Added MATLAB/Octave versions of the Python scripts

parabolic_collimated.m

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+clc
+clear
+
+focal_length = 100; % focal length in mm
+angle_deg = 0; % angle of incidence of the incident beam in degrees
+rays = 21; % number of rays
+
+p = 2 * focal_length; % parameter of the parabola equation y**2 = 2*p*z
+a = 1.1 * focal_length;  % mirror field
+inc_ang = -angle_deg * pi / 180;
+if angle_deg < 0.000001
+  inc_ang = 0.000001 * pi / 180;  % incident ray angle in radians
+end
+var = -a:0.1:a;
+
+% mirror equation z = -y^2 / (2 * p)
+function s = surface(y, p)
+    s = -y .^ 2 / (2 * p);
+end
+
+% reflection angle
+function angle = refl_ang(y, inc_ang, p)
+    angle = 2 * atan(y / p) - inc_ang;
+end
+
+
+% incident ray vector (y_start, y_end)
+% x_vec is vector (x_start, x_end)
+function v = inc_vec(y, inc_ang, x_vec, p)
+    v = tan(-inc_ang) * (x_vec - surface(y, p)) + y;
+end
+
+
+% reflected ray vector (y_start, y_end)
+% x_vec is vector (x_start, x_end)
+function v = refl_vec(y, inc_ang, x_vec, p)
+    sigma = refl_ang(y, inc_ang, p);
+    v = tan(sigma) * (x_vec - surface(y, p) + y / tan(sigma));
+end
+
+
+figure
+hold on
+plot(surface(var, p), var) % mirror surface visualization
+plot([-p 0], [0 0]) % axis of the mirror
+plot([-focal_length], [0], 'o') % focal point
+
+y = linspace(-focal_length, focal_length, rays);
+for i = 1:length(y)
+    x_vec = [-p surface(y(i), p)];
+    
+    plot(x_vec, inc_vec(y(i), inc_ang, x_vec, p), 'k')
+
+    r = refl_ang(y, inc_ang, p);
+    if (r < pi / 2 & r > -pi / 2)
+        plot(x_vec, refl_vec(y(i), inc_ang, x_vec, p), 'r')
+    else
+        x_vec_out = [surface(y(i), p) 0];
+        plot(x_vec_out, refl_vec(y(i), inc_ang, x_vec_out, p), 'r')
+    end
+end
+
+title(sprintf("Focal length = %.1f mm. Incident angle = %.1f{\\deg}. Number of rays = %d", focal_length, angle_deg, rays))
+xlabel("z, mm")
+ylabel("r, mm")
+ylim([-a a])
+xlim([-p 0])
+grid on