Manipulating the contents of the `spy in` node with `tikz` `spy` library

Question

Consider this code:

\documentclass{article}
\usepackage{tikz}

\usetikzlibrary{calc}
\usetikzlibrary{spy}

\begin{document}

\begin{tikzpicture}
  [spy using outlines={circle, magnification=7, size=3cm, connect spies}]

  \draw[->, very thick] (0,0) -- (5,0);
  \path (2,2) node[fill, rectangle, inner sep=2pt, minimum height=1cm] (n) {};

  \draw[dotted] (n.south west) -- (n.south west |- 0,0);
  \draw[dotted] (n.south east) -- (n.south east |- 0,0);

  \spy on ($(n.south east |- 0,0)!0.5!(n.south west |- 0,0)$) 
    in node at (3,-2);
\end{tikzpicture}

\end{document}

This is the output:

There are two problems:

1. The dotted lines become a couple of dots. Can I change the style of the line inside the spy in node (leaving the original one unchanged) so that the frequency of the dot symbols is higher and the dotted line appears as such in the spy in node as well?
2. Can I reference nodes or coordinates inside the spy in nodes in some way? That's because I'd need to draw a distance measurment mark between the zoomed versions of the two dotted lines.

Answer 1

I feel that if you want to make such drastic changes, you may not want to use spy at all, but just draw whatever you like in a circle node.

\documentclass{article}
\usepackage{tikz}

\usetikzlibrary{calc}
\usetikzlibrary{spy}

\begin{document}

\begin{tikzpicture}
  [spy using outlines={circle, magnification=7, size=3cm, connect spies}]

  \draw[->, very thick] (0,0) -- (5,0);
  \path (2,2) node[fill, rectangle, inner sep=2pt, minimum height=1cm] (n) {};

  \draw[dotted] (n.south west) -- (n.south west |- 0,0);
  \draw[dotted] (n.south east) -- (n.south east |- 0,0);

  \draw  let \p1=($(n.south east)-(n.south west)$)
   in   ($(n.south east |- 0,0)!0.5!(n.south west |- 0,0)$)
   node[circle,draw,inner sep=0pt,minimum size=3cm/7](small){}
    (3,-2)
   node[circle,draw,inner sep=0pt,minimum size=3cm,
   path picture={
   \draw[line width=7*0.8pt] 
   (path picture bounding box.west) -- (path picture bounding box.east);
   \draw[thick,dotted] (-7*\x1/2,0) --  (-7*\x1/2,3) 
    (7*\x1/2,0) --  (7*\x1/2,3); 
   \draw[|<->|] (-7*\x1/2,0.8) -- (7*\x1/2,0.8)
    node[midway,fill=white,minimum size=0pt,rectangle]{$\Delta x$};  }]
   (big){} (small) -- (big);
\end{tikzpicture}

\end{document}

You may use this to annotate the spy node.

\documentclass{article}
\usepackage{tikz}

\usetikzlibrary{calc}
\usetikzlibrary{spy}

\begin{document}

\begin{tikzpicture}
  [spy using outlines={circle, magnification=7, size=3cm, connect spies}]

  \draw[->, very thick] (0,0) -- (5,0);
  \path (2,2) node[fill, rectangle, inner sep=2pt, minimum height=1cm] (n) {};

  \draw[densely dotted] (n.south west) -- (n.south west |- 0,0);
  \draw[densely dotted] (n.south east) -- (n.south east |- 0,0);

  \spy on ($(n.south east |- 0,0)!0.5!(n.south west |- 0,0)$) 
    in node at (3,-2);
  \draw  let \p1=($(n.south east)-(n.south west)$),\n1={7*\x1/2-7*0.2pt}
   in  (3,-2)
   node[circle,draw,inner sep=0pt,minimum size=3cm,
   path picture={
   \draw[|<->|] (-\n1,0.8) -- (\n1,0.8)
    node[midway,fill=white,minimum size=0pt,rectangle]{$\Delta x$};  }]
   (big){}; 
\end{tikzpicture}

\end{document}