Lab 3: Wave Plates and Polarization of Light – Physical Science Version
I. Purpose :
To observe the effect that wave plates have on plane polarized light.
II. Theory:
The wave plates operate on the principle that two orthogonally oriented polarization states
experience two different indices of refraction. Consequently, one polarization of light travels
faster in the wave plate compared to the other. The birefringent material of the wave plate are
asymmetric in that they have a different index of refraction in one polarization direction
compared to the other. The “optical” or fast axis is usually indicated on the wave plate. Light
polarized along this axis experience a smaller index of refraction than light polarized
perpendicular to this axis. The two orthogonal components of light, one polarized along the
optical axis and one polarized perpendicular to that axis, enter the wave plate with a phase
difference of zero and emerge with a phase difference of  or /2 corresponding to either ½ or ¼
wavelength delay.
In the case of a half wave plate, incident polarized light at an angle  to the optical axis is
rotated by an angle 2. A quarter wave plate causes linearly polarized light to become circularly
polarized for an angle of orientation of 450.
III. Procedure :
1) Set up the equipment as shown. For this experiment, you do not need to know the absolute
orientation of the polarizers and waveplates since you will be making relative measurements.
chopper
He-Ne
Lock-in amp.
Waveplate
ND filter (optional)
P1
P2
Polarizer in rotation stage
2)
Photodetector
on translation
stage
Setup for
verification
of
the Law of
Malus
Make sure the two polarizers are parallel. To do this, keep the first polarizer fixed and rotate
the second polarizer until you observe a minimum in transmission. At this point the
polarizers are oriented 90o apart. Rotate the second polarizer 90o so that the polarizers are
now parallel.
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3)
As a test of how well the polarizers are aligned, attempt to verify the Law of Malus :
I  I 0 cos2   . Keeping Polarizer P1 fixed, rotate the polarizer P2 in 100 increments from 900 to 900. Take readings of the intensity (voltage of the photodetector) at each angle. Make
sure that the optical beam is centered on the photodetector and that the detector is linear (Lab
7).
4)
The next step is to align the orientation of the half wave plate. With only the two polarizers
in place, rotate polarizer P2 so that you observe a minimum in transmission. At this point, the
angular orientation between the two polarizers is 90 degrees. Place the half wave plate in the
1” rotation stage and put it in between the polarizers. Rotate the half wave plate until you see
a minimum in intensity. This corresponds to the half wave plate making an angle of 0o with
respect to P1 polarizer. This position corresponds to 0o orientation of the waveplate.
5)
While keeping the rotation of the half-wave plate FIXED at 0 degrees (and the rotation of P1
fixed), rotate the polarizer P2 back to zero degrees. Record the voltage from the
photodetector. At this point ALL of the optics (P1, waveplate, and P2) are oriented at zero
degrees. Next, rotate P2 (P1 and waveplate stay fixed) in 100 increments from -900 to 900.
For each rotation position of P2, take readings of the intensity (voltage of the photodetector).
6)
Repeat the above step for FIXED half-waveplate rotations of 20, 45, and 90 degrees.
7)
To check alignment, arrange the polarizers WITHOUT the waveplate to be crossed polarized.
Place the quarter wave plate in the 1” rotation stage and put it in between the polarizers.
Rotate the waveplate and rotate it until you see a minimum in intensity. This corresponds to
the quarter waveplate making an angle of 0o with respect to polarizer P1.
8)
While keeping the rotation of the quarter-wave plate FIXED at 0 degrees (and the rotation of
P1 fixed), rotate the polarizer P2 in 100 increments from -900 to 900. Take readings of the
intensity (voltage of the photodetector) at each angle.
9)
Repeat the above measurements for fixed quarter-wave plate rotations of 20 and 45 degrees
of orientation.
IV. Discussion:
1) In your lab report, plot your experimental data (as points with no line) and theoretical data
(as solid line) of III.3 on the same graph. Plot both the experimental and theoretical data as
P/Po (or V/Vo) on the y axis and  on the x axis. For Vo, use the highest voltage value for the
0 degree measurement. How well does theory (Law of Malus) correspond to experiment?
2) In your lab report, plot your experimental (as individual points, no line) and theoretical data
(solid line) of III.5 and III.6 on the same graph. Plot both the experimental and theoretical
data as P/Po (or V/Vo) on the y axis and  on the x axis. For Vo, use the highest voltage value
for the 0 degree measurement. How well does theory correspond to experiment? For the
theoretical data, you can use P / Po  cos 2 (  2 ) where the angles  and  are defined in
Figure 2 (were the ¼ plate in the figure is a ½ waveplate). NOTE: In the above equation, the
use of the plus or minus sign depends on WHICH direction you rotated the waveplate.
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3)
Plot your data of III.8 and III.9 (00, 200, and 450 for the rotation of the 1/4 wave plate) on the
same plot (individual points, no line) with the theoretical predictions (solid line). For Vo, use
the highest voltage value for the 0 degree measurement. EXPLAIN YOUR RESULTS. For
the theoretical curve, the normalized detected power is given by (see Figure 2 for definition
of angles):
2
2
P
 cos 2  cos   cos  sin  sin    sin  cos  sin   sin 2  cos  
Po
The derivation of this equation will be covered in class. For your reference, the
THEORETICAL plots should look like the following. You should make sure that your
theoretical plots of the above equation look similar.
1
0.9
0 Degrees
0.8
20 Degrees
0.7
45 degrees
angle θ from Fig. 2
P/Po
0.6
0.5
0.4
0.3
0.2
0.1
0
0
50
100
Angle (degrees)
4)
150
200
angle φ from Fig. 2
Knowing that a mirror reverses the “handedness” of circularly polarized light, describe a how
the optical components in Figure 3 act as an ‘optical diode’. In other words the light reflected
by mirror M1 does not pass through polarizer P1 and hit the laser.
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