faraday rotation effect - iucaa-rpl · 2018. 10. 13. · • michael faraday (england) : in 1845...
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FARADAY ROTATION EFFECT
Jaydeep Sanjay BelapureM.Sc. II,
Dept. of Physics, University of Pune
Under the guidance of
Joydeep BagchiVSP-2007, IUCAA
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INTRODUCTION
• Michael Faraday (England) :
In 1845 Discoveredthe First effect connecting Magnetismand Light,
“The Faraday Rotation Effect”.
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Faraday Rotation Effect
• The incident Plane of linearlypolarized light Rotates by an angle when it passes through the medium.
“Magnetic Birefringence”
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Rotation Angle
• The faraday rotation ‘θ’ is proportional to Magnetic field and the length traversed.
( )R Ld n n zπθλ
= − ( )R Ln n B− ∝
VBzθ =
3 2
2 2 2 20
4( )NeV
m cπ ωω ω
=−
Where,
V = Verdet constantnR = Refractive Index for
Right Circular lightnR = Refractive Index for
Left Circular lightωo = Resonance frequencyN = Number density of
electrons
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EXPERIMENTAL SETUP
LASERSOLENOID
ANALYSERPHOTODIODE
AMPLIFIER
CURRENT SOURCE
POLARIZER
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Solenoid
zpL.
z2 1
• L: 15 cm • r1 : 0.88 cm• r2 : 1.87 cm
• 160 turns/layer• 10 layers
0 2 12 2 2 22 1
2iN z zBL z r z r
µ = − + +
Finite length (shell) :
2 2 2 22 2 2 1 2 20
2 12 2 2 22 1 2 1 1 1 1 1
ln ln2( )
z r r z r riNB z zr r L z r r z r rµ + + + +
= −− + + + +
Finite Thickness :
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( ).L
V B z dzθ = ∫
Magnetic Field along the solenoid length.We consider a shell of average radius r = 1.38 cm, with same total current
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Central Magnetic field as a function of current
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Observation Method
Malus’s Curve NO Magnetic field
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Faraday Rotation
MagneticField OFF
Magneticfield ON
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New Observation Method
α
ImaxImax
α – θ
θ rotation
Sin2
(α)
Cos2(α ) Cos2(α - θ )
Sin2(α - θ )
Without Magnetic Field With Magnetic Field
1tan yx
α − =
1tan rot
rot
yx
θ α − = −
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Observations
• We use the New Method to Measure“Faraday Rotation Angle”
• WITH –• Different Magnet fields• Materials: Lead silicate glass, Water, Benzene• Laser sourses : Red (650 nm), Green (543 nm)
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Faraday Rotation Measured for Lead Silicate Glass
Wavelength Dependance of Rotation angle
Red Laser
Green Laser
V
V
3 2
2 2 2 20
4( )Ne Bz
m cπ ωθω ω
= −
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Faraday Rotation Measured for Water
Green Laser
Red Laser
V
V
3 2
2 2 2 20
4( )Ne Bz
m cπ ωθω ω
= −
Wavelength Dependence of Rotation angle
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Comparing Verdet Constants
Lead silicate GlassGreen Laser
Red Laser
WaterGreen
Red
Benzene (Red)
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Wavelength Dependence of Verdetconstant
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Astrophysical Application of Faraday Rotation Effect
int( ) ( )obs λ λΨ = Ψ +∆Ψ3
2int 2 4( ) ( ) ( ) ( )
2
L
obs ee o
e n l B l dlm c
λ λ λπ
Ψ = Ψ +
∫
Rotation Measure (RM) (rad/m2)Plotting Y= C + X*RM
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Radio Jet CGCG049-033• GMRT• 1.3GHz• Resolution: 11 arc sec
The largest and highlycollimated radio jet~400kpc large
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• VLA• 1.4GHz• Resolution =
45 arc sec
• Max Planck 100m• 8.4GHz• Resolution =
84 arc sec
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Acknowledgement
I wish to thank my guide Prof Bagchi, Prof K Subramanian, Dr Joe Jacob, Viral andall my VSP friends during my stay at IUCAA. ☺
☺