Review
Final Set of Labs
&
Formal Report
Session 6
Physics 2CL
Summer 2009
Outline
• Review the last set of labs
• Review formal write-up
• Review error/uncertainty analysis
Last set of labs
• Choose 2 of remaining 4
• Topics include:
– Microwaves: refraction & interference
– Magnetic fields: RC integrator, force balance
– Laser: interference, diffraction
– Human eye: lens equation, lens in series
Exp. 4 –Microwave refraction and
interference
• Measure n for wax
• Make use of refraction and reflection
Refraction
n1 sin θ1 = n2 sin θ2
Uncertainties
• What is
uncertainty of n1 ?
n1 sin θ1 = n2 sin θ2
n1 = n2 sin θ2/ sin θ1
εn12 = ε(sin θ2)2 + ε(sin θ1)2
δ(sin θ2) = [δ(sin θ2)/δθ2]δθ2
δ(sin θ2) = cos θ2 δθ2
ε(sin θ2) = cos θ2 δθ2/sin θ2
Exp. 4 – total internal reflection
total internal reflection : sin θC = n2/n1
Interference Theory
constructive
φ = 0o
φ = 0o
λ
φ = 360o
Interference Theory
destructive
φ = 180o
Exp. 4 –Interference apparatus
2d = mλ (for max)
Exp. 5 – Magnetic Fields
• Basic RC integration circuit
• Measure value for magnetic field
– Flipped coil
– Current balance
An RC Integrating Circuit
Why?
Flip Coil Integrating Circuit
Total change in B upon thrusting loop into field
is B itself
Flipped coil
Decay through Circuit
Current balance
Measure magnetic force
Forces on current loop
Exp 6 – Laser diffraction &
interference
• Use light from visible range
• λ is relatively small so objects are
similarly small
• Lithography
• Basic ideas for X-ray diffraction
Diffraction & Interference
• Extension of ideas
in experiment 4
• Make use of
interference
leading to diffraction
d sin θ = nλ
Single Slit Diffraction Pattern
Multi-Slit Interference
Single slit envelope
Interference between
slits
Exp. 7 – Lenses & Human Eye
• Model for lens of
the human eye
• Detection of blind
spot
Lenses
Converging lens
Diverging lens
Thins Lens equation
Combination of lens
Exp. 7 Objectives
Convergent and divergent lenses
Verify thin lens equation
Power of lens
Accomodation
Glasses
Check of Blind Spot
Formal Report
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•
•
•
•
•
5 pages
Title page
Introduction
Theory
Experiment
Results
Title page
– Title page
•
•
•
•
Experiment title
Name, institution
Date
Abstract
– 150 word limit
– Succinct summary of results and significance
Introduction
• Overall description
• Background
• Objectives
Theory
• Review theory – give references
• Predictions
• Diagrams
Experiment
•
•
•
•
Apparatus - diagrams
Procedure
Make clear all tools
Easily understood
Results
• Raw data
– Tables
– Graphs
– organization
• Analysis of data
– Sample and clear calculations
– Uncertainty analysis
– Tables, graphs
– units
Discussion
• Summarize data
• Quantitative comparison with theory
• Discuss in terms of δ, σ, and t analyses
Summary of propagation
formulae
summation
q = x+ y−z
δq = (δx) 2 + (δy ) 2 + (δz ) 2
q = x× y ÷ z
multiplication
εq = (εx) 2 + (εy ) 2 + (εz ) 2
q = Bx
constants
δq = B δx
εq = εx
Number measurements
Distributions
4
3
2
±1σ
1
68 %
±2σ
95 %
0
69.4
69.6
69.8
70.0
70.2
70.4
height (inches)
1
G X ,σ ( x) =
exp(− ( x − x) 2 2σ 2 )
σ 2π
Number measurements
Distributions
4
a
3
2
b
1
0
69.4
69.6
69.8
70.0
70.2
70.4
height (inches)
b
1
G X ,σ ( x) =
exp(− ( x − x) 2 2σ 2 )
a σ 2π
∫
Remember
• Lab Writeup
• Read next week’s lab description, do
prelab
• Homework 6 due with last lab (Taylor
8.1, 8.6, 8.10)