thomas young’s double slit experiment
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Thomas Young’s
Double Slit Experimentby
Charity I. Mulig
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Historical BackdropPublication of Christian Huygen’s treatise on light (1690). He believed that there is a medium between the eye and the objects and the object does something to cause an effect in that medium.
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Historical BackdropMid 17th century Fransesco Grimaldi observed the bending of light through narrow slits
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Historical BackdropThe pervading idea of the nature of light is Newton’s Corpuscular Theory (1704). This is despite the fact that he noticed interference fringes on the edges of the prism that he used.
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Historical BackdropIn 1801 Thomas Young performed his 2-slit experiment. Augustin-Jean Fresnel’s biprism experiment was later conducted in support to Young’s experiment. Fresnel’s experiment to a large extent was responsible for convincing the scientific community of the wave nature of light.
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Historical Backdrop
In the mid 19th century James Clerk Maxwell publish his famous
equations.
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Prerequisite Information
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Electromagnetic Wave• Produced by
accelerating charges• E and B are mutually
perpendicular to their direction of propagation
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Huygen’s Principle
Drawings from Huygen’s book Treatise on Light.
“The wave fronts of light waves spreading out from a point source can be regarded as the overlapped crests of tiny secondary waves – wave fronts are made up of tinier wave fronts”
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Huygen’s Principle
Huygen’s principle applied to reflection and refraction of wave fronts.
Huygen’s principle applied to spherical and plane wave fronts.
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Diffraction
Simple proof of diffraction. Waves are bent at corners and edges. The smaller the opening, the greater the diffraction.
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Diffraction
The shadow is fuzzier when the opening is narrower.
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Interference
“…the phenomena that occurs when two or more waves overlap in the same region or space”
Interference patterns of overlapping waves from two vibrating sources.
Young’s original drawing of 2-source (pinholes) interference pattern.
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Principle of Superposition
“When two or more waves overlap, the resultant displacement at any point and at any instant is found by adding the instantaneous displacements that would be produced at the point by individual waves if each were present alone.”
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Requirements for …
Constructive Interference Destructive Interference
r2 – r1 = mλ where m is an integer
r2 – r1 = mλ where m is a non-whole number
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The Experimental Set-up
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Geometry of the Set-up
Actual Geometry Approximate Geometry
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Interference Pattern
Destructive Interference
where m = 0, ±1, ±2, ±3,…
Constructive Interference
md sinwhere m = 0, ±1, ±2, ±3,…
21sin md
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From the geometry of the set-up
But R>>d; θ is very small and we can make the assumption
So that for small angles
tanRym
tansin
dRmRym
sin
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The wavelength of the light can then be solved as
INTERESTING FACT:The Young’s experiment was the first
direct measurement of light
Rmdym
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Improvements
• Use of diffraction gratings instead of slits
• Fresnel’s Biprism experiment
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Intensity of Interference
Pattern
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Intensity of Each Source
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1 cEI
where
tEtEtEtE
cos)()cos(
2
1
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Phasor Diagram for E1 and E2
Using the following relationships:
Cosine law
2cos2cos1 2
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2cos2
ave
c0
0
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Solving for EP
2cos2
2cos22
cos12
cos12
cos2
222
22
22
2222
EE
EE
EE
EE
EEEE
p
p
p
p
p
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Poynting Vector in Vacuum
BxES
1
•Has a direction along the propagation of the wave since the electric and magnetic fields are perpendicular to each other
0EBS
•Its magnitude is equal to the energy flow per unit area per unit time through a cross-section area perpendicular to the propagation direction
“The average value of the magnitude of the poynting vector at a point is called the intensity of the
radiation.”
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I for Sinusoidal Wave in a Vacuum
cEIS
Ec
EIS
c
andcBIS
kxtBEtxS
then
aa
aa
from
kxtBEtxS
kxtBtxBkxtEtxE
where
txBtxEtxS
ave
ave
ave
02max
0
02max
0
2max
200
max
0
maxmax
2
22
2
0
maxmax
max
max
0
21
21
2
1
)(2cos12
),(
22cos1sin
1cos2sin12cos
)(sin),(
)sin(),(),sin(),(
),(),(),(
0I21I
212avecos
from2
φ2cos0II
2cE02ε0I2
φ2cos2cE02ε2PcE0ε2
1Ithen
2φcos2EpE
substitute
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I for Interference Pattern
0
2
20
200
220
20
21
21cos
2cos
2
2cos221
2cos2
II
from
II
cEI
cEcEI
then
EE
substitute
ave
P
p
“The intensity of the central bright spot is 4x that of the individual sources
…but the average intensity of the whole interference pattern is just twice the intensity of the individual sources.”
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Phase and Path Differences
00
0
1212
12
12
2
22
2
nknk
n
rrkrr
rrrr
n
Where•k is the wave number in the material•ko is the wave number in the material•n is the index of refraction•λ is the wavelength of light in the material•λo is the wavelength of light in vacuum
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Phase and Path Differences
sincos2
cos
sin2sin
sin
22
12
12
dIII
dkdrrk
drrdR
ooIntensity far
from two sources
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For 2-slit interference, I may also be expressed as…
RdyI
RkdyII oo
22 cos2
cos
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Bonus!!!Question: What then?Answer:
1. Experiment on electron interference.2. De Broglie Wavelength3. Davisson-Germer Experiment4. Duality of Nature5. Heisenberg’s Uncertainty Principle
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Final TriviaThomas Young read fluently at the age of 2; by 4, he had read the Bible twice; by 14, he knew
eight languages. In adult life, he was a physician and scientist, contributing to an
understanding of fluids, work and energy, and elastic properties of materials. He was the first
person to make progress in deciphering Egyptian hieroglyphics. No doubt about it –
Thomas Young was a bright guy!
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Sources• University Physics by Young and Freedman• Fundamental Physics by Resnick • Conceptual Physics by Hewitt• Beautiful Science:
http://www.huntington.org/exhibitions/beautifulscience/timelines/light_web.html
• Maths.TCD : http://www.maths.tcd.ie/pub/HistMath/People/Huygens/RouseBall/RB_Huygens.html
• Physics 2000:http://www.colorado.edu/physics/2000/schroedinger/electron_interference.html#evidence
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