193 lines
4.4 KiB
Python
193 lines
4.4 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 degrees to radians
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angle = lambda x, y, z: (x + y/60 + z/3600) * np.pi/180
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t0 = angle(180,0,0) # angle offset
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te = angle(0,0,1) # angle uncertainty
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##
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## Part I
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##
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l = 5893e-10 # sodium doublet wavelength
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n = array(1, 2) # line order
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# line angles
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t = array(angle(200,0,16) - angle(159,0,8),
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angle(225,0,24) - angle(134,1,5))/2
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# spacing (m⁻¹)
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d = ufloat((n*l/np.sin(t)).mean(), 0.01e-6)
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print(mformat('''
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# Part I: diffraction grating spacing
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## Na lamp
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d: {} lines/mm
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''', 1/d*1e-3))
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##
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## Part II
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##
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## lamp B
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# line angles
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t = uarray(te, angle(195,0,2 ), # violet
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angle(195,0,15),
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angle(195,1,1 ),
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angle(195,1,20),
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angle(195,1,30),
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angle(199,1,9 ), # green
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angle(200,1,21)) # orange
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# wavelengths
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l = d*unp.sin(t-t0)
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print('''
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# Part II
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## lamp B - Xe?
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λ:''', '\n '.join(mformat('{}', i) for i in l*1e9), 'nm')
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## lamp C
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# line angles
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t = uarray(te, angle(193,1,11), # violet
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angle(195,1,14),
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angle(196,1,11), # green
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angle(197,0,25),
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angle(197,1,23),
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angle(200,1,27),
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angle(204,0,1 ))
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# wavelengths
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l = d*unp.sin(t-t0)
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print('''
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## lamp C - Kr?
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λ:''', '\n '.join(mformat('{}', i) for i in l*1e9), 'nm')
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## lamp D
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# line angles
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t = uarray(te, angle(194,1,12), # violet
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angle(194,1,23),
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angle(195,0,8 ),
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angle(195,0,15),
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angle(195,0,25),
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angle(196,0,2 ), # blue
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angle(196,0,10),
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angle(196,1,13), # green
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angle(198,0,15),
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angle(198,0,22),
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angle(198,1,5 ),
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angle(199,1,2 ), # yellow
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angle(199,1,12),
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angle(200,0,0 ),
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angle(200,0,11), # orange
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angle(200,0,23),
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angle(201,0,2 ),
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angle(201,0,8 ),
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angle(201,1,11)) # red
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# wavelengths
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l = d*unp.sin(t-t0)
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print('''
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## lamp D
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λ:''', '\n '.join(mformat('{}', i) for i in l*1e9), 'nm')
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##
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## Part III
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##
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## Hg lamp
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# prism angle
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a = ufloat(angle(60,0,0), te)
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# spectral line angles
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t = array(
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(angle(230,50,11), angle(230,44, 1), angle(230,1,21), angle(229,1,19), angle(228,16,4), angle(228,1,25), angle(228,1,19)),
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(angle(230,50,25), angle(230,44,10), angle(230,1,28), angle(229,1,21), angle(228,16,4), angle(228,1,22), angle(228,1,21)),
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(angle(230,50,11), angle(230,44, 5), angle(230,1,15), angle(229,1,12), angle(228,16,3), angle(228,1,13), angle(228,1,12)),
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(angle(230,50,15), angle(230,44, 7), angle(230,1,20), angle(229,1,14), angle(228,16,2), angle(228,1,11), angle(228,1,10)))
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# calculate mean values
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t = uarray(1e-3, *map(np.mean, t.T))
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# refractive index
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n = unp.sin((a+t-t0)/2) / unp.sin(a/2)
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# spectral lines wavelengths
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l = array(4047e-10, # violet I
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4077e-10, # violet II
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4358e-10, # blue
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4916e-10, # green I
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5460e-10, # green II
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5769e-10, # yellow I
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5790e-10) # yellow II
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# fit and plot n(λ)
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f, (a,b) = curve(l, nominal(n), lambda x, a, b: a+b/x**2, sigma(n), guess=[1, 0.001])
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alpha = chi_squared_fit(l, nominal(n), f, sigma(n))
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x = np.linspace(400e-9, 580e-9, 100)
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print(mformat('''
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# Part III
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## Hg lamp
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a: {}
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b: {}
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χ² test: α={}
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''', a, b, alpha))
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plt.figure(1)
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plt.xlabel('wavelength (nm)')
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plt.ylabel('refractive index')
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plt.scatter(l*1e9, nominal(n), color='#4f28fc')
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plt.errorbar(l*1e9, nominal(n), yerr=sigma(n), linestyle='', color='#286bfc')
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plt.plot(x*1e9, f(x), color='#5671c9')
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plt.show()
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## lamp B
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t = array(angle(124,1,15), # violet
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angle(125,0,0 ),
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angle(125,0,5 ),
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angle(125,0,16), # blue
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angle(125,0,24),
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angle(127,0,0 ), # green
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angle(127,0,19), # yellow
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angle(127,0,26), # orange
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angle(127,1,12), # red
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angle(128,0,25)) # red
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## lamp C
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t = array(angle(232,1,24), # red
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angle(233,0,18),
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angle(234,1,1 ), # yellow
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angle(236,1,3 ), # green
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angle(237,0,7 ),
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angle(237,1,28), # blue
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angle(239,0,10)) # violet
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