oung'sY two slit experiment - Informationen zum …davidlv/teaching-files/twoslit.pdfoung'sY two slit experiment prepared for Foundations of Physics 1 LPHYS1122 MPhys Physics and Astronomy

Young's two�slit experiment

prepared for Foundations of Physics 1 LPHYS1122

MPhys Physics and Astronomy � Level One

Durham University

David López-Val [02/09/2015]

September 2, 2015

Foundations of Physics 1 LPHYS1122 Young's two�slit experiment

Young's two�slit experiment

♠ Context:

Foundations of Physics 1 LPHYS1122

Level One MPhys Physics and Astronomy Durham University

♠ Situation in the syllabus:

Content: Optics: Geometric optics. Lenses and mirrors. Optical instruments. Interference ,

di�raction, and polarization.

Learning outcomes: They will have knowledge of the principles that describe the propagation

of light in free space, dielectric materials, and lens/mirror systems, and will be familiar with

the concepts of polarisation and Interference .

♠ Aspects covered:

♠ Historical context ♠ Experimental setup ♠ Empirical facts

♠ Interpretation ♠ Analytical treatment ♠ Finer structure

♠ Work suggestions ♠ Links to upcoming topics


Context

The nature of light - a longstanding controversy

♠ Newton's corpuscular paradigm:

Luminous bodies emit light in the form of tiny particles

♠ Huygens, Fresnel & Young's ondulatory interpretation:

Light propagation is governed by the same laws of wave mechanics

♠ Young's [1773 - 1829] key contributions:

1801 On the theory of light and color

1802 Two�slit experiment • light undergoes interference

• nicely accounted for by Huygens' principle


Context

The nature of light - a longstanding controversy

♠ Newton's corpuscular paradigm:

Luminous bodies emit light in the form of tiny particles

♠ Huygens, Fresnel & Young's ondulatory interpretation:

Light propagation is governed by the same laws of wave mechanics

♠ Young's [1773 - 1829] key contributions:

1801 On the theory of light and color

1802 Two�slit experiment • light undergoes interference

• nicely accounted for by Huygens' principle


Setup

Young's two�slit interferometer

♠ Sunlight passes through a tiny slit

♠The primary light source is directed towards twoparallel slits, with relative separation d

♠ Light is emitted from these secondary sources andprojected onto a screen at distance D.

Expected outcome:

light as classical particles

follow a straight line

generate an image matching the slits'size and shape

light as waves

interfere (as water or sound)

generate a pattern of bright & darkbands


Setup

Young's two�slit interferometer

♠ Sunlight passes through a tiny slit

♠The primary light source is directed towards twoparallel slits, with relative separation d

♠ Light is emitted from these secondary sources andprojected onto a screen at distance D.

Expected outcome:

light as classical particles

follow a straight line

generate an image matching the slits'size and shape

light as waves

interfere (as water or sound)

generate a pattern of bright & darkbands


Experimental facts

♠ Observations:

A series of luminous and dark fringes, equally spaced along the viewing plane

Try it yourself using JaVaOptics [http://www.ub.edu/javaoptics/indexen.html]


Experimental facts

♠ Relevant variables:

Wavelength λ Slit separation d Viewing plane distance D

♠ Observations:

Spacing between consecutive peaks reduces with decreasing wavelength



Experimental facts



♠ Observations:

Spacing between consecutive peaks reduces with decreasing wavelength



Experimental facts



♠ Observations:

Spacing between consecutive peaks shrinks with increasing slit separation



Experimental facts



♠ Observations:

Spacing between consecutive peaks increases for more distant viewing plane



Conceptual framework

Double�path experiment INTERFERENCE Genuine wave behavior

Interpretation

The primary wavefront is separated into two cylindrical wavefronts

Each slit emits light with common amplitude, polarization, frequency and phase

Wavefronts overlap at the observation point ⇒ individual amplitudes add up

Di�erent travel distance (optical path) ⇒ relative phase shift

Addition (cancellation) of individual wavefront amplitudes

⇒ Regions with increased (suppressed) intensity

Huygens' principle:

Each point on a wavefrontgenerates a secondary sphericalwavelet, which propagates withthe same velocity and frequencyas that of the primary wave




Interpretation







Huygens' principle:





Interpretation







Huygens' principle:



Analytical treatment

♠ Geometry

Two slits S1, S2 atz = −D

Symmetric w.r.t OZ

Parallel to OX

Viewing pointP(x, y, z = 0)

♠ Optical path (n = 1 for de�niteness)

♠ ∆ = |S1 − S2| =√D2 + y2 + (x+ d/2)2 −

√D2 + y2 + (x− d/2)2

♠ ∆ (S1 + S2) = 2xd

♠ Far��eld approximation ♠ D ∼ O(m) ♠ d ∼ O(0.1mm) d� D

S1 + S2 ' 2D ∆ 'xd

Dδ = k∆ =

2π

λ

xd

D



♠ Geometry


Symmetric w.r.t OZ

Parallel to OX



♠ ∆ = |S1 − S2| =√D2 + y2 + (x+ d/2)2 −

√D2 + y2 + (x− d/2)2

♠ ∆ (S1 + S2) = 2xd


S1 + S2 ' 2D ∆ 'xd

Dδ = k∆ =

2π

λ

xd

D



♠ Geometry


Symmetric w.r.t OZ

Parallel to OX



♠ ∆ = |S1 − S2| =√D2 + y2 + (x+ d/2)2 −

√D2 + y2 + (x− d/2)2

♠ ∆ (S1 + S2) = 2xd


S1 + S2 ' 2D ∆ 'xd

Dδ = k∆ =

2π

λ

xd

D



♠ Combined wavefront

EPS1

= E0 sin(ωt− k r)

EPS2

= E0 sin(ωt− k r + δ)

}⇒

Amplitude E = 2E0 cos

(δ

2

)sin(ωt− k r + δ)

Intensity: I = 4I0 cos2

(δ

2

)

♠ Interference pattern

♠ Location of maxima: ⇒ ∆ = mλ or δ = 2πm m ∈ N

♠ Location of minima: ⇒ ∆ =

(2m+ 1

2

)λ or δ = (2m+ 1)π

♠ Interference order m: ⇒ # of wavelengths by which the travel distance of theinterfering wavefronts di�er for a given peak

♠ Spacing between consecutive maxima: ⇒ |xm − xm+1| =λD

d

♠ Pattern geometry: ⇒xd

D= ct: ♦ equally spaced fringes ♦ parallel to OY



♠ Combined wavefront

EPS1

= E0 sin(ωt− k r)

EPS2

= E0 sin(ωt− k r + δ)

}⇒

Amplitude E = 2E0 cos

(δ

2

)sin(ωt− k r + δ)

Intensity: I = 4I0 cos2

(δ

2

)

♠ Interference pattern

♠ Location of maxima: ⇒ ∆ = mλ or δ = 2πm m ∈ N

♠ Location of minima: ⇒ ∆ =

(2m+ 1

2

)λ or δ = (2m+ 1)π

♠ Interference order m: ⇒ # of wavelengths by which the travel distance of theinterfering wavefronts di�er for a given peak

♠ Spacing between consecutive maxima: ⇒ |xm − xm+1| =λD

d

♠ Pattern geometry: ⇒xd

D= ct: ♦ equally spaced fringes ♦ parallel to OY


Summary & outlook

Key ideas

Double path experiment ⇒ Di�erent travel distance ⇒ Relative phase

Light by light gives shadow !

♠ Series of bright/dark bands constant interfringe spacing d,D, λ dependence

♠ Explained by: Huygen's principle additive/subtractive interference

⇒ Strong evidence for wave nature of light propagation

Modern version

Taylor (1909): double slits with very low�intensity (∼ single�photon interference)

⇒ Quantum nature of light and matter:

♠ Wave�particle duality ♠ Complementarity principle


Summary & outlook

Key ideas






Modern version





Summary & outlook

Key ideas






Modern version





To train yourself

♠ Some Physics intuition:

• A paramount observation in Young's two�slit experiment are the dependences on the key

variables d,D and λ .

♠ Consider the limiting cases, e.g. d→ 0 or D →∞; can you interpret them intuitively?

♠ Approximations:

♠ Discuss qualitatively how would the description of the interference pattern change withcorrections to the far��eld approximation.

♠ What would be the impact of considering that the light emitted from each of the slightshas a slightly di�erent: i) frequency?; ii) amplitude?; iii) polarization?

♠ Alternative experimental settings:

♠ Consider Lloyd's mirror and Fresnel's biprism. i) Discuss how these devices generateinterference patterns analogous to Young's two�slit setup. ii) Is the mirror case somewhatsubtle?


To go beyond: �ner structure

♠ Finite�size:

♠ Finite slit width ⇒ set of independent emitters

⇒ spatially incoherent light

• Interference bands from each of them have slightly di�erent peak positions

⇒ (S, S + δS) → (x, x+ δx) .

• A series of band sets with displaced peaks overlap ⇒ poorer contrast

♠ Corrections to monochromaticity:

λ→ λ+ δλ ⇒ xm → xm + δxm = xm +mD

dδλ

⇒ Blueish maxima @ inner edges Reddish maxima @ outer edges

⇒ Handle to measure λ : Young's estimates: λviolet ' 400 nm λred ' 2λviolet


To go beyond: �ner structure

♠ Finite�size:

♠ Finite slit width ⇒ set of independent emitters

⇒ spatially incoherent light

• Interference bands from each of them have slightly di�erent peak positions

⇒ (S, S + δS) → (x, x+ δx) .

• A series of band sets with displaced peaks overlap ⇒ poorer contrast

♠ Corrections to monochromaticity:

λ→ λ+ δλ ⇒ xm → xm + δxm = xm +mD

dδλ

⇒ Blueish maxima @ inner edges Reddish maxima @ outer edges

⇒ Handle to measure λ : Young's estimates: λviolet ' 400 nm λred ' 2λviolet


ADDITIONAL MATERIAL

TEACHING PHILOSOPHY


Teaching view

LANGUAGE CONTEXT

STUDENT

INTUITION ANALOGY


In�class practice

♠ Predict & anticipate ♠ View & experience

♠ Draw & sketch ♠ Code & simulate

♠Words before equations ♠ Intuition before numbers

♠ Think broadly ♠ Connect & bridge �elds

♠ Summarize & extract keywords ♠ Read the sources

♠ Science& Society ♠ Applications & implications


ADDITIONAL MATERIAL

RESEARCH PLANS


Development plans

♠ Theoretical High Energy Physics :

♠ beyond the Standard Model ♠ LHC

♠Extended Higgs sectors ♠ Electroweak symmetry breaking

♠Phenomenology

♠ Electroweak corrections in the singlet extension of the SM

Electroweak renormalization: a systematic scheme comparison (in progress)

Heavy�to�light Higgs boson decays. Improved predictions for the H BRs (in progress)

Singlet model @NLO in the Feynrules-NLOCT setup.

Additional CP phases; o��shell physics & �nite width e�ects


Development plans

♠ Theoretical High Energy Physics :

♠ beyond the Standard Model ♠ LHC

♠Extended Higgs sectors ♠ Electroweak symmetry breaking

♠Phenomenology

♠ Electroweak corrections in the singlet extension of the SM

Electroweak renormalization: a systematic scheme comparison (in progress)

Heavy�to�light Higgs boson decays. Improved predictions for the H BRs (in progress)

Singlet model @NLO in the Feynrules-NLOCT setup.

Additional CP phases; o��shell physics & �nite width e�ects


Development plans

♠Methods

♠E�ective Field Theories

E�ective �eld theories versus UV�complete models: a comparison beyond theleading�order (in progress)

Matching procedures: a systematic comparison. Prospects for automated methods.

Implications for LHC searches: heavy resonances, Dark Matter

♠ Improved search strategies for new physics resonances at the LHC

Innovative methods (e.g. Voronoi's tesselation) to distinguishing boosted scalars fromboosted QCD jets

♠Theoretical aspects

♠ Linking scales through Higgs physics

Cosmological implications of a time�varying Higgs vev (in progress)

Constraining new physics from EW�scale observables, vacuum stability and theRenormalization Group: in�ation, reheating, non�standard electroweak symmetrybreaking mechanisms (scale�invariant, Higgs portal�induced)


Documents

oung'sY two slit experiment - Informationen zum …davidlv/teaching-files/twoslit.pdfoung'sY two slit experiment prepared for Foundations of Physics 1 LPHYS1122 MPhys Physics and Astronomy