From 744cf1f45e43316259dbd43594796b9211649a23 Mon Sep 17 00:00:00 2001
From: BrokenVoodooDoll <44895553+BrokenVoodooDoll@users.noreply.github.com>
Date: Thu, 21 Jan 2021 18:13:33 +0300
Subject: [PATCH] Added files

Added script for visualization of the path of rays emitted by a point source and reflected from a parabolic mirror
---
 parabolic_point_source.py | 85 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 85 insertions(+)
 create mode 100644 parabolic_point_source.py

diff --git a/parabolic_point_source.py b/parabolic_point_source.py
new file mode 100644
index 0000000..ba9fa86
--- /dev/null
+++ b/parabolic_point_source.py
@@ -0,0 +1,85 @@
+import matplotlib.pyplot as plt
+import numpy as np
+from numpy.lib.function_base import angle
+
+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 = np.linspace(-p, p, 1000)
+
+# mirror equation z = -y^2 / (2 * p)
+def surface(y):
+    return -y ** 2 / (2 * p)
+
+def phi(y):
+    return np.arctan(y / p)
+
+# 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
+def epsilon(y, inc_angle):
+    return inc_angle - phi(y)
+
+# angle of reflected ray
+def ref_angle(y, inc_angle):
+    return phi(y) - epsilon(y, inc_angle)
+
+# the z-coordinate of the intersection of the reflected ray with the axis
+def ref_z(y, inc_angle):
+    if inc_angle == 0:
+        return 0
+    tg_sigma = np.tan(inc_angle)
+    z = -(y - source_pos * tg_sigma) / tg_sigma
+    return y / np.tan(ref_angle(y, inc_angle)) + z
+
+# the y-coordinate of the intersection of the incident ray with the mirror 
+def height(inc_angle):
+    if inc_angle == 0:
+        return 0
+    tg_sigma = np.tan(inc_angle)
+    return -p / tg_sigma * (1 - np.sqrt(1 + 2 * source_pos / p * tg_sigma**2))
+
+# line equation for extension of the reflected ray
+def line(ref_angle, z, z0):
+    return np.tan(ref_angle) * (z - z0)
+
+
+plt.figure(figsize=(13, 8))
+plt.plot(surface(y), y) # mirror surface visualization
+plt.plot([-2 * p, 0], [0, 0]) # axis of the mirror
+plt.plot([-focal_length], [0], 'o') # focal point
+
+for ang in np.linspace(-angle_d, angle_d, num_rays):
+    inc_angle = ang * np.pi / 180
+    h = height(inc_angle)
+
+    z_inc = np.array([-source_pos, surface(h)])
+    y_inc = np.array([0, h])
+    plt.plot(z_inc, y_inc, 'k', lw=1) # draw incident beam
+
+    z_0 = ref_z(h,  inc_angle)
+    if np.isnan(z_0):
+        z_0 = -2 * p
+
+    if source_pos >= focal_length:
+        z_0 = -z_0 if z_0 > 0 else z_0
+    else:
+        z_0 = z_0 if z_0 > 0 else -z_0
+    
+    z_ref = np.array([surface(h), -2 * p])
+    y_ref = np.array([h, line(ref_angle(h, inc_angle), -2 * p, z_0)])   
+    plt.plot(z_ref, y_ref, 'r', lw=1)
+
+plt.title("Focal length = {:.1f} mm. Source position = {:.1f} mm.\nMaximum incident angle = {:.1f} deg. Number of rays = {}".format(focal_length, -source_pos, angle_d, num_rays))
+plt.xlabel("z, mm")
+plt.ylabel("y, mm")
+plt.ylim(-p, p)
+plt.xlim(-2 * p, 0)
+plt.grid()
+plt.show()
\ No newline at end of file