Lecture22 - Wake Forest...

4/24/2012

1

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



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

2


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


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


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

3


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


Example: =0.5 rad ‐‐ plotting snapshot of EM wave

Example: =3 rad – plotting snapshot of EM wave

Intensity as a function of :

/(2)


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

4


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:


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


λ

πcosπ2

λ

πsin2

π2λπ2

sinπ2λπ2

sin),(

2121max

2max

1max

rrft

rrE

ftr

Eftr

EtPE

sintan sin12 LLydrr

cos2max

L

ydII

4/24/2012

5


Webassign hints:


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


Webassign hint:

mnt

mnt

2 :ceinterferen eDestructiv

2

12 :ceinterferen veConstructi

:caseon illustratiIn

4/24/2012

6


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


Ideal infinitely thin 2‐slit pattern

Finite thickness 2‐slit pattern

slit width

separationslit

sincos

2

2max

a

d

Lya

Lya

L

ydII


Effects of diffraction when you may not want it – images of small objects near the “diffraction” limit

4/24/2012

7


λθsinπ

sin

λθsinπ

sinπ2

λ

2πsin

π2λ

π2sin),(

max

max

d

dN

ftr

E

ftr

EtPE

av

i

i

Enhancement of diffraction – diffraction gratings


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


2

λ

θsinπsin

λ

θsinπsin

max

d

dN

II

N=2

N=5

N=10

Intensity pattern from multiple slit grating:

4/24/2012

8


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


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


thin multiple slits

fat single slit

fat double slits

thin double slits

4/24/2012

9


Diffraction gratings in nature ‐‐ crystals

Model of NaCl

Typical atomic distancesa =0.1‐1.0 nm


mdII d

dN

sin when maxima

:gratingfor pattern n diffractio of form Recall2

λ

θsinπsin

λ

θsinπsin

max


X‐ray diffraction geometry:

md sin2

:condition Bragg -- spotsbright ray -X

4/24/2012

10


Note that in this case d=a/2

Example of X‐ray scattering for NaCl


Example of X‐ray diffraction data at different temperatures


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

11


Polarization of light

In this case, E is polarized in y direction.


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


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

12


Plot of reflectivity R versus

E perpendicular to scattering plane

E parallel to scattering plane

Brewster’s angle1

2tann

nP

Lecture22 - Wake Forest...

Documents

Transcript of Lecture22 - Wake Forest...