4/24/2012
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4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 1
PHY 114 A General Physics II11 AM‐12:15 PM TR Olin 101
Plan for Lecture 22 (Chapter 38):
Diffraction of light
1. Diffraction gratings
2. X‐ray diffraction
3. Other properties of light
4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 2
4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 3
www.wfu.edu/physics/sps/spszone52012conf/welcome.html
Part of SPS zone 5 conferenceApril 20‐21, 2012
Offer 1 point extra credit for attendance*
*After the lecture, email me that you attended. In the following email exchange you will be asked to answer one question about the lecture.
4/24/2012
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4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 4
3rd exam solutions• Solutions posted on web• Exam review session??
Would you like to attend an exam review session?(A) yes (B) no
If you would like a review session, can you meet(A) Today Tuesday at 2 PM (here)(B) Today Tuesday at 5 PM Olin 107(C) Tomorrow Wed. at 1 PM Olin 107(D) Tomorrow Wed. at 2 PM Olin 107(E) Other?
• Similar problems may appear on final exam
4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 5
Fourth exam – scheduled during the week of April 23 (evenings 6‐10 PM) Note: Content mostly on material in Chapters 35‐38, optics, diffraction, plus possibly some ideas of Quantum Mechanics and possibly some topics from Exam 3
Which of these times are you likely to prefer:A. Monday 4/23B. Tuesday 4/24C. Wednesday 4/25D. Thursday 4/26E. Friday 4/27
k
4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 6
Wave phenomena associated with light
vtxEtxEy λπ2
sin),( max
),(),(),(
portion) field (electric wavesneticelectromag twoofion Superposit21 txEtxEtxE yy
toty
2cos
2
1
λ
π2sin2
λ
π2sin
λ
π2sin),(
max
maxmax
vtxE
vtxEvtxEtxEtoty
Plane polarized electromagnetic waveat an instant of time:
4/24/2012
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4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 7
2cos
2sin4)sin()sin( :magnitude Squared
2cos
2sin2)sin()sin(
:identity tric trigonome thefrom followsresult that thisNote
222 BABABA
BABABA
2cos
2cos
2
41
: wavesEM theofIntensity
2max
2
max0
2
0
IEc
Ec
SIavg
totyavg
Rapidly changing in time
Constant in time
2cos
2
1
λ
π2sin2
λ
π2sin
λ
π2sin),(
:caseour In
max
maxmax
vtxE
vtxEvtxEtxEtoty
4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 8
Example: =0.5 rad ‐‐ plotting snapshot of EM wave
Example: =3 rad – plotting snapshot of EM wave
Intensity as a function of :
/(2)
4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 9
2cos
2
1
λ
π2sin2
λ
π2sin
λ
π2sin),(
max
maxmax
vtxE
vtxEvtxEtxEtoty
What is the significance of this result?
A. No significance – only an evil physics professor could love such a result.
B. Shows that any two electromagnetic waves can interfere
C. Shows that two electromagnetic wave with the same amplitude, wavelength, and velocity can interfere if they have different phases
4/24/2012
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4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 10
λ θsin π
λπ 21 mdm
rr
λπ
cosπ2λ
πsin2
π2λπ2
sinπ2λπ2
sin),(
2121max
2max
1max
rrft
rrE
ftr
Eftr
EtPE
θsinδ21 drr
intensity maxima occur for
Young’s double slit geometry:
Mathematical analysis of bright fringes:
4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 11
λ θsin π
λπ 21 mdm
rr
Diffraction pattern from a plane wave incident on a double slit:
λπ
cosπ2λ
πsin2
π2λπ2
sinπ2λπ2
sin),(
2121max
2max
1max
rrft
rrE
ftr
Eftr
EtPE
θsinδ21 drr
intensity maxima occur for
4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 12
λ
πcosπ2
λ
πsin2
π2λπ2
sinπ2λπ2
sin),(
2121max
2max
1max
rrft
rrE
ftr
Eftr
EtPE
sintan sin12 LLydrr
cos2max
L
ydII
4/24/2012
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4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 13
Webassign hints:
4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 14
d
mm
d
d
mm
d
dII
21
sin 2
1sin when fringesdark
sin sin
when fringesbright
sincos
:form thehaspattern intensity slit -2 that theRecall
2max
4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 15
Webassign hint:
mnt
mnt
2 :ceinterferen eDestructiv
2
12 :ceinterferen veConstructi
:caseon illustratiIn
4/24/2012
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4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 16
Light intensity patterns seen on screen for very thin double slit
Assuming that d and L are the same which plot corresponds the the greater wavelength?
1> 2 2> 1
1
2
4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 17
Ideal infinitely thin 2‐slit pattern
Finite thickness 2‐slit pattern
slit width
separationslit
sincos
2
2max
a
d
Lya
Lya
L
ydII
4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 18
Effects of diffraction when you may not want it – images of small objects near the “diffraction” limit
4/24/2012
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4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 19
λθsinπ
sin
λθsinπ
sinπ2
λ
2πsin
π2λ
π2sin),(
max
max
d
dN
ftr
E
ftr
EtPE
av
i
i
Enhancement of diffraction – diffraction gratings
4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 20
Diffraction pattern for N slits – diffraction grating
λθsinπ
sin
λθsinπ
sinπ2
λ
2πsin
π2λ
π2sin),(
max
max
d
dN
ftr
E
ftr
EtPE
av
i
i
λ θsin
at maximaIntensity
md
4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 21
2
λ
θsinπsin
λ
θsinπsin
max
d
dN
II
N=2
N=5
N=10
Intensity pattern from multiple slit grating:
4/24/2012
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4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 22
2
λ
θsinπsin
λ
θsinπsin
max
d
dN
II
Sanity check:If the intensity pattern for N slits is given by
what happened to the formula two‐slit intensity pattern?A. NEVER trust your physics professorB. More evidence that physics does not make senseC. The formula look different, but are equivalent for
N=2
4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 23
2
λ
θsinπsin
λ
θsinπsin
max
d
dN
II
λ
θsinπcos'
cos'
sin
cossin2
sin
2sin
:2For
2max
2max
2
max
2
max
2
λ
θsinπsin
λ
θsinπ2sin
max
dI
I
I
III
N
d
d
4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 24
thin multiple slits
fat single slit
fat double slits
thin double slits
4/24/2012
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4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 25
Diffraction gratings in nature ‐‐ crystals
Model of NaCl
Typical atomic distancesa =0.1‐1.0 nm
4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 26
mdII d
dN
sin when maxima
:gratingfor pattern n diffractio of form Recall2
λ
θsinπsin
λ
θsinπsin
max
4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 27
X‐ray diffraction geometry:
md sin2
:condition Bragg -- spotsbright ray -X
4/24/2012
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4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 28
Note that in this case d=a/2
Example of X‐ray scattering for NaCl
4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 29
Example of X‐ray diffraction data at different temperatures
4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 30
Constituents of Li10GeP2S12:
eV 19.10
GeSLi **44
H
Pnma
eV 28.8
PSLi 43*
H
PnmaeV36.8
2 PSLi 143*
H
Pmn
*K. Homma et al, Solid State Ionics 182, 53‐58 (2011)**M. Murayama et al, Solid State Ionics 154‐155, 789‐794 (2002)
eV 12.8
PSLi 43
H
Pbcn- α*
SLiPGe
4/24/2012
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4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 31
Polarization of light
In this case, E is polarized in y direction.
4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 32
General case – reflection and refraction
2
1n1
n2
1
12
12
0
1
12
1
0
2
21
2
0For
nn
nn
E
E
nn
n
E
E
R
2211
2211
0
1
2211
11
0
2
221122
221122
0
1
221122
121
0
2
coscos
coscos
coscos
cos2
plane scattering ofout polarized For
coscos
coscos
coscos
cos2
planescatteringin polarized For
nn
nn
E
E
nn
n
E
E
E
nnn
nnn
E
E
nnn
nn
E
E
E
R
R
4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 33
General case – reflection and refraction
2
1n1
n2
1
2211
2
2211
2211
2
0
1
2
2112
2112
2
0
1
sinsin :law sSnell'
coscos
coscos
plane scattering ofout polarized For
coscos
coscos
plane scatteringin polarized For
nn
nn
nn
E
ER
E
nn
nn
E
ER
E
R
R
4/24/2012
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4/24/2012 PHY 114 A Spring 2012 ‐‐ Lecture 22 34
Plot of reflectivity R versus
E perpendicular to scattering plane
E parallel to scattering plane
Brewster’s angle1
2tann
nP
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