Added MATLAB/Octave versions of the Python scripts

spherical_point_source.m

@@ -0,0 +1,90 @@
+clc
+clear
+
+radius = 100; % curvature radius of the mirror in mm (must be positive)
+angle_d = 30; % maximum angle of incidence of the incident beam in degrees
+num_rays = 21; % number of rays
+source_pos = 80; % source position in mm (must be positive)
+
+focal_length = radius / 2; % focal length of the mirror
+y = linspace(-radius, radius, 1000);
+
+% mirror equation z = sqrt(R^2 - y^2) - R
+function s = surface(y, r)
+    s = sqrt(r ^ 2 - y .^ 2) - r;
+end
+
+% angle between the incident ray and the line connecting the point of incidence
+% of the ray on the mirror and the center of curvature of the mirror
+function e = epsilon(inc_angle, r, s)
+    q = r - s;
+    e = asin(q / r * sin(inc_angle));
+end
+
+% angle of reflected ray
+function r = ref_angle(inc_angle, r, s)
+    r = inc_angle - 2 * epsilon(inc_angle, r, s);
+end
+
+% the z-coordinate of the intersection of the reflected ray with the axis
+function z = ref_z(inc_angle, r, s)
+    q = r * sin(-epsilon(inc_angle, r, s)) / sin(ref_angle(inc_angle, r, s));
+    z = r - q;
+end
+
+% the y-coordinate of the intersection of the incident ray with the mirror 
+function h = height(inc_angle, r, s)
+    phi = ref_angle(inc_angle, r, s) + epsilon(inc_angle, r, s);
+    h = r * sin(phi);
+end    
+
+% line equation for extension of the reflected ray
+function l = line(inc_angle, z, z0)
+    l = tan(inc_angle) * (z - z0);
+end    
+
+figure
+hold on
+plot(surface(y, radius), y) % mirror surface visualization
+plot([-2 * radius 0], [0 0]) % axis of the mirror
+plot([-focal_length], [0], 'o') % focal point
+
+angles = linspace(-angle_d, angle_d, num_rays);
+for i = 1:length(angles)
+    inc_angle = angles(i) * pi / 180;
+    h = height(inc_angle, radius, source_pos);
+
+    z_inc = [-source_pos surface(h, radius)];
+    y_inc = [0 h];
+    plot(z_inc, y_inc, 'k') % draw incident beam
+
+    z_0 = ref_z(inc_angle, radius, source_pos);
+    if isnan(z_0)
+        z_0 = -2 * radius;
+    end 
+
+    if source_pos >= focal_length
+        if z_0 > 0
+            z_0 = -z_0; 
+        end
+    else
+        if z_0 < 0
+            z_0 = -z_0; 
+        end
+    end    
+        
+    z_ref = [surface(h, radius) -2 * radius];
+    y_ref = [h line(ref_angle(inc_angle, radius, source_pos), -2 * radius, z_0)];
+    if abs(source_pos) < abs(2 * focal_length) & abs(source_pos) > abs(focal_length) & abs(z_0) > abs(2 * radius)
+        z_ref = [surface(h, radius) z_0]
+        y_ref = [h 0]
+    end
+    plot(z_ref, y_ref, 'r')
+end
+
+title(sprintf("Radius = %.1f mm. Focal length = %.1f mm. Source position = %.1f mm.\nMaximum incident angle = %.1f{\\deg}. Number of rays = %d", radius, focal_length, -source_pos, angle_d, num_rays))
+xlabel("z, mm")
+ylabel("r, mm")
+ylim([-radius radius])
+xlim([-2 * radius 0])
+grid on