function waste_at_the_end = solution_visualization(q0,x0, qf, xf, optics, lambda)



x=linspace(x0,xf,1000); % we will calculate beam profile between x0 and xf
%fprintf('======== Forward propagation ======\n')
q_forward=gbeam_propagation(x,q0,x0,optics);
[w_forward,r_forward]=q2wr(q_forward, lambda);

%fprintf('======== Backward propagation =====\n')

q_backward=gbeam_propagation(x,qf,xf,optics);
[w_backward,r_backward]=q2wr(q_backward, lambda);

%fprintf('========= Plotting ================\n')
plot ( ...
	x,w_forward, '-r',  ...
	x,-w_forward, '-r', ...
	x, w_backward, '-.b', ...
	x, -w_backward, '-.b')
legend({'forward propagation', '', 'backward propagation', ''})      

[waste_at_the_end,radius_at_the_end]  = q2wr(q_forward(end), lambda);
%waste_at_the_end
%radius_at_the_end