/.initial=1.7,R1/.initial=3.6,R2/.initial=-3.9,d/.initial=0.6,
   h/.initial=1.8,alpha/.initial=20]
  %short cut 
  \def\pv#1{\pgfkeysvalueof{/tikz/lens/#1}} 

  \draw [fill=lightgray!50, very thick]  
    ({-\pv{d}/2-cos(90-startangle(\pv{h},\pv{R1}))},\pv{h})
    arc[start angle={startangle(\pv{h},\pv{R1})},delta 
    angle={-2*startangle(\pv{h},\pv{R1})},radius=\pv{R1}]
    --++ ({\pv{d}+cos(90-startangle(\pv{h},\pv{R1}))+cos(90+startangle(\pv{h},\pv{R2}))},0)
    arc[start angle={-startangle(\pv{h},\pv{R2})},delta 
    angle={2*startangle(\pv{h},\pv{R2})},radius=\pv{R2}]  
    -- cycle;
   \draw[very thick,dashed] (0,-1.2*\pv{h}) --  (0,1.2*\pv{h});
   \draw[very thick] (-1.2*\pv{R1}-\pv{d}/2,0) -- (-1.2*\pv{R2}+\pv{d}/2,0);
   \draw[cyan,dashed,thick] ({-\pv{d}/2-\pv{R1}},0)   
    node[bullet,label=below:$C_1$]{}
   -- node[sloped,above]{$R_1$} ++ (\pv{alpha}:\pv{R1});
   \path ({-lensf(\pv{n},\pv{d},\pv{R1},\pv{R2})},0) 
    node[bullet,label=below:$F_2$]{};
   \draw[cyan,dashed,thick] ({\pv{d}/2-1*\pv{R2}},0)    
    node[bullet,label=above:$C_2$]{}
   -- node[sloped,below]{$R_2$} ++ (\pv{alpha}:\pv{R2});
   \path ({lensf(\pv{n},\pv{d},-1*\pv{R2},-1*\pv{R1})},0) 
    node[bullet,label=above:$F_1$]{};
 \end{tikzpicture}
\end{document}