149 lines
3.1 KiB
Python
149 lines
3.1 KiB
Python
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# 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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import uncertainties.umath as um
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import uncertainties.unumpy as unp
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import numpy as np
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import matplotlib.pyplot as plt
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# convert micrometer readings to SI unit
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length = lambda x,y,z: x*1e-4 + y*1/4*1e-4 + z*1e-6
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##
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## Part I
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##
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k = 60 # number of wavefronts
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l0 = ufloat(633, 1)*1e-9 # laser wavelength
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# micrometer calibration
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d0 = k*l0/2 # expected value
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d = length(0,3,10) # measured value
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df = d - d0 # offset
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# laser wavelength measure
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d = sample(length(*i)-df.n for i in [(0,3,9.5), (0,3,10),
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(0,3,10.5), (0,3,10)]).tval()
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l1 = 2*d/k
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print(mformat('''
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# Part I (Fabry-Perot interferometer)
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offset: {} μm
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λ: {} nm
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''', df*1e6, l1*1e9))
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##
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## Part II
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##
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df = length(2,0,1) # micrometer offset
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k = 70 # number of wavefronts
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# laser wavelength measure
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d = sample(length(*i)-df for i in [(2,0,22.5), (2,0,23.5), (2,0,23.5),
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(2,0,23.5), (2,0,23), (2,0,23)]).tval()
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l2 = 2*d/k
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print(mformat('''
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# Part II (Michelson interferometer)
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λ: {} nm''', l2*1e9))
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## compare wavelengths
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alpha = check_measures(l1, l2)
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l = combine_measures(l1, l2)
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print(mformat('''
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comparibility test λ₁ - λ₂
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α={:.2f} α>ε: {}
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λbest: {} nm
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''', alpha, alpha>epsilon, l*1e9))
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##
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## Part III
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##
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d = 3e-2 # air cavity thickness
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Patm = 101.3e3 # atmosferic pressure
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k = array(17, 20, 17, 18, 19) # number of wavefronts
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P = array(82e3, 83e3, 84e3, 83e3, 84e3) # gauge pressure
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m = sample(*(k*l.n/(2*d*P)))
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print(mformat('''
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# Part III (air refraction index)
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m: {} Pa⁻¹
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''', m.tval()))
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##
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## Part IV
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##
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d = ufloat(6, 1)*1e-3 # glass pane thickness
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t = ufloat(12, 1)*np.pi/180 # angle
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k = sample(162, 112, 124, 122).tval() # number of wavefronts
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n = (2*d-k*l) / (2*d-k*l/(1-um.cos(t))) # refraction index
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print(mformat('''
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# Part IV (glass refraction index)
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n: {}
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''', n))
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##
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## Part V
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##
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# peak position
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S = array(8.9, 10.7, 11.7, 12.7, 13.4,
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14.1, 14.7, 15.6, 16.3, 16.7,
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17.3, 18.0, 18.3, 18.9)*1e-2
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# uncertainty
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sigmaS = 2e-3
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# peak number
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n = np.arange(1, len(S))
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d = ufloat(1e-3, 0) # slit length
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L = ufloat(125.1, 0.5)*1e-2 # screen distance
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ti = um.atan(S[0]/L) # incidence angle
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# drop first peak
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S = S[1:]
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x = np.linspace(0, 13, 200)
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peak = lambda n, t, l: L.n*np.sqrt(1/(np.cos(t)-n*l/d.n)**2 - 1)
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f, (tio, lo) = curve(n, S, peak, sigmaS, guess=[ti.n, l.n])
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plt.xlabel('peak order')
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plt.ylabel('distance from center (m)')
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plt.errorbar(n, S, sigmaS, color='#604848', linestyle='', linewidth=1.1)
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plt.scatter(n, S, color='#a17e3e')
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plt.plot(x, f(x), color='#65788f')
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plt.show()
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alpha = check_measures(l, lo)
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beta = chi_squared_fit(n, S, f, sigmaS)
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print(mformat('''
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# Part V (ruler diffraction)
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λₒ: {} nm
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θₒ: {} rad
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compatibility test λ - λₒ:
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α={:.2f}, α>ε: {}
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χ² test:
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α={:.2f}, α>ε: {}
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''', lo*1e9, tio
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, alpha, alpha>epsilon
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, beta, beta>epsilon))
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