Learning Goals for Chapter 36 Diffraction vs Interference Singleslit vs Multipleslit diffraction Calculating intensity at points in singleslit pattern X ray diffraction reveals ID: 687128
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Slide1
Diffraction
Chapter 36
© 2016 Pearson Education Inc.Slide2
Learning Goals for Chapter 36
Diffraction
vs.
Interference
Single-slit vs. Multiple-slit diffractionCalculating intensity at points in single-slit pattern.X-ray diffraction reveals arrangement of atoms in crystal.Diffraction limits on smallest details Holograms!
© 2016 Pearson Education Inc.Slide3
Diffraction
Shadows created by straight edge SHOULD form a perfectly sharp line.
Nope!
Wave nature of light causes interference patterns, which blur the edge of the shadow.
© 2016 Pearson Education Inc.Slide4
DiffractionSlide5
Diffraction
Razor blade halfway between a pinhole, illuminated by monochromatic light, and a photographic film.
Film recorded shadow cast by razor blade.
Note fringe pattern around blade outline, caused by
diffraction.
© 2016 Pearson Education Inc.Slide6Slide7
Diffraction from a single slit
© 2016 Pearson Education Inc.Slide8
Diffraction from a single slitSlide9
Actual Single Slit DiffractionSlide10
Actual Single Hole DiffractionSlide11
Diffraction
vs. Interference?
Both use same
p
rinciple! PATH LENGTH DIFFERENCES create PHASE differences in arriving light intensitiesBut with diffraction, EVERY slit creates its own interference pattern! And multiple slits reinforce that pattern!
© 2016 Pearson Education Inc.Slide12
Pattern arises because different points along
the opening (the slit)
create
wavelets
that
interfere with each other
just
as a double slit would.
Diffraction by a Single
Slit
or DiskSlide13
Diffraction vs. Interference?
Path length difference
d
= [d(edge) – d(center)]
Phase difference Df = d /2pl = kd
a
d (center)
d (edge)Slide14
How does distance affect Diffraction?
If screen is far away, d >> a
If screen is close, d ~ or < a?
a
d (center)
d (edge)
a
d (center)
d (edge)Slide15
Fresnel
vs. Fraunhofer
Diffraction
© 2016 Pearson Education Inc.
CLOSE screen d
<< ka
2 means LARGE phase changes (Fresnel Diffraction)
FAR screen d
>>
ka
2
means
SMALL phase changes (
Fraunhofer
Diffraction
)
Check out
https://
www.youtube.com/watch?v=aEd4FFeBV6U
Slide16
Fresnel
vs. Fraunhofer
Diffraction
© 2016 Pearson Education Inc.
Fresnel Diffraction (near-field)
Divide aperature “a” into multiple point sources
Treat light as cylindrical or spherical waveletsCalculate path length d on near screen
You can see these!Slide17
Fresnel
diffraction by single slit
© 2016 Pearson Education Inc.Slide18
Fresnel
diffraction by a single slit
© 2016 Pearson Education Inc.Slide19
Fraunhofer
diffraction by a single slit
Check out
http://
www.physics.usyd.edu.au/teach_res/hsp/sp/mod31/m31_singleSlit.htm Slide20
Fresnel
vs. Fraunhofer
Diffraction
Fresnel Diffraction (near-field
)
You can see these!Fraunhofer
Diffraction (far-field)Hard to see without lensSlide21
Locating
dark fringes
Fraunhofer
diffraction pattern
(vertical!) from a single horizontal slit.Central bright fringe @ θ = 0, surrounded by series of dark fringes.
Central bright fringe
twice as wide as other bright fringes.© 2016 Pearson Education Inc.Slide22
Locating
dark fringes
a/2
d (center)
d
q
q
1
st
dark fringe
a/2 sin(
q
) =
d
d
= l/2
for minimum
sin(
q
) =
l/
aSlide23
Intensity in single-slit pattern
D
erive expression for intensity distribution for single-slit diffraction pattern using
phasor
-addition. Imagine plane wave front at slit subdivided into a large number of strips. At center point O, phasors all in phase.
© 2016 Pearson Education Inc.Slide24
Intensity in single-slit pattern
C
onsider wavelets arriving from different strips at
P.Path length differences create phase differences between wavelets coming from adjacent strips.Vector sum of phasors is now part of “perimeter” of a many-sided polygon.
© 2016 Pearson Education Inc.Slide25
Intensity in single-slit pattern
C
onsider wavelets arriving from different strips at
P.Path length differences create phase differences between wavelets coming from adjacent strips.Vector sum of phasors is now part of “perimeter” of a many-sided polygon.
© 2016 Pearson Education Inc.Slide26
Intensity maxima in a single-slit pattern
Intensity versus angle in single-slit diffraction pattern.
Most of wave power goes into central intensity peak
between
m = 1 & m = −1 intensity minima. © 2016 Pearson Education Inc.Slide27
Width of single-slit pattern
Pattern depends on
ratio
of slit width
a to the wavelength l. For a ~ l can’t even see second order + minima!© 2016 Pearson Education Inc.Slide28
Width of single-slit pattern
Pattern depends on
ratio
of slit width
a to the wavelength lPattern when a = 5λ (left) Pattern when a = 8λ (right).
© 2016 Pearson Education Inc.Slide29
The
minima
of the single-slit diffraction pattern occur when
Diffraction
by a Single Slit or Disk
a
a
a
a
a
a
aSlide30
Width of single-slit
diffraction pattern
Pattern depends on
ratio
of slit width a to the wavelength l. © 2016 Pearson Education Inc.
a
a a
a a aSlide31
What???
Wait a minute!
The
minima
of single-slit diffraction pattern occur when
The
maxima
of double-slit interference pattern
occured
when
d
aSlide32
Diffraction
vs. Interference?
© 2016 Pearson Education Inc.
a =
size
of single slit
D
d = distance
BETWEEN
SLITSSlide33
Single-slit
diffraction
vs.
Double-slit
Interference
aSlide34
Single-slit
diffraction
vs.
Double-slit
Interference
Single-slit diffraction
Slit Diameter = a (or ‘s’ or ‘D’)a is small!a sin q
= ml for minima sin q = ml /
a
minima
at large
q
&
if
l ~
a, none!
aSlide35
Single-slit
diffractionSlide36
Single-slit
diffraction vs.
Double-slit Interference
Double-slit interference
Slit SPACING =
d
d > a typicallyd sin q = m
l for maxima sin q = ml/d
bright
fringes at small
qSlide37
Single-slit
diffraction vs.
Double-slit InterferenceSlide38
Combining Diffraction & Interference!
© 2016 Pearson Education Inc.
See
Hyperphysics
:
http://
hyperphysics.phy-astr.gsu.edu/hbase/phyopt/mulslid.html#c1 Slide39
Combining Diffraction & Interference!
© 2016 Pearson Education Inc.Slide40
Diffraction
from Two slits of finite width
Pattern from two slits with width
a
, separated by a distance (between centers) d = 4a.Two-slit peaks are @ same positions; intensities modulated by single-slit pattern.Single-slit diffraction “envelopes” intensity function.
© 2016 Pearson Education Inc.Slide41
Diffraction
from Two slits of finite width
Look even more closely!!
Interference
minima are present too!But what happened to fourth interference maximum??Oh! Interference max cancelled by diffraction minima!
© 2016 Pearson Education Inc.Slide42
Diffraction
AND Interference
Diffraction minima are labeled by integer
m
d = ±1, ±2, … (“d” for “diffraction”). Compare with interference pattern formed by two very narrow slits with distance d between slits, Here d is four times as great as the single-slit width
a (“i” is for “interference.”)
© 2016 Pearson Education Inc.Slide43
Diffraction
from Two slits of finite width
© 2016 Pearson Education Inc.Slide44
Diffraction & InterferenceSlide45
Several slits
A
rray of 8 narrow slits, distance
d
between adjacent slits.Constructive interference occurs for rays at angle θ arriveing at P with path difference equal to integral
# of l.
© 2016 Pearson Education Inc.Slide46
Interference pattern of several slits
Eight slit pattern:
Large maxima,
(principal maxima)
@ same positions as a two-slit pattern, but much narrower.
© 2016 Pearson Education Inc.Slide47
Interference pattern of several slits
16 slit pattern:
H
eight of principal
maximum is proportional to N 2, Energy conservation means width of each principal maximum proportional to 1/N
.© 2016 Pearson Education Inc.Slide48
D
iffraction grating
L
arge # of parallel slits
GG’ = cross section of grating.Slits perpendicular to plane.Diagram shows six slits; actual grating may contain 1000’s.
© 2016 Pearson Education Inc.Slide49
R
eflection grating
R
ainbow-colored reflections from surface of DVD are
reflection-grating effect.DVD grooves are tiny pits 0.12 mm deep in surface, with a uniform radial spacing of 0.74 mm = 740 nm. Information coded on DVD by varying length of pits. Reflection-grating aspect of disc is aesthetic feature!
© 2016 Pearson Education Inc.Slide50
CDs vs. DVDs
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Multi-slit interference depends on
l
© 2016 Pearson Education Inc.Slide52
Resolution of a grating spectrograph
In spectroscopy it is often important to distinguish slightly differing wavelengths.
The minimum wavelength difference
Δ
λ that can be distinguished by a spectrograph is described by the chromatic resolving power R.For a grating spectrograph with a total of N slits, used in the m
th order, the chromatic resolving power is:
© 2016 Pearson Education Inc.Slide53
X-ray diffraction
When x rays pass through a crystal, the crystal behaves like a diffraction grating, causing
x-ray
diffraction. © 2016 Pearson Education Inc.Slide54
A simple model of x-ray diffraction
To better understand x-ray diffraction, we consider a two-dimensional scattering situation.
The path length from source to observer is the same for all the
scatterers
in a single row if θa = θr = θ.© 2016 Pearson Education Inc.Slide55
Circular apertures
The diffraction pattern formed by a circular aperture consists of a central bright spot surrounded by a series of bright and dark rings.
© 2016 Pearson Education Inc.Slide56
Diffraction by a circular aperture
Airy disk = central bright spot in diffraction pattern from circular aperture.
Radius of Airy disk from angular radius
θ
1 of first dark ring:© 2016 Pearson Education Inc.Slide57
Diffraction & Image resolution
Diffraction limits
resolution
of optical equipment, such as telescopes.
Larger aperture = better resolutionLonger wavelength = worse resolution
Rayleigh’s criterion for r
esolution of two point objects:Two objects are just barely resolved (distinguishable) if center of one diffraction pattern coincides with first minimum of the other.© 2016 Pearson Education Inc.Slide58
Smaller light, better resolution
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Bigger light, worse resolution
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Bigger light, worse resolution
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Bigger telescope, better resolution
Because of diffraction, large-diameter telescopes, such as the VLA radio telescope below, give sharper images than small ones.
© 2016 Pearson Education Inc.Slide62
What is holography?
By using a beam splitter and mirrors, coherent laser light illuminates an object from different perspectives.
Interference effects provide the depth that makes a three-dimensional image from two-dimensional views.
© 2016 Pearson Education Inc.Slide63
Viewing holograms
H
ologram is record on film of interference pattern formed with light from a coherent source & light scattered from object.
Images formed when light
is projected back through hologram.Observer sees virtual image formed behind hologram.© 2016 Pearson Education Inc.Slide64
An example of holography
© 2016 Pearson Education Inc.