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
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
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
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
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
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
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
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
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
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
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]
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
Experimental facts
♠ Relevant variables:
Wavelength λ Slit separation d Viewing plane distance D
♠ Observations:
Spacing between consecutive peaks reduces with decreasing wavelength
Try it yourself using JaVaOptics [http://www.ub.edu/javaoptics/indexen.html]
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
Experimental facts
♠ Relevant variables:
Wavelength λ Slit separation d Viewing plane distance D
♠ Observations:
Spacing between consecutive peaks reduces with decreasing wavelength
Try it yourself using JaVaOptics [http://www.ub.edu/javaoptics/indexen.html]
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
Experimental facts
♠ Relevant variables:
Wavelength λ Slit separation d Viewing plane distance D
♠ Observations:
Spacing between consecutive peaks shrinks with increasing slit separation
Try it yourself using JaVaOptics [http://www.ub.edu/javaoptics/indexen.html]
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
Experimental facts
♠ Relevant variables:
Wavelength λ Slit separation d Viewing plane distance D
♠ Observations:
Spacing between consecutive peaks increases for more distant viewing plane
Try it yourself using JaVaOptics [http://www.ub.edu/javaoptics/indexen.html]
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
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
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
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
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
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
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
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
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
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
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
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
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
Analytical treatment
♠ 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
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
Analytical treatment
♠ 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
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
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
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
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
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
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
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
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?
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
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
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
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
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
ADDITIONAL MATERIAL
TEACHING PHILOSOPHY
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
Teaching view
LANGUAGE CONTEXT
STUDENT
INTUITION ANALOGY
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
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
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
ADDITIONAL MATERIAL
RESEARCH PLANS
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
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
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
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
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment
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)
Foundations of Physics 1 LPHYS1122 Young's two�slit experiment