Added MATLAB/Octave versions of the Python scripts

parabolic_point_source.m

@@ -0,0 +1,102 @@
+clc
+clear
+
+focal_length = 100; % focal length in mm
+angle_d = 25; % maximum angle of incidence of the incident beam in degrees
+num_rays = 21; % number of rays
+source_pos = 400; % source position in mm (must be positive)
+% there is a bug when source_pos = focal_length because of very small
+% angles of reflectance.
+% Instead, better to choose source_pos = focal_length + 0.01 or something like
+% this
+
+p = 2 * focal_length; % parameter of the parabola equation y**2 = 2*p*z
+y = linspace(-p, p, 1000);
+
+% mirror equation z = -y^2 / (2 * p)
+function s = surface(y, p)
+    s = -y .^ 2 / (2 * p);
+end
+
+function angle = phi(y, p)
+    angle = atan(y / p);
+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 angle = epsilon(y, inc_angle, p)
+    angle = inc_angle - phi(y, p);
+end
+
+% angle of reflected ray
+function angle = ref_angle(y, inc_angle, p)
+    angle = phi(y, p) - epsilon(y, inc_angle, p);
+end
+
+% the z-coordinate of the intersection of the reflected ray with the axis
+function z = ref_z(y, inc_angle, p, s)
+    if inc_angle == 0
+        z = 0;
+        return
+    end
+    tg_sigma = tan(inc_angle);
+    z_0 = -(y - s * tg_sigma) / tg_sigma;
+    z = y ./ tan(ref_angle(y, inc_angle, p)) + z_0;
+end
+
+% the y-coordinate of the intersection of the incident ray with the mirror 
+function h = height(inc_angle, p, s)
+    if inc_angle == 0
+        h = 0;
+        return
+    end
+    tg_sigma = tan(inc_angle);
+    h = -p / tg_sigma * (1 - sqrt(1 + 2 * s / p * tg_sigma ^ 2));
+end
+
+% line equation for extension of the reflected ray
+function l = line(ref_angle, z, z0)
+    l = tan(ref_angle) * (z - z0);
+end
+
+figure
+hold on
+plot(surface(y, p), y) % mirror surface visualization
+plot([-2 * p 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, p, source_pos);
+
+    z_inc = [-source_pos surface(h, p)];
+    y_inc = [0 h];
+    plot(z_inc, y_inc, 'k') % draw incident beam
+
+    z_0 = ref_z(h, inc_angle, p, source_pos);
+    if isnan(z_0)
+        z_0 = -2 * p;
+    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, p) -2 * p];
+    y_ref = [h line(ref_angle(h, inc_angle, p), -2 * p, z_0)];
+    plot(z_ref, y_ref, 'r')
+end
+
+title(sprintf("Focal length = %.1f mm. Source position = %.1f mm.\nMaximum incident angle = %.1f{\\deg}. Number of rays = %d", focal_length, -source_pos, angle_d, num_rays))
+xlabel("z, mm")
+ylabel("y, mm")
+ylim([-p p])
+xlim([-2 * p 0])
+grid on