% Rainbows - Sun ray entering a rain drop
% Author: David Fokkema
\documentclass{article}
\usepackage{tikz}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{10pt}%
\usetikzlibrary{calc,decorations.markings}

% Draw an arc denoting an angle using start and delta angles
\newcommand{\drawarcdelta}[4]{
  \draw ($#1+(#2:#4)$) arc[start angle=#2, delta angle=#3, radius=#4];
}

% Draw an arc with label denoting an angle using start and delta angles
\newcommand{\drawlabeledarcdelta}[6]{
  \drawarcdelta{#1}{#2}{#3}{#4}
  \node at ($#1+(#2+#3/2:#6)$) {#5};
}

\begin{document}
\begin{tikzpicture}[xscale=-1,
    ray/.style={decoration={markings,mark=at position .5 with {
      \arrow[>=latex]{>}}},postaction=decorate}
  ]

  % Radius of raindrop
  \pgfmathsetlengthmacro{\r}{3cm}
  % Position where the incoming ray enters the raindrop, as a fraction of
  % the height of the drop.  If 0., the ray will enter in the middle of the
  % drop, if 1., the ray will enter at the top of the drop.
  \pgfmathsetmacro{\f}{.7}

  % Various radii for drawing angle arcs and labels
  \pgfmathsetlengthmacro{\arcradius}{.8cm}
  \pgfmathsetlengthmacro{\dotradius}{.6cm}
  \pgfmathsetlengthmacro{\arclabelradius}{1cm}

  % Calculation of the angle of incidence
  \pgfmathsetmacro{\incidentangle}{asin(\f)}

  % Coordinates of origin and point of entry
  \coordinate (O) at (0, 0);
  \coordinate (A) at (\incidentangle:\r);

  % Draw the drop and the incoming ray, as well as the angle of incidence
  \draw (O) circle (\r);
  \draw[ray] (A  -| \r*3, 0) -- (A);
  \draw[gray] (O) -- ($(O)!1.5!(A)$) node[pos=1.05] {$n$};
  \drawarcdelta{(A)}{0}{\incidentangle}{\arcradius-1pt}
  \drawlabeledarcdelta{(A)}{0}{\incidentangle}{\arcradius+1pt}
    {$i$}{\arclabelradius}

  % For each red and blue ray.  The index of refraction for red light is
  % slightly exaggerated, it should be 1.33.
  \foreach \index/\color in {1.32/red, 1.34/blue} {
    % Calculate angle of refraction
    \pgfmathsetmacro{\refractedangle}{asin(sin(\incidentangle) / \index)}
    % Calculate top angle (at O) in the triangle formed by O, the point of
    % entry, and the point of internal reflection
    \pgfmathsetmacro{\angleindrop}{180 - 2*\refractedangle}

    % Coordinate of point of reflection
    \coordinate (A') at (\incidentangle+\angleindrop:\r);
    % Coordinate of point of exit
    \coordinate (A'') at (\incidentangle+2*\angleindrop:\r);

    \begin{scope}[opacity=.5, color=\color]
      % Draw the light rays
      \draw[ray] (A) -- (A');
      \draw[ray] (A') -- (A'');
      \draw[ray] (A'') -- ($(A'')+(2*\incidentangle+2*\angleindrop:2*\r)$);

      % Draw the normal lines
      \draw (O) -- ($(O)!1.5!(A')$) node[pos=1.05] {$n$};
      \draw (O) -- ($(O)!1.5!(A'')$) node[pos=1.05] {$n$};

      % Draw the arcs and labels
      \drawlabeledarcdelta{(A)}{\incidentangle+180}{-\refractedangle}
        {\arcradius}{$r$}{\arclabelradius}
      \drawarcdelta{(A')}{\incidentangle+\angleindrop+180}{\refractedangle}
        {\arcradius}
      \drawarcdelta{(A')}{\incidentangle+\angleindrop+180}{-\refractedangle}
        {\arcradius}
      \drawarcdelta{(A'')}{\incidentangle+2*\angleindrop+180}{\refractedangle}
        {\arcradius}
    \end{scope}

    % Draw the arcs of the angles of the rays leaving the raindrop.  Note
    % that the angles are identical to the original angle of incidence.
    \drawarcdelta{(A'')}{\incidentangle+2*\angleindrop}{\incidentangle}
      {\arcradius-1pt}
    \drawarcdelta{(A'')}{\incidentangle+2*\angleindrop}{\incidentangle}
      {\arcradius+1pt}
  }

  % Mark the center of the raindrop
  \draw[fill] (O) circle (1.5pt);
\end{tikzpicture}
\end{document}
