Diffraction Chapter 36 © 2016 Pearson Education Inc. - PowerPoint Presentation

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Diffraction Chapter 36 © 2016 Pearson Education Inc. - PPT Presentation

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

2016 diffraction education pearson diffraction 2016 pearson education slit pattern single interference slits width light intensity minima grating resolution

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Slide1

Diffraction

Chapter 36

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!

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.

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.

Diffraction from a single slit

Diffraction from a single slitSlide9

Actual Single Slit DiffractionSlide10

Actual Single Hole DiffractionSlide11

Diffraction

vs. Interference?

Both use same

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!

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(edge) – d(center)]

Phase difference Df = d /2pl = kd

d (center)

d (edge)Slide14

How does distance affect Diffraction?

If screen is far away, d >> a

If screen is close, d ~ or < a?

d (center)

d (edge)

d (center)

d (edge)Slide15

Fresnel

vs. Fraunhofer

Diffraction

CLOSE screen d

<< ka

2 means LARGE phase changes (Fresnel Diffraction)

FAR screen d

means

SMALL phase changes (

Fraunhofer

Diffraction

)

Check out

https://

www.youtube.com/watch?v=aEd4FFeBV6U

Slide16

Fresnel

vs. Fraunhofer

Diffraction

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

Fresnel

diffraction by a single slit

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

Locating

dark fringes

a/2

d (center)

dark fringe

a/2 sin(

) =

= l/2

for minimum

sin(

) =

aSlide23

Intensity in single-slit pattern

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.

Intensity in single-slit pattern

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.

Intensity in single-slit pattern

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.

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

Width of single-slit pattern

Pattern depends on

ratio

of slit width

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).

The

minima

of the single-slit diffraction pattern occur when

Diffraction

by a Single Slit or Disk

aSlide30

Width of single-slit

diffraction pattern

Pattern depends on

ratio

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

aSlide32

Diffraction

vs. Interference?

a =

size

of single slit

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 /

minima

at large

l ~

a, none!

aSlide35

Single-slit

diffractionSlide36

Single-slit

diffraction vs.

Double-slit Interference

Double-slit interference

Slit SPACING =

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!

See

Hyperphysics

http://

hyperphysics.phy-astr.gsu.edu/hbase/phyopt/mulslid.html#c1 Slide39

Combining Diffraction & Interference!

Diffraction

from Two slits of finite width

Pattern from two slits with width

, 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.

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!

Diffraction

AND Interference

Diffraction minima are labeled by integer

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.”)

Diffraction

from Two slits of finite width

Diffraction & InterferenceSlide45

Several slits

rray of 8 narrow slits, distance

between adjacent slits.Constructive interference occurs for rays at angle θ arriveing at P with path difference equal to integral

# of l.

Interference pattern of several slits

Eight slit pattern:

Large maxima,

(principal maxima)

@ same positions as a two-slit pattern, but much narrower.

Interference pattern of several slits

16 slit pattern:

eight of principal

maximum is proportional to N 2, Energy conservation means width of each principal maximum proportional to 1/N

iffraction grating

arge # of parallel slits

GG’ = cross section of grating.Slits perpendicular to plane.Diagram shows six slits; actual grating may contain 1000’s.

eflection grating

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!

CDs vs. DVDs

Multi-slit interference depends on

Resolution of a grating spectrograph

In spectroscopy it is often important to distinguish slightly differing wavelengths.

The minimum wavelength difference

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:

X-ray diffraction

When x rays pass through a crystal, the crystal behaves like a diffraction grating, causing

x-ray

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

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.

Diffraction by a circular aperture

Airy disk = central bright spot in diffraction pattern from circular aperture.

Radius of Airy disk from angular radius

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

Bigger light, worse resolution

Bigger telescope, better resolution

Because of diffraction, large-diameter telescopes, such as the VLA radio telescope below, give sharper images than small ones.

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.

Viewing holograms

ologram is record on film of interference pattern formed with light from a coherent source & light scattered from object.

Images formed when light

An example of holography