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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

202

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

21

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