Added MATLAB/Octave versions of the Python scripts

spherical_collimated.m

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+clc
+clear
+
+radius = 100; % curvature radius of the mirror in mm
+angle_deg = 0; % angle of incidence of the incident beam in degrees
+rays = 21; % number of rays
+
+focal_length = radius / 2; % focal length of the mirror
+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
+function s = surface(y, r)
+    s = sqrt(r ^ 2 - y .^ 2) - r;
+end
+
+% reflection angle
+function angle = refl_ang(y, inc_ang, r)
+    angle = inc_ang - 2 * asin((-y / tan(inc_ang) - surface(y, r)) / r * sin(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, r)
+    v = tan(-inc_ang) * (x_vec - surface(y, r)) + 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, r)
+    sigma =  refl_ang(y, inc_ang, r);
+    v = tan(sigma) .* (x_vec - surface(y, r) + y ./ tan(sigma));
+end
+
+figure
+hold on
+plot(surface(var, radius), var) % mirror surface visualization
+plot([-2 * radius 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 = [-radius surface(y(i), radius)];
+    plot(x_vec, inc_vec(y(i), inc_ang, x_vec, radius), 'k')
+    
+    r = refl_ang(y(i), inc_ang, radius);
+    if (r < pi / 2 & r > -pi / 2)
+        plot(x_vec, refl_vec(y(i), inc_ang, x_vec, radius), 'r')
+    else
+        x_vec_out = [surface(y(i)) 0];
+        plot(x_vec_out, refl_vec(y(i), inc_ang, x_vec_out, radius), 'r')
+    end
+end
+
+title(sprintf("Radius = %.1f mm. Focal length = %.1f mm.\nIncident angle = %.1f{\\deg}. Number of rays = %d", radius, focal_length, angle_deg, rays))
+xlabel("z, mm")
+ylabel("r, mm")
+ylim([-a a])
+xlim([-radius 0])
+grid