PHYSICS 2DL – SPRING 2010
MODERN PHYSICS
LABORATORY
Monday April 19, 2010
Prof. Brian Keating
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Homework
• Problems listed on 2DL Spring 2010 -Web
Site.
• All HW problems are found in Taylor
• Hand-in HW to TA in Lab
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This is the technique you’ll need to memorize and use often.
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Ch4: Analysis of Random Uncertainties
uncertainty of
mean
standard deviation
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Ch4: Analysis of Random Uncertainties
uncertainty of
mean
standard deviation
standard deviation of11 the mean
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Distributions and histograms
Grades
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Distributions and histograms
Grades
bin
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Distributions and histograms
Grades
bin
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Distributions and histograms
Grades
bin
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Distributions and histograms
bin
Grades
Limiting distribution f(x)
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Limiting distribution
f(x)
Grades
A
B
B
= ???
A
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Next time:
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Integrating Gauss distribution
0.5σ 0.5σ
1.7σ
1.7σ
tσ
tσ
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Gauss distribution and x, σx
most probable x
_
Xbest = x = X
σx = σ
σ σ
X+σ
=
= 68%
X-σ
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Gauss distribution and x, σx
most probable x
_
Xbest = x = X
σx = σ
σ σ
X+σ
=
= 68%
X-σ
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t=1
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t=1.47
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Limiting Distributions;
Normal Distribution (Ch.5)
Plan:
•Limiting distributions: physical meaning
•Normal (Gauss) distribution
•Addition in quadrature, SDOM, etc
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Limiting distribution
f(x)
probability to get an answer
between x and x+dx
f(x)dx
=1
???
dx
B
=
A
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Limiting distribution
probability to get an answer
between x and x+dx
f(x)dx
f(x)
dx
Fraction of students scoring xk
… or probability of xk
score
# of times
xk appears
f(xk)dxk
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Gauss distribution and random errors
Grades
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Gauss distribution and random errors
Intensity
x
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Normal (Gauss) distribution
X=45
X=93
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Normal (Gauss) distribution
σ=7
σ = 15
X=45
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Gauss distribution and x, σx
pr
ob
ab
ili
ty
most probable x
_
Xbest = x = X
σx = σ
f(x)dx
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Accepted Value of h=6.626 × 10-34 J.sec
You measure freq = 45 THz with uncertainty:
dF=4.5 THz
What is best estimate for the Uncertainty in Energy = hF?
E = 3.0 ± 0.3 × 10-20 J
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Next time: LEAST SQUARES FITTING
y = f(x)
1.
2. Minimize χ2:
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