145 lines
3.3 KiB
Python
145 lines
3.3 KiB
Python
# coding: utf-8
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from __future__ import print_function, division, unicode_literals
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from lab import *
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import numpy as np
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import matplotlib.pyplot as plt
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np.set_printoptions(precision=2)
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epsilon = 0.05
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##
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## Parte 1
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## test Snell Law and calculate n
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i_a = sample(5,10,15,20,25,30,35) # direct path
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r_a = sample(8,15,23,30,40,48,59)
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i_b = sample(8,15,23,30,40,48,59) # reversed path
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r_b = sample(6,10,16,20,26,30,36)
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# linear regression y=kx, where y=sin(r^) x=sin(i^)
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x = np.linspace(0, 1, 100)
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ka = simple_linear(sin(i_a), sin(r_a), sin(1))
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kb = simple_linear(sin(i_b), sin(r_b), sin(1))
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# plot r^ - i^
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plt.figure(1)
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plt.xlim(0,1.0)
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plt.ylim(0,1.0)
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plt.xlabel('sin(angolo incidenza)')
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plt.ylabel('sin(angolo rifrazione)')
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plt.scatter(sin(i_a), sin(r_a), color='gray')
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plt.plot(x, ka.n*x, '#72aa3d')
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plt.scatter(sin(i_b), sin(r_b), color='gray')
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plt.plot(x, kb.n*x, '#3d72aa')
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plt.show()
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# χ^2 test
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alpha_a = chi_squared_fit(sin(i_a), sin(r_a), lambda x: ka.n*x, sin(1))
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alpha_b = chi_squared_fit(sin(i_b), sin(r_b), lambda x: kb.n*x, sin(1))
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print('''
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χ^2 tests:
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α={:.3f}, α>ε: {}
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α_rev={:.3f}, α>ε: {}
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'''.format(alpha_a, alpha_a>epsilon,
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alpha_b, alpha_b>epsilon))
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#compare n, 1/n_rev
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alpha = check_measures(ka, 1/kb)
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n_best = combine_measures(ka, 1/kb)
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print('''
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n: ({})
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n_rev: ({})
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α: {:.2f}
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n_best: ({})
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'''.format(ka, kb, alpha, n_best))
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##
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## Parte 2
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## calculate n from minimum deviation δ
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delta_min = ufloat(38,1) # minimum deviation angle
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alpha = ufloat(60,0) # equilater triangle prism
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n = sin(delta_min/2+alpha/2)/sin(alpha/2)
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print('''
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n: ({})
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n_rev: ({})
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n_δ: ({})
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'''.format(ka, kb, n))
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##
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## Part 3
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## test thin lens equation, find focal lengths
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## lens with f=200mm
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d = 1.5 # transversal object length (cm)
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s = sample(110.0,100.0,90.0,80.0) # screen distance (p+q)
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p = sample(24.9,26.3,28.1,32.6) # object - lens distance
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q = sample(84.7,73.7,61.5,46.8) # lens - sceen dinstance
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t = sample(5.1,4.2,3.3,2.1) # transversal image length
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t_ = d*q/p # theoretical length
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# linear fit y=a+bx, where x=1/p, y=1/q
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x = np.linspace(0.030, 0.041, 100)
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a, b = linear(1/p, 1/q, 2e-4) # 1/f, -1
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f = 1/a # focal length
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# plot y=a+bx, where x=1/p, y=1/q
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plt.figure(2)
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plt.xlabel('1/p (cm)')
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plt.ylabel('1/q (cm)')
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plt.scatter(1/p, 1/q, color='#ba6b88')
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plt.plot(x, a.n + b.n*x, '#ba6b88')
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plt.show()
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# χ^2 test
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alpha = chi_squared_fit(1/p, 1/q, lambda x: a.n + b.n*x, 2e-4)
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print('χ^2: α={:.3f}, α>ε: {}'.format(alpha, alpha>epsilon))
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print('''
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lente 200mm
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f: ({})cm
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t: {}cm
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t°: {}cm
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'''.format(f, np.asarray(t), np.asarray(t_)))
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## lens with f=100mm
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s = sample(80,70,60,50) # see above
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p = sample(12.5,13.0,13.7,15.4) #
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q = sample(67.2,57.0,46.3,34.4) #
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t = sample(7.9,6.7,5.5,3.3) #
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t_ = d*q/p #
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# linear fit y=a+bx
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x = np.linspace(0.064, 0.081, 100)
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a, b = linear(1/p, 1/q, 2e-4) # 1/f, -1
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f = 1/a # focal length
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# plot y=a+bx, where x=1/p, y=1/q
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plt.figure(3)
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plt.xlabel('1/p (cm)')
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plt.ylabel('1/q (cm)')
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plt.scatter(1/p, 1/q, color='#6b88ba')
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plt.plot(x, a.n + b.n*x, '#6b88ba')
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plt.show()
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# χ^2 test
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alpha = chi_squared_fit(1/p, 1/q, lambda x: a.n + b.n*x, 2e-4)
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print('χ^2: α={:.3f}, α>ε: {}'.format(alpha, alpha>epsilon))
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print('''
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lente 100mm
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f: ({})cm
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t: {}cm
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t°: {}cm
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'''.format(f, np.asarray(t), np.asarray(t_)))
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