Interference Pattern

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\documentclass[border=2pt]{standalone}
% Drawing
\usepackage{tikz}
% Tikz Library
\usetikzlibrary{calc, shapes}
% Styles
\tikzstyle{ray} = [line width = 0.85, color = red]
\tikzstyle{vertical} = [line width = 0.85, dashed]
% Newcommand            
\newcommand{\lline}[4]{\draw[vertical] (#1) -- ({#2*cos(#4)-#3*sin(#4)},{+#2*sin(#4)+#3*cos(#4)});}
\usetikzlibrary{backgrounds}
\begin{document}
        
    \begin{tikzpicture}[semic/.style args={#1,#2}{semicircle,minimum width=#1,draw,anchor=arc end,rotate=#2},outer sep=0pt,line width=.7pt]
        
        % Grid
%       \draw[dotted] (0,0) grid (11,4);
%       \foreach \i in {0,...,10}
%       {
%           \node at (-2ex,\i) {\i};
%           \node at (\i,-2ex) {\i};
%       }
        
        % Coordinates
        \coordinate (S) at (0.5,1);
        \coordinate (P) at (11,1.5);
        \coordinate (A) at (6,1);
        
        % Nodes
        \node[draw, rectangle, minimum width=1cm, minimum height=0.5cm] at (S) {$S$};
        \node (p') [semic={1cm,-90}, label={[rotate=0, below left, yshift=-0.7cm, black!50]}, black!50, rotate= 40] at (10.2,3.8) {};
        \node (p) [semic={1cm,-90}, label={[rotate=0]$P$}] at (P) {};
        \node (p'') [semic={1cm,-90}, label={[rotate=0, below left, yshift=-0.7cm, black!50]}, black!50, rotate= -38] at (10.85,-1.) {};
        
        % Slit
 
 
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