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MAGNETO-OPTICAL FARADAY
ROTATION .
INTRODUCTION :
If any transparent solid or liquid is placed in a uniform magnetic field, and a beam of plane polarized light
is passed through it in the direction parallel to the magnetic lines of force (through holes in the pole shoes
of a strong electromagnet), it is found that the transmitted light is still plane polarized, but that the plane
of polarization is rotated by an angle proportional to the field intensity. This "optical rotation" is called
the Faraday rotation (or Farady effect) and differs in an important respect from a similar effect, called
optical activity, occurring in sugar solutions.
In a sugar solution, the optical rotation proceeds in the same direction, whichever way the light is
directed. In particular, when a beam is reflected back through the solution it emerges with the same
polarization as it entered before reflection. In the Faraday effect, however, the direction of the optical
rotation, as viewed when looking into the beam, is reversed when the light traverses the substance
opposite to the magnetic field direction; that is, the rotation can be reversed by either changing the field
direction or the light direction. Reflected light, having passed twice through the medium, has its plane of
polarization rotated by twice the angle observed for single transmission.
AIM AND OBJECTIVE :
The purpose of this experiment is to observe the effect of a magnetic field on the transmission of linearly
polarized light through a dispersive medium , to measure the Verdet constant of dense flint glass at
several wavelengths, and to test the validity of the classical theory of magnetic circular birefringence,
known as the Faraday Effect.
Test the experimental apparatus. Plot the transmission vs. angle for a rotating analyzer and verify that it
goes a :
I = Io Cos2
∆ 𝜽
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DISCUSSION OF APPARATUS :
Electromagnet.
Magnet power supply.
50V-5A DC.
32 & 140 V AC.
RU #00048664).
Gauss-meter (RFL Industries).
High Intensity.
Tungsten Filament Lamp.
Three interference filters.
Volt-ammeter (DC).
Nicol prisms (2).
Glass samples (extra dense flint (EDF).
Light flint.
Sample holder (PVC).
HP 6235A Triple output power supply.
HP 34401 Multi-meter.
Si photodiode detector. .
THEORY AND BACKGROUND OF EXPERIMENT :
The relation between the angle of rotation of the polarization and the magnetic field in the transparent
material is given by Becquerel's formula:
= VBd
Where the is the angle of rotation, d is the length of the path where the light and magnetic field interact
(d is the sample thickness for this experiment), B is the magnetic field component in the direction of the
light propagation and V is the Verdet constant for the material (MKS units: radian/Tesla meter). This
empirical proportionality constant varies with wavelength and temperature and is tabulated for various
materials.
The Verdet Constant, V, depends on the dispersion of the refractive index, dn/d where n is the index of
refraction is the wavelength. As shown in the appendix:
V = /dB = -
1
2
𝑒
𝑚
𝜆
𝑐
𝑑𝑙
𝑑𝜆
Here e/m is the charge to mass ratio of the electron and c is the speed of light.
EXPERIMENTAL SETUP :
Set up the Teachspin Faraday Effect system in accordance with the manual (red binder). Then
follow steps (b) – (f) for each of the three lasers (Red, Green, and Blue)
Check if the laser output is polarized. If the laser is not polarized, use an initial Polarizer polaroid
P after the laser to polarize the beam before entering the glass rod
Use solenoid current set to 0 use the photodiode detector to measure the he transmitted light
intensity I as a function of the angular setting of the analyzer polaroid. You should observe a
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Malus’ Law dependence I = I0cos (θ) where θ is the relative angle between the plane of
polarization of the polarized laser beam and the transmission axis of the analyzer A. This check
of Malus’ law dependence is a good test that your input beam is polarized.
Now measures the angle of rotation of the plane of polarization of the beam. Do not exceed 3
Amps for the solenoid current.
Plot your measured Faraday effect rotation angles ΔΦ vs. the applied magnetic field B.
Compare your measured value of CV for the glass rod with published (handbook) data for similar
types of glass.
Plot CV vs. λ.
CALCULATIONS :
It can be shown that the verdet constant is expected to be :
V = /dB = -
1
2
𝑒
𝑚
𝜆
𝑐
𝑑𝑙
𝑑𝜆
For the normal dispersion :
𝑑𝑛
𝑑𝜆
∝ 1/ λ3
Which means :
V ∝ 1/ λ2
So there should be a large difference between the V’s for red and blue light. Some numerical values of
are tabulated below :
RESULT ANALYSIS :
Magneto-optic effect is a phenomenon in which an electromagnetic wave propagates through a medium
and gets affected by the presence of a quasistatic magnetic field. Verdet constant describes the strength of
Faraday Effect for a particular material. The objective of this work was to measure the Verdet constant for
different transparent materials. The Verdet constant is measured by using the Faraday Effect which is a
magneto-optical phenomenon; mean it describes the rotation of the plane of polarization of light with in a
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medium when it is placed in an external magnetic field. So this experiment determines the rotation of the
plane of polarization with respect to the wavelength and the magnetic field.
