File:Snells law wavefronts.png

% Illustration of Snell's law
function main()
   n1=1.0;
   n2=1.5;

   figure(1); clf; hold on; axis equal; axis off;
   sign = -1;% is the source up or down?
   O=[0, -1*sign];
   k=500;

   
% KSmrq's colors
   red    = [0.867 0.06 0.14];
   blue   = [0, 129, 205]/256;
   green  = [0, 200,  70]/256;
   yellow = [254, 194,   0]/256;
   white = 0.99*[1, 1, 1];
   black = [0, 0, 0];
   gray = 0.5*white;

   color1=red;
   color2=blue;
   color3=gray;
   lw = 4;
   
   plot_line=0;
   Theta=linspace(0, 2*pi, k);
   V=0*Theta; W=0*Theta;
   S0=4;
   spacing=0.45;
   p=floor(S0/spacing);
   S=linspace(0, S0, p+1)+0.1*spacing;

   % plot the interface between diellectrics
   L=3.8;
   plot([-L, L], [0, 0], 'color', color3, 'linewidth', lw);


% plot a ray
   plot_line=1;
   s=5.2;
   theta=pi/3; wfr(s, theta, n1, n2, O, sign, plot_line, color1, lw);

% plot the wafefronts
   plot_line=0;
   for i=1:p
      for j=1:k
	 s=S(i);
	 theta=Theta(j);
	 [V(j), W(j)]=wfr(s, theta, n1, n2, O, sign, plot_line, color1, lw);
      end
      plot(V, W, 'color', color2, 'linewidth', lw);
   end


   % dummy point to enlarge the bounding box
   plot(0, S0+1.5*spacing, '*', 'color', white);

   saveas(gcf, 'Snells_law_wavefronts.eps', 'psc2')


function [a, b]=wfr(s, theta, n1, n2, O, sign, plot_line, color1, lw);

   X=O+s*[sin(theta), sign*cos(theta)];

  if( sign*X(2) > 0 )
    t=-sign*O(2)/cos(theta);
    X0=O+t*[sin(theta), sign*cos(theta)];
    
    if (plot_line == 1) 
      plot([O(1), X0(1)], [O(2), X0(2)], 'color', color1, 'linewidth', lw, 'linestyle', '--');
    end

    d = norm(O-X0);
    r = (s-d)*(n2/n1)^(sign);

    theta2=asin(n1*sin(theta)/n2);
    XE=X0+r*[sin(theta2), sign*cos(theta2)];
  else
    XE = X;
  end  
  a = XE(1);
  b = XE(2); 

  if (plot_line==1)
    plot([X0(1), XE(1)], [X0(2), XE(2)], 'color', color1, 'linewidth', lw, 'linestyle', '--');
  end