# Fig169.tex

\begin{center}
\begin{pspicture}(-8,-6)(8,6)
\begin{psclip}{\psframe[linestyle=none](-6,-6)(6,6)}
\multido{\i=-10+1}{21}{%
\parametricplot{-6}{6}{%
/c 0.1 def
/b 4.1 def
/X t def
/Y X 80 dup sin exch cos div mul
b \i\space mul c \i\space dup mul mul sub
sub
def
X Y}}
\multido{\i=-10+1}{21}{%
\parametricplot{-6}{6}{%
/c 0.1 def
/b 4.1 def
/X t def
/Y X 80 dup sin exch cos div mul neg
b \i\space mul c \i\space dup mul mul add
def
X Y}}
% paraboles
\multido{\i=-4+1}{8}{%
\parametricplot[linecolor=red]{-6}{6}{%
/c 0.1 10 sin mul def
/b 4.1 10 sin mul def
/X t def
/Y c X dup mul mul 10 cos dup mul mul
b c \i\space mul add dup mul 10 sin mul div
b \i\space mul 2 div 10 sin div
\i\space dup mul c mul 4 div 10 sin div
def
X Y}}
\psline[linestyle=dashed,linecolor=blue](0,6)(0,-6)
\end{psclip}
\rput(-7.5,0){%
\psline(0,-2)(0,4)
\psline(-1,0)(1,0)
\uput[90](0,4){$y$}
\uput[90](1,0){$x$}
\psline(4;80)
\psline(4;100)
\uput[0](4;80){$\mathrm{S_1}$}
\uput[180](4;100){$\mathrm{S_2}$}
\uput[225](0,0){O}
\psarc(0,0){2}{80}{90}
\psarc(0,0){1.8}{90}{100}
\uput[85](2;85){$\THETA$}
\uput[95](1.8;95){$\THETA$}
}
\end{pspicture}
\end{center}