![Page 1: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/1.jpg)
1
Thomas Young’s
Double Slit Experimentby
Charity I. Mulig
![Page 2: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/2.jpg)
2
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.
![Page 3: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/3.jpg)
3
Historical BackdropMid 17th century Fransesco Grimaldi observed the bending of light through narrow slits
![Page 4: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/4.jpg)
4
Historical Backdrop
The 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.
![Page 5: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/5.jpg)
5
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.
![Page 6: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/6.jpg)
6
Historical Backdrop
In the mid 19th century James Clerk Maxwell publish his famous
equations.
![Page 7: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/7.jpg)
7
Prerequisite Information
![Page 8: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/8.jpg)
8
Electromagnetic Wave• Produced by
accelerating charges• E and B are mutually
perpendicular to their direction of propagation
![Page 9: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/9.jpg)
9
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”
![Page 10: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/10.jpg)
10
Huygen’s Principle
Huygen’s principle applied to reflection and refraction of wave fronts.
Huygen’s principle applied to spherical and plane wave fronts.
![Page 11: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/11.jpg)
11
Diffraction
Simple proof of diffraction. Waves are bent at corners and edges. The smaller the opening, the greater the diffraction.
![Page 12: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/12.jpg)
12
Diffraction
The shadow is fuzzier when the opening is narrower.
![Page 13: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/13.jpg)
13
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.
![Page 14: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/14.jpg)
14
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.”
![Page 15: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/15.jpg)
15
Requirements for …
Constructive Interference Destructive Interference
r2 – r1 = mλ where m is an integer
r2 – r1 = mλ where m is a non-whole number
![Page 16: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/16.jpg)
16
The Experimental Set-up
![Page 17: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/17.jpg)
17
Geometry of the Set-up
Actual Geometry Approximate Geometry
![Page 18: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/18.jpg)
18
Interference Pattern
Destructive Interference
where m = 0, ±1, ±2, ±3,…
Constructive Interference
md sinwhere m = 0, ±1, ±2, ±3,…
2
1sin md
![Page 19: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/19.jpg)
19
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
d
RmRym
sin
![Page 20: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/20.jpg)
20
The wavelength of the light can then be solved as
INTERESTING FACT:The Young’s experiment was the first
direct measurement of light
Rm
dym
![Page 21: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/21.jpg)
21
Improvements
• Use of diffraction gratings instead of slits
• Fresnel’s Biprism experiment
![Page 22: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/22.jpg)
22
Intensity of Interference
Pattern
![Page 23: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/23.jpg)
23
Intensity of Each Source
202
1cEI
where
tEtE
tEtE
cos)(
)cos(
2
1
![Page 24: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/24.jpg)
24
Phasor Diagram for E1 and E2
Using the following relationships:
Cosine law
2cos2cos1 2
2
1
2cos2
ave
c0
0
![Page 25: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/25.jpg)
25
Solving for EP
2cos2
2cos22
cos12
cos12
cos2
222
22
22
2222
EE
EE
EE
EE
EEEE
p
p
p
p
p
![Page 26: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/26.jpg)
26
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
0EB
S •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.”
![Page 27: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/27.jpg)
27
I for Sinusoidal Wave in a Vacuum
cEIS
Ec
EIS
c
and
cBIS
kxtBE
txS
then
aa
aa
from
kxtBE
txS
kxtBtxB
kxtEtxE
where
txBtxEtxS
ave
ave
ave
02max
0
02max
0
2max
200
max
0
maxmax
2
22
2
0
maxmax
max
max
0
2
1
2
1
2
1
)(2cos12
),(
2
2cos1sin
1cos2sin12cos
)(sin),(
)sin(),(
),sin(),(
),(),(),(
0I21I
212
avecos
from2
φ2cos0II
2cE02ε0I
2φ2cos2cE02ε2
PcE0ε21I
then2φcos2EpE
substitute
![Page 28: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/28.jpg)
28
I for Interference Pattern
0
2
20
200
220
20
2
121cos
2cos
2
2cos22
1
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.”
![Page 29: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/29.jpg)
29
Phase and Path Differences
00
0
1212
12
12
2
22
2
nkn
k
n
rrkrr
rr
rr
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
![Page 30: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/30.jpg)
30
Phase and Path Differences
sincos
2cos
sin2sin
sin
22
12
12
dIII
dkdrrk
drr
dR
oo
Intensity far from two
sources
![Page 31: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/31.jpg)
31
For 2-slit interference, I may also be expressed as…
R
dyI
R
kdyII oo
22 cos2
cos
![Page 32: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/32.jpg)
32
Bonus!!!Question: What then?Answer:
1. Experiment on electron interference.2. De Broglie Wavelength3. Davisson-Germer Experiment4. Duality of Nature5. Heisenberg’s Uncertainty Principle
![Page 33: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/33.jpg)
33
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!
![Page 34: Thomas Young’s Double Slit Experiment by Charity I. Mulig 1](https://reader035.vdocuments.site/reader035/viewer/2022062421/56649d9c5503460f94a85a93/html5/thumbnails/34.jpg)
34
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