Modern Phys Lab Diffraction 1

statics/physics/modern-phys-lab/diffraction.py

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+import numpy as np
+import matplotlib.pyplot as plt
+
+# Current units: pixels
+# Format: d[0 = small, 1 = large][voltage][0 = inner, 1 = outer]
+diameter_measured = np.array([
+    [[570, 646], [567, 725], [623, 750], [730, 866], [800, 962], [861, 1051]],
+    [[968, 1090], [1034, 1147], [1036, 1183], [1311, 1461], [1405, 1624], [1476, 1600]]
+])
+diameter_error = 100
+
+voltages = np.array(np.arange(5000, 2500 - 1, -500)) #-1 to include 2500
+voltages_inv_sqrt = 1 / np.sqrt(voltages)
+
+# New units: m
+diameter_measured = diameter_measured / 19440
+diameter_measured_error = 100 / 19440
+
+# Average inner and outer
+# New format: d[0 = small, 1 = large][voltage]
+diameter_measured = np.average(diameter_measured, axis=2)
+
+# Find actual diameter
+L = 138 / 1000
+r = 63 / 1000
+diameter_actual = L * diameter_measured / (r + np.sqrt(r**2 - diameter_measured**2 / 4))
+diameter_actual_error = (((L * (r + np.sqrt(r**2 - diameter_measured**2 / 4)) + diameter_measured**2 / (2 * np.sqrt(r**2 - diameter_measured**2 / 4)) / 2 * L)/ (r + np.sqrt(r**2 - diameter_measured**2 / 4))**2) * diameter_measured_error)
+
+fig, axs = plt.subplots(len(diameter_measured), 2, sharex='all')
+fig.tight_layout()
+for size in range(len(diameter_measured)):
+    ax = axs[size][0]
+    size_name = 'small' if size == 0 else 'large'
+
+    ax.set_xlabel(r'$1/\sqrt{U_0}$')
+    ax.set_ylabel(f'$D_M$ ({size_name}) (meters)')
+    ax.set_title(r'$1/\sqrt{U_0}$ ' + f'vs $D_M$ ({size_name})')
+    #ax.scatter(voltages_inv_sqrt, diameter_measured[size], label='Data')
+    ax.errorbar(voltages_inv_sqrt, diameter_measured[size], fmt='o', yerr=diameter_measured_error, capsize=5)
+
+    # Trendlines
+    line = np.polynomial.Polynomial.fit(voltages_inv_sqrt, diameter_measured[size], deg=1)
+    ax.plot(voltages_inv_sqrt, line(voltages_inv_sqrt), label='Trendline', linestyle='--', color='purple')
+    ax.legend()
+
+    ax=axs[size][1]
+    ax.set_xlabel(r'$1/\sqrt{U_0}$')
+    ax.set_ylabel(f'$D_E$ ({size_name}) (meters)')
+    ax.set_title(r'$1/\sqrt{U_0}$ ' + f'vs $D_E$ ({size_name})')
+    #ax.scatter(voltages_inv_sqrt, diameter_measured[size], label='Data')
+    ax.errorbar(voltages_inv_sqrt, diameter_actual[size], fmt='o', yerr=diameter_actual_error, capsize=5)
+
+    # Trendlines
+    line = np.polynomial.Polynomial.fit(voltages_inv_sqrt, diameter_actual[size], deg=1)
+    ax.plot(voltages_inv_sqrt, line(voltages_inv_sqrt), label='Trendline', linestyle='--', color='purple')
+    ax.legend()
+
+plt.show()