102 lines
2.8 KiB
Matlab
102 lines
2.8 KiB
Matlab
clc
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clear
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focal_length = 100; % focal length in mm
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angle_d = 25; % maximum angle of incidence of the incident beam in degrees
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num_rays = 21; % number of rays
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source_pos = 400; % source position in mm (must be positive)
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% there is a bug when source_pos = focal_length because of very small
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% angles of reflectance.
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% Instead, better to choose source_pos = focal_length + 0.01 or something like
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% this
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p = 2 * focal_length; % parameter of the parabola equation y**2 = 2*p*z
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y = linspace(-p, p, 1000);
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% mirror equation z = -y^2 / (2 * p)
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function s = surface(y, p)
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s = -y .^ 2 / (2 * p);
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end
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function angle = phi(y, p)
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angle = atan(y / p);
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end
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% angle between the incident ray and the line connecting the point of incidence
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% of the ray on the mirror and the center of curvature of the mirror
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function angle = epsilon(y, inc_angle, p)
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angle = inc_angle - phi(y, p);
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end
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% angle of reflected ray
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function angle = ref_angle(y, inc_angle, p)
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angle = phi(y, p) - epsilon(y, inc_angle, p);
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end
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% the z-coordinate of the intersection of the reflected ray with the axis
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function z = ref_z(y, inc_angle, p, s)
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if inc_angle == 0
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z = 0;
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return
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end
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tg_sigma = tan(inc_angle);
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z_0 = -(y - s * tg_sigma) / tg_sigma;
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z = y ./ tan(ref_angle(y, inc_angle, p)) + z_0;
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end
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% the y-coordinate of the intersection of the incident ray with the mirror
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function h = height(inc_angle, p, s)
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if inc_angle == 0
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h = 0;
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return
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end
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tg_sigma = tan(inc_angle);
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h = -p / tg_sigma * (1 - sqrt(1 + 2 * s / p * tg_sigma ^ 2));
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end
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% line equation for extension of the reflected ray
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function l = line(ref_angle, z, z0)
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l = tan(ref_angle) * (z - z0);
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end
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figure
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hold on
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plot(surface(y, p), y) % mirror surface visualization
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plot([-2 * p 0], [0 0]) % axis of the mirror
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plot([-focal_length], [0], 'o') % focal point
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angles = linspace(-angle_d, angle_d, num_rays);
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for i = 1:length(angles)
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inc_angle = angles(i) * pi / 180;
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h = height(inc_angle, p, source_pos);
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z_inc = [-source_pos surface(h, p)];
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y_inc = [0 h];
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plot(z_inc, y_inc, 'k') % draw incident beam
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z_0 = ref_z(h, inc_angle, p, source_pos);
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if isnan(z_0)
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z_0 = -2 * p;
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end
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if source_pos >= focal_length
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if z_0 > 0
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z_0 = -z_0;
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end
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else
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if z_0 < 0
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z_0 = -z_0;
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end
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end
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z_ref = [surface(h, p) -2 * p];
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y_ref = [h line(ref_angle(h, inc_angle, p), -2 * p, z_0)];
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plot(z_ref, y_ref, 'r')
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end
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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))
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xlabel("z, mm")
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ylabel("y, mm")
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ylim([-p p])
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xlim([-2 * p 0])
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grid on |