Drawing a conical mirror in pst-optexp

Question

I need to draw an optical system which contains a conical mirror, which in the 2D projection is just a triangle or angled mirror. I would like to implement the drawing in pst-optexp. However, I don't see an option to have a polygon mirror, just flat, curved and parabolic ones. Of course I could just put two connected mirrors, but depending on the connection angle the graphical representation wouldn't be nice (extending line edges for acute angles). I'm new to pst-optexp, and maybe I have overseen the corresponding command.

The sketch below should illustrate the setup. I have two mirrors in my setup (in Green). The lower one is just a flat one, the upper one an angled one, which should reflect the light into two directions. In 3D this corresponds to a cone mirror as illustrated in the picture at the end.

Answer 1

There is no ready-to-use component for your task, but you can quite easily define your own component.

pst-optexp offers plain, curved and path interfaces (see e.g. https://tex.stackexchange.com/a/209818/33933 for an advanced example).

Here are the main steps

1. Define a new component with \newOptexpDipole{conicalmirror}. You could also use \newOptxpTripole. The differences in your case would only be that you need two or three nodes for positioning.

2. Define the actual appearance of the component with \def\conicalmirror@comp

3. Define the optical interfaces inside \conicalmirror@nodes using \newOptexpComp. Here, we use a PathIfc, which takes a previously defined, arbitrary path as interface using pst-intersect.

The full drawing:

\documentclass[margin=5pt]{standalone}
\usepackage[dvipsnames,svgnames,pdf]{pstricks}
\usepackage{auto-pst-pdf}
\usepackage{pst-optexp}
\SpecialCoor
\makeatletter
% Define a custom dipole command
\newOptexpDipole{conicalmirror}
%
% Define how the dipole component is drawn
\def\conicalmirror@comp{%
  \pspolygon[fillstyle=solid,fillcolor=gray,linestyle=none](1,-1)(0,0)(1,1)(2,1)(2,-1)
  \pspolygon[fillstyle=solid,fillcolor=green!50!black,linestyle=none]%
    (1,-1)(1.1,-0.9)(0.2,0)(1.1,0.9)(1,1)(0,0)
}
% Define the optical interfaces of the component
\def\conicalmirror@nodes{%
  % save the path, a triangle, which defines the optical interface
  \pssavepath[linestyle=none]{\oenode@Path{A}}{%
    \psline(1,-1)(0,0)(1,1)}
  % define the optical interface for use to draw beams
  \newOptexpComp{%
    {0 0} tx@IntersectDict /\PIT@name{\oenode@Path{A}} get 0 0 refl {PathIfc} 1
  }%
}%
\makeatother
\begin{document}
\begin{pspicture}(10,6)
  \pnode(0,1){Input}
  \pnode(5,1){Mirror}
  \pnode(5,4){ConicalMirror}
  \pnode(2,4){End1}
  \pnode(8,4){End2}
  \begin{optexp}
    \lenslens=3 3 2, n=1.6, compname=Lens(Mirror)
    \newpsstyle{ExtendedMirror}{fillstyle=solid, fillcolor=green!50!black}
    \mirrormirrorwidth=3, linestyle=none, mirrordepth=0.1414, mirrortype=extended, compname=Mirror(Mirror)(ConicalMirror)
    \conicalmirrorposition=end, compname=ConicalMirror(ConicalMirror)
    \optplateposition=end, plateheight=3, platelinewidth=0.3, compshift=-0.5, compname=End1(End1)
    \optplateposition=end, plateheight=3, platelinewidth=0.3, compshift=0.5, compname=End2(End2)
    %
    % First, only draw the filled beam, otherwise the fillings overlap with boundary beams
    \newpsstyle{Beam}{fillstyle=solid, fillcolor=red!10, linestyle=none}
    \drawwidebeambeamdiv=20, beamangle=-10.01{Lens}{Mirror}{ConicalMirror}{End1}
    \drawwidebeambeamdiv=20, beamangle=10.01{Lens}{Mirror}{ConicalMirror}{End2}
    %
    % now draw the boundary beams
    \newpsstyle{Beam}{linecolor=red, linewidth=0.5\pslinewidth}
    \drawbeambeamangle=20{Lens}{Mirror}{ConicalMirror}{End2}
    \drawbeambeamangle=0.01{Lens}{Mirror}{ConicalMirror}{End2}
    \drawbeambeamangle=-0.01{Lens}{Mirror}{ConicalMirror}{End1}
    \drawbeambeamangle=-20{Lens}{Mirror}{ConicalMirror}{End1}
  \end{optexp}
\end{pspicture}
\end{document}