EXPERIMENT - VI
PRODUCTION AND ANALYSIS OF POLARIZED LIGHT
NOTE: The first thing is switching on the Hg spectral lamp so that it can warm up and stabilize.
1- OBJECTIVE AND THEORETICAL BASIS
According to the theory of polarization, from a monochromatic light beam it is possible to
obtain any kind of polarized light by using a linear polarizer and a /4 wave plate. With a second
polarizer (sometimes referred to as analyzer) it is possible to analyze the resulting polarized beam.
 The first objective of this experiment is to establish the electric field oscillation
(polarization plane) of a linearly polarized beam transmitted by a linear polarizer. There is an easy
way to do this by putting a dielectric surface in the way of the beam (i.e. a prism glass of index n)
and observing the reflected light. By changing the angle of incidence, we shall reach an angle for
which the component of the field contained in the plane of incidence is not reflected, so that the
reflected beam is polarized with the remaining light, i.e. in the plane perpendicular to the plane of
incidence. (Plane of incidence: that containing the incident direction and the surface normal). The
angle of incidence for which this phenomenon occurs is called the “Brewster angle”, after Brewster,
the Scottish physicist who discovered its existence. Once we are on it, we change the orientation of
the polarizer. By doing this, at some point we shall produce a beam with its electric field fully
contained in the plane of incidence. For this situation we must have no reflected beam at all. In
other words, for Brewster incidence we don’t have reflected parallel component, and by selecting
the incident polarization, we don’t have perpendicular reflected component either, therefore
obtaining null reflection (Fig.1). By finding this null, we can be certain of the polarization direction
being parallel to the plane of incidence and also of the incident angle being the Brewster angle.
Prism
n

No reflection!
P
Source
Fig.1 Description of the situation in which no
light is reflected on the polished surface of the
prism. This is a combined effect of: a) the
incident polarization, given by polarizer P,
(parallel to the plane of incidence, the plane of
the paper in this drawing); and b) the angle of
incidence  (equal to the Brewster angle ).
 The second objective is the production of light with circular polarization. When a beam is
incident on a quarter-wave plate “/4” (Fig. 2) a /2 phase shift is introduced between the two
orthogonal components of the electric field: the ordinary and extraordinary components, the first
one perpendicular to the optical axis of the anisotropic material of which the plate is made, and the
second parallel to it (in the case of retarder plates). For this geometry both components travel in the
same direction, though at different speed, so that the outgoing beam is composed of two phaseshifted fields. For other geometries (i.e. incidence different than perpendicular) these components
may have different propagation directions. This is the reason why they are also referred to as
ordinary and extraordinary rays. The directions of these components on the plate are often named
“neutral lines” of the plate. The reason is this: if the incident beam is linearly polarized along one of
these lines, only one component will be excited, and no change in the polarization will be noticed.
Let us see, however, what happens for an incident field linearly polarized and oriented in a given
direction, forming an angle  with a neutral line. The ordinary and extraordinary waves will be both
excited, will propagate at different speed, and after crossing the plate they will have relative phase
shift. This means that the polarized state of the beam has changed. The birefringence and the
thickness of the plate are made so that the phase shift is exactly /2. In these conditions (see Fig.2),
the resulting polarization is a centred ellipse, with different values for the main axes (the projections
of the amplitude, Ecos and Esin) located along the direction of the neutral lines.
E cos
E cos
E sen
E sen
E
E
Fig.2 Pass of a linearly
polarized light beam through a
wave ”/4” plate producing a
centred elliptically polarized
beam.

In order to obtain circularly polarized light, the ellipse axes must be equal in magnitude
(Ecos = Esin). This is achieved for a particular polarization angle of the incident field: =45°.
Then, the ordinary and extraordinary components have the same amplitude, and the outgoing beam
will be circularly polarized. To check the result we place an analyzer after the “/4” and notice how
the transmitted intensity is constant for any transmission direction we choose for the analyzer. If the
starting position of the polarizer P is, for instance, parallel to one the neutral lines, we should rotate
the polarizer an angle 1=45° in order to obtain circular polarization after the quarter-wave plate.
 The third objective is the production of an elliptically polarized light beam, whose
associated electrical field ellipse has certain ellipticity “e”. As we will see later, and because of the
procedure we follow in this experiment, the ellipse has its main axes parallel and perpendicular to
the horizontal plane, roughly the plane of the laboratory table. If the ellipticity is defined as
e = ( Minor axis
/ Major axis )
Then, if we assume the polarizer in the position parallel to a horizontal neutral line, there must be
two angles, 1 y 2, for the polarizer to rotate so that an ellipse of a given ellipticity “e” is reached:
1 (< 45°)
such that
e = ( sin1 / cos 1 ) = tan 1 ,
(a horizontal ellipse is obtained), and
2 (> 45°)
such that
e = ( cos2 / sin 2 ) = cotan 2 ,
(a vertical ellipse is obtained. This is the case represented in Fig.2).
In order to obtain the same value e in both cases, 1 y 2 must verify: tan1 = cotan2 , and
1 and 2 appear as being complementary [1 = /2 - 2]
Assuming a starting position with the light polarized in the direction of a horizontal neutral
line, then we would only need to rotate the polarizer an angle 1=arctan(e) in order to obtain a
horizontal ellipse of ellipticity e. By rotating 2=arc tan(e) a vertical ellipse of the same ellipticity is
obtained.
[COMMENT: In both cases the direction of the polarizer rotation is optional. Depending on the choice, the resulting
ellipse will be dextro- (cw rotation of the field if the light comes to the observer) or levo- (ccw rotation of the electric
field). As a result, we may obtain four ellipses with the same ellipticity value e]
In summary, by keeping the /4 phase plate in a position where its neutral lines are
horizontal and vertical, all ellipses originated from incident linear polarized light will be centred on
these axes, and the ellipticity will be controlled by producing certain rotation in the incident
polarization direction. In order to check that the resulting beam has the desired polarization we
measure the maximum and minimum intensity transmitted through an analyzer along its 360º
rotation for the transmission direction. Remind that the intensity is proportional to the square of the
electric field amplitude. Thus, these intensities are related to the ellipticity as follows:
(Minimum Intensity / Maximum Intensity) = ( Ellipse Minor Axis / Ellipse Major Axis )2 = e2
e
I m ín
I m áx
2-MATERIALS
• Spectral lamp (Hg).
• Goniometer.
• External collimator for calibrating the goniometer.
• Glass prism.
• Two polarizers (one with angular scale).
• A /4 phase plate.
• Photo detector device.
• Optical bench.
• Filter for the green emission line of the Hg lamp.
• Small diaphragm, suitable for the collimator arm of the goniometer.
3- ALIGNMENT AND EXPERIMENTAL SET-UP
Place the polarizer and the filter between the lamp and the entrance pupil of the collimator
arm of the goniometer, trying to obtain an homogeneous exit beam. Be careful with the lamp, it can
be hot. If the output beam is already correct, don’t change it.
Goniometer set-up: The fixed arm of the goniometer (collimator) has a lens, in which object
focal point is placed a diaphragm. There is also a small holder where a second tiny diaphragm
(about 1mm in diameter) can be slipped in. The second arm of the goniometer, a mobile telescope
arm, will be used later to analyze the reflected light.
Preparing the telescope arm: (This is a general procedure for any measurement carried out
with the goniometer. Because in this experiment we only use this instrument to detect the null in the
reflected light, the calibration is not a critical point, though it is always convenient). Place the small
diaphragm in its place in the collimating arm.
Focus the eyepiece of the telescope arm of the goniometer on the cross by moving it along
inside its housing. With the lateral wheel of the telescope, and without changing the conditions of
the eyepiece, focus is to infinity. (This is easy with an external collimator. Hold it in front of the
telescope arm and focus the cross of the external collimator by moving the wheel. At this points you
can see two reference crosses). Place the prism on the platform, and this at the correct height so that
the beam reaches one of the prism faces.
Now move the telescope arm, aiming at the collimating arm. Then, try to observe the image
of the diaphragm. To get a sharp image move the wheel of the collimating arm. When done, the
collimator is producing an image of the diaphragm in the infinity, easily observed with the
telescope. We may put apart the telescope arm temporarily and remove the small diaphragm, so that
we have a brilliant (though somewhat divergent) collimated beam that will be used to align the rest
of elements. On the bench we shall place the /4 phase plate, the analyzer and the photo detector,
all of them in the correct height and position as to be properly reached by beam. (Fig. 3 describes
the order of the elements). Now, place again the small diaphragm in its holder.
Polarizer
Lamp
Goniometer’s “/4” Analyzer
Diaphragm
Collimator Arm
Photo detector
Amplifier
/ Display
Fig. 3 Series of elements on the bench for generating different kinds of polarized light
4- OPERATING METHOD
1.- Horizontal transmission of the first polarizer. Place the prism on the main platform of the
goniometer. The platform must be horizontal (perpendicular to the rotation axis of the goniometer
arm). This is achieved with the small screws under the platform. Adjust the height of the platform.
The beam will reflect on a prism face with an angle o incidence equal to the Brewster angle, and the
reflection should be observed through the telescope arm.
We now turn the platform, in such a way that the angle of incidence on the prism approaches
the Brewster angle (lets remind that this angle is measured from the surface normal). For a typical
glass n 1.5, and tanB = n2/n1  1.5 => B  56° => The angle formed by the light and the face
of the prism will be approximately 90-56=34º, and the angle formed by the incident and reflected
beams, slightly over 110°. This is a good starting point to find the right position in a short time. The
reflected beam has to be found with the telescope arm in such situation: We should observe only the
sharp image of the small circular diaphragm, not a prolate figure, or a blurred image with a faint
orange phantom, thus meaning that we are observing the light after some refractions in the prism.
We can check now that the intensity of the image changes is we rotate the transmission direction of
the incident polarizer, and we fix it in the minimum. Now, to get closer to Brewster incidence, we
must slightly change the angle of incidence by rotating the central platform of the goniometer and
following the reflected beam through the telescope arm, which must be rotated accordingly. This
can be done in a few small steps, trying to obtain an intensity minimum as low as possible. Though
zero is not possible (cause there is always an interval around Brewster), the intensity can be really
low. You can check this zero with the person supervising the experiment, if you don’t feel sure
about it. At this point, the polarizer transmission points in a direction parallel to the plane of
incidence (the horizontal direction). We must take the angular position found for the polarizer. This
measurement is done on a scale in 2º steps, with a vernier of 10 units, thus producing a 0,2º (12’)
precision. This position will be our reference for horizontal polarization.
2.-Production of circularly polarized light. We first remove the small diaphragm and the
prism used in the first part, and put the telescope arm apart, because it won’t be used again during
the experiment. The linearly polarized beam goes through the /4 wave plate, the analyzer and the
photo detector.
Depending on the photo detector used for the experiment, an adequate procedure must be
followed for the measurements. For instance, the “zero” of the photo detector must be adjusted to
the background level of light in the laboratory. The zero is the darkness light, and the light coming
from the lamp will be the measured intensity signal. Each time we change the scale, or change any
other light source in the lab, the zero must be adjusted. In order to do it, the light coming from the
Hg lamp must be blocked, but not the ambient background light coming from the lab. Very often
photo detectors have a protection cap that must be removed, and sometimes they have two buttons
for the coarse and fine adjustment of the zero.
Remove temporarily the holder with the /4 wave plate, and rotate the analyzer till the photo
detector signal gets as low as possible. (Sometimes this level is slightly under the calibrated zero,
because the ambient light is partially polarized and is also modified by rotating the analyzer). At
this point the polarizer and analyzer have orthogonal transmission directions (“crossed” polarizers).
Let both polarizers in those positions and place again the /4 wave plate in its former location on
the bench. An immediate increase in the detected signal will be observed. However, by rotating the
/4 wave plate we should be able to reach the former minimum. Actually, we are calibrating the
wave plate by aligning its neutral lines with the transmission direction of the polarizers (horizontal
and vertical). If we now rotate 45° the first polarizer, the wave plate will produce circularly
polarized light. This must be checked with a slow and complete turn on the analyzer. The maximum
and minimum signal should be very similar (ideally equal, as corresponding to a constant
projection). The ellipticity of the resulting light is:
e = ( Minimum intensity / Maximum Intensity )1/2
3.- Production of elliptically polarized light of a given ellipticity e: (the actual value of e
will be provided by the person supervising the experiment). First, we take the first polarizer to the
initial position (horizontal transmission lines). From this position it will be rotated by:
1 :
e = tan 1 => 1 = arc tan (e)
;
2 :
e = cotan 2 => 2 = arc cotan (e) ;
1 + 2 = /2]
After the wave plate we shall obtain elliptically polarized light, whose corresponding field
axes will be found by measuring the minimum and maximum transmitted intensity in the detector
when the analyzer is rotated. The actual value for the ellipticity is again given by:
e = ( Minimum intensity / Maximum Intensity )1/2
Finally, and if you have some time left, the first polarizer is taken again to the initial position
(horizontal transmission lines), and the same two rotations are made, 1 and 2, though this time in
the opposite direction to that chosen in the first place. Again we check the ellipticity of the resulting
polarizing ellipses with the analyzer and detector.
5- QUESTIONS
1.- To what extent do you think that parts 2 and 3 (production of circularly and elliptically polarized
light) depend on the result of part 1 (linear polarization characterization)? In other words, do you
think that the desired elliptically polarized beam can be obtained without previously finding the
Brewster angle?
2.- What do you think is the difference between a polarizer and an analyzer?
3.- What would you expect from an experiment like this performed with the same elements but
using, for instance, an orange spectral line, instead of the Hg green one? What do you think that
would be different, and what would remain the same?
4.- Identify the main sources of error when producing polarized light in this experiment?