I am trying to draw a picture using TikZ in LaTeX. In this example, I have drawn two curved lines and a vertical line. I would like to make the lower curved line only visible to the right of the vertical line. In other words, I would like to clip the lower curved line. However, I do not want to clip the entire picture. I would still like to view the entire top curve. Is this possible in TikZ?
\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=5]
\draw (.1,1.6) .. controls (.6,1.6) and (1.5,1) .. (2,1);
\draw (.1,1) .. controls (.6,1) and (1.5,.4) .. (2,.4);
\draw[dashed] (1,0) -- (1,2);
\end{tikzpicture}
\end{document}

