In this experiments we experimentally APPARATUS We plot our results below. First we show the
determine the Verdet constant of a glass rod with determined Verdet constant as a function of average B
specification SF-59 to be 0.2375rad/mT*cm. We The goal of the experiment is to determine the Verdet constant of
field over the glass dielectric. Our first set of data was
observed a rotation in the plane of polarization of a transparent dielectric. The experimental apparatus that allows us to determine
taken without a hood.
linearly polarized monochromatic beam of light, the above value consists of 4 basic components: a linearly polarized
which we obtained by shining a red laser through an monochromatic light source, an analyzer polaroid, a solenoid, and an optical
analyzer polaroid. The rotation occurs as the beam detector. A linearly polarized monochromatic light source is obtained by shining
propagates through a dielectric in the presence of a a red laser through an analyzer polarizer. The solenoid is 150mm long, and 10
magnetic field and the magnitude of the rotation is layers. The solenoid is constructed with #18 double insulated copper wire. Finally
related to both the Verdet constant and projection of the detector is simply a photodiode. The apparatus setup is shown in Fig. 2.
the magnetic field in the direction propagation of the
laser beam. In this manner we determine the Verdet
constant of SF-59. Finally to achieve a greater
accuracy we model the magnetic field to take into Fig 4. Verdet constant as a function of Avg. B field without hood.
account that the field is non constant inside the First thing we notice is that the Verdet constant varies
solenoid. Finally we conduct the experiment once strongly with a weak magnetic field. We think this is a
without a hood and once with a hood to keep out result of electronic noise in the photodetector which
stray light to check if it makes a difference. We becomes insignificant as we raise the B field. The
Fig 2. Note the apparatus use specifically in our experiment uses a red laser as a light source and a glass rod for
discovered that the hood did indeed make a the dielectric. Verdet constant settles to a constant for values of avg.
difference. B field greater than 0.035. We determine the Verdet
PROCEDURE constant to be 0.4827rad/mT*cm with a variance of
In order to determine the Verdet constant of material SF-59, we propagate 0.0836rad/mT*cm.
a laser beam through this material in the presence of a known magnetic field. We
then measure the rotation of the plane of polarization using an analyzer polaroid.
To determine the Verdet constant accurately we do not treat the solenoid as ideal.
By doing so the magnetic field that induces the rotation is non constant.
Equation 1 generalizes as such
The Faraday effect, first observed by Michael B(l ) dl. (2)
Faraday in 1845, provided the first evidence of a glass rod
connection between light and magnetism. Faraday To determine the Verdet constant, then we must model the magnetic field inside
found that linearly polarized light propagating the solenoid. We do this by treating the solenoid as a series of current loops with Fig 5. Verdet constant as a function of Avg. B field with hood.
through a dielectric parallel to a static magnetic field 10 radial layers. Then we calculate the field at a point inside the solenoid by We repeated the measurement with a hood to reduce
had an observable rotation in its plane of summing over every loop, the contribution to the field from each particular loop. stray light entering the photodetector and as we did
polarization. This is represented pictorially below in The field as well as the integral in equation 2 are evaluated numerically. One for the measurement with a hood we determine a
Fig. 1. additional piece is necessary to compute the magnetic field, the current running Verdet constant of 0.2375rad/mT*cm with a variance
through the solenoid. We can continuously measure the voltage across the of 0.0981rad/mT*cm. The variance with a hood is
solenoid and via, greater however that is more likely due to the fact that
the hood measurements were taken after the no hood
V RI (3) measurements, where the measurements were taken
will little time in between and the solenoid over a few
Fig .1 Plane of polarization of light rotated as it propagates through
where V is the voltage, R is the resistance, and I is the current, we may determine runs did heat up enough for a non-negligible change
dielectric in presence of parallel magnetic field. the current if we know R. We measured the voltage and current of across the in the resistance.
solenoid for a few points and then plot voltage as a function of current.
This effect is a result of a magnetic field induced
circular birefringence in the linearly polarized laser Voltage(Volts) as Function of Current(Amps)
beam in a dielectric material. In a constant magnetic 10
field the rotation may be quantitatively described by 6
We measured a Verdet constant of 0.2375rad/mT*cm
y = 2.5464x + 0.0274
2 R2 = 0.9994
where Δθ is the rotation angle of the plane of
0 0.5 1 1.5 2 2.5 3 3.5
and 0.4827rad/mT*cm with and without a hood
polarization, ν is the Verdet constant, B is the
respectively. Clearly using the hood impacts the
magnitude of the magnetic field, and l is the length Fig 3. Measured voltage as a function of current used in determining the resistance of solenoid. determination of the constant. In the future this
of the glass rod. The Verdet constant is a material experiment could be improved by letting the solenoid
From this we can conclude that the resistance is 2.5464Ω. The solenoid heats up
property of dielectrics and it is the constant of cool in between data runs to insure that the resistance
when current is running through it, increasing the resistance. However we turn
proportionality between the angle of rotation and the remains the same throughout the experiment.
on the current for short enough time intervals so that the increase in resistance is
magnitude of the magnetic field. negligible. Now all we must do is measure voltage across the solenoid and
The Faraday effect is used in the fabrication of rotation of the plane of polarization and we may obtain the Verdet constant.
optical isolators to prevent unwanted backreflections.
The susceptibility of materials and carrier densities
Frank J. Loeffler, “A Faraday rotation experiment for undergraduate physics laboratory.” Am. J. Phys. 51 (7) July
in semiconductors may also be inferred by 1983
measuring the magnitude of the Faraday rotation. Aloke Jain et. al., “A simple experiment for determining Verdet constant using alternating current magnetic
fields.” Am. J. Phys. 67(8) August 1999.
Meyrath, Todd, “Electromagnet Design Basics for Cold Atom Experiments.” Phys. Rev. A 35 November 2004.