174 lines
4.7 KiB
Python
174 lines
4.7 KiB
Python
# coding: utf-8
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from __future__ import division, print_function, unicode_literals
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from lab import *
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from math import pi, sqrt
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import matplotlib.pyplot as plt
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import matplotlib.mlab as mlab
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##
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## measure focal length
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##
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# convert micrometer readings (mm)
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length = lambda x,y,z: x+0.5*y+0.01*z
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# object - lens distance (mm)
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p = ufloat(4608, 10, tag='p')
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# object size (mm)
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h0 = array(10.00, 15.00, 18.60, 20.00, 25.00, 30.00, 35.00, 40.00, 45.00, 50.00)
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# image size (mm)
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h1 = array(length(11, 0, 11.5) - length(10, 1, 1.5),
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length(11, 0, 39.5) - length(10, 1, 1.5),
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length(11, 0, 27.5) - length(10, 0, 20.5),
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length(11, 0, 41.0) - length(10, 0, 27.0),
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length(11, 0, 34.5) - length( 9, 1, 42.0),
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length(11, 0, 46.5) - length( 9, 1, 28.0),
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length(11, 1, 3.0) - length( 9, 1, 3.0),
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length(11, 1, 32.0) - length( 9, 1, 1.5),
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length(11, 0, 23.5) - length( 8, 1, 14.5),
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length(12, 0, 5.0) - length( 9, 0, 22.0))
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# linear fit
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sigma_h = 0.03
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x = np.linspace(5, 55, 10)
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k = simple_linear(h0, h1, sigma_h)
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k.tag = 'k'
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f = ufloat(252, 1)
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f0 = p*k/(k+1)
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# tests
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alpha = chi_squared_fit(h0, h1, lambda x: k.n*x, sigma_h, s=1)
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beta = check_measures(f0, f)
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print(mformat('''
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# focal lenth measure
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k: {}
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fₒ: {}
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χ² test: α={:.2f}
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t-test fₒ-f: α={:.2f}
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''', k, f0, alpha, beta))
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plt.figure(1)
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plt.title('focal length (f=252mm)')
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plt.xlabel('object size (mm)')
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plt.ylabel('image size (mm)')
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plt.scatter(h0, h1, color='#206a99')
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plt.errorbar(h0, h1, sigma_h, color='#1a567c',linestyle='')
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plt.plot(x, k.n*x, color='#1a567c')
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plt.show()
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f = f0*1e-3
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##
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## measure Δs
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##
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ds = sample(
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length(12,0,5.5) - length(11,1,21.5),
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length(12,0,4.5) - length(11,1,20.0),
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length(12,0,5.5) - length(11,1,21.0),
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length(12,0,4.5) - length(11,1,20.5),
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length(12,0,6.5) - length(11,1,22.5),
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length(12,0,6.5) - length(11,1,21.0),
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length(12,0,6.5) - length(11,1,21.0),
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length(12,0,3.5) - length(11,1,20.0),
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length(12,0,5.5) - length(11,1,21.0),
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length(12,0,5.5) - length(11,1,20.5),
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length(12,0,6.5) - length(11,1,22.0),
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length(12,0,4.5) - length(11,1,21.0),
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length(12,0,3.5) - length(11,1,20.0),
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length(12,0,5.5) - length(11,1,21.5),
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length(12,0,7.5) - length(11,1,22.5),
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length(12,0,4.5) - length(11,1,21.0),
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length(12,0,4.0) - length(11,1,21.0),
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length(12,0,6.5) - length(11,1,22.0),
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length(12,0,6.0) - length(11,1,21.0),
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length(12,0,6.5) - length(11,1,22.0),
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length(12,0,4.5) - length(11,1,20.0),
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length(12,0,6.5) - length(11,1,21.5),
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length(12,0,6.5) - length(11,1,21.0),
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length(12,0,5.5) - length(11,1,22.0),
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length(12,0,5.5) - length(11,1,20.5),
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length(12,0,5.5) - length(11,1,22.0),
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length(12,0,7.5) - length(11,1,22.5),
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length(12,0,4.5) - length(11,1,20.0),
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length(12,0,7.5) - length(11,1,22.5),
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length(12,0,5.5) - length(11,1,21.5),
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length(12,0,4.5) - length(11,1,21.0),
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length(12,0,5.5) - length(11,1,21.0),
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length(12,0,5.5) - length(11,1,20.0),
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length(12,0,5.5) - length(11,1,20.0),
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length(12,0,8.5) - length(11,1,22.5),
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length(12,0,6.5) - length(11,1,20.0),
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length(12,0,6.5) - length(11,1,22.0),
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length(12,0,5.5) - length(11,1,20.5),
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length(12,0,4.5) - length(11,1,20.5),
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length(12,0,5.5) - length(11,1,20.0),
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length(12,0,6.5) - length(11,1,22.5),
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length(12,0,4.5) - length(11,1,20.5),
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length(12,0,4.5) - length(11,1,22.0),
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length(12,0,7.5) - length(11,1,22.5),
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length(12,0,4.0) - length(11,1,20.0),
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length(12,0,4.5) - length(11,1,20.0),
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length(12,0,5.5) - length(11,1,22.0),
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length(12,0,5.5) - length(11,1,21.0),
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length(12,0,4.5) - length(11,1,20.5),
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length(12,0,7.5) - length(11,1,22.5))
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## Δs histogram
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plt.figure(2)
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plt.xlabel('displacement (mm)')
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plt.ylabel('frequency')
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# gaussian best fit
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x = np.linspace(ds.min-1e-3, ds.max+1e-3, 300)
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gauss = mlab.normpdf(x, ds.mean, ds.std)
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# χ² test
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O, B, _ = plt.hist(np.asarray(ds), bins=6, normed=1, facecolor='#506d72')
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alpha = chi_squared(ds, O, B)
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print('''
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# Δs histogram
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χ² test: α={:.2f}
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'''.format(alpha))
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# plot
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plt.plot(x, gauss, 'black', linewidth=1)
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plt.show()
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ds = sample(*1e-3*ds).val()
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ds.tag = 'Δs'
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##
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## calculate c
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##
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B = ufloat(0.292, 0.001, tag='B') # lens-rotating mirror distance
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D = ufloat(5.491, 0.005, tag='D') # rotating-fixed mirrors distance
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w = ufloat(3000, 2, tag='ω') # motor angular velocity
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A = (B+D)*f/(B+D-f)
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c0 = 8*np.pi * A*D**2 * w / ((D+B)*ds) # speed of light
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print(mformat('''
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# speed of light
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c: {}
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σc/c: {:.2f}%
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error components:''',c0, c0.s/c0.n*100))
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for p, sigma in c0.error_components().items():
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print(' {}: {:.2f}%'.format(p.tag, abs(sigma/c0.n)*100))
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# t-test cₒ-c
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c = ufloat(299792458,0)
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alpha = check_measures(c0, c)
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print(mformat('t-test cₒ-c: α={:.2f}', alpha))
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exit()
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