Thomas Young’s Double Slit Experiment by Charity I. Mulig 1.
-
Upload
clinton-francis -
Category
Documents
-
view
217 -
download
1
Transcript of Thomas Young’s Double Slit Experiment by Charity I. Mulig 1.
1
Thomas Young’s
Double Slit Experimentby
Charity I. Mulig
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.
3
Historical BackdropMid 17th century Fransesco Grimaldi observed the bending of light through narrow slits
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.
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.
6
Historical Backdrop
In the mid 19th century James Clerk Maxwell publish his famous
equations.
7
Prerequisite Information
8
Electromagnetic Wave• Produced by
accelerating charges• E and B are mutually
perpendicular to their direction of propagation
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”
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.
11
Diffraction
Simple proof of diffraction. Waves are bent at corners and edges. The smaller the opening, the greater the diffraction.
12
Diffraction
The shadow is fuzzier when the opening is narrower.
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.
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.”
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
16
The Experimental Set-up
17
Geometry of the Set-up
Actual Geometry Approximate Geometry
18
Interference Pattern
Destructive Interference
where m = 0, ±1, ±2, ±3,…
Constructive Interference
md sinwhere m = 0, ±1, ±2, ±3,…
2
1sin md
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
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
21
Improvements
• Use of diffraction gratings instead of slits
• Fresnel’s Biprism experiment
22
Intensity of Interference
Pattern
23
Intensity of Each Source
202
1cEI
where
tEtE
tEtE
cos)(
)cos(
2
1
24
Phasor Diagram for E1 and E2
Using the following relationships:
Cosine law
2cos2cos1 2
2
1
2cos2
ave
c0
0
25
Solving for EP
2cos2
2cos22
cos12
cos12
cos2
222
22
22
2222
EE
EE
EE
EE
EEEE
p
p
p
p
p
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.”
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
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.”
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
30
Phase and Path Differences
sincos
2cos
sin2sin
sin
22
12
12
dIII
dkdrrk
drr
dR
oo
Intensity far from two
sources
31
For 2-slit interference, I may also be expressed as…
R
dyI
R
kdyII oo
22 cos2
cos
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
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!
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