Part 2: Investigating Classical Polarization
Timing: This worksheet will take at least 60 minutes. It is worth taking this time in any unit looking at
waves or light. It provides many counter-intuitive and visually beautiful and cheap demonstrations. It
provides a clear application of vectors in action. It is needed for 3-D movies and LCD flat screen displays.
Key Concepts: Light can be polarized, which means that light is behaving like a transverse wave. Our
eyes can’t sense this property so we need to use polarizing filters.
Assumptions of Student Background Knowledge: This lesson assumes that students already know
about the wave nature of light through diffraction, refraction and interference. It also assumes that they are
familiar with vectors, components and trigonometry.
Materials Each student needs a pair of linear 3-D glasses and two halves. See below for suppliers. Each
small group needs a Slinky and a pair of circular 3-D glasses.
The answers and extra information for teachers is in red and needs to be removed before photocopying
and printing the student worksheet.
Polarization is a property of transverse waves and describes the direction in which the wave is vibrating.
Polarizing filters in 3-D glasses can both change and measure the polarization of light.
Looking Through Two Filters:
1) Put on a pair of glasses and close one eye. Position a second filter in front of your open eye so that you
are looking through two filters and then rotate the one in your hand. Describe what you see.
The amount of absorption changes gradually from nothing to 100% as it rotates through 90o.
2) What happens if you switch which eye you are using? What does this suggest about the two lenses?
The lenses have opposite effects. If one is dark, the other is light. This suggests that the filters must be at
90o to each other.
3) Use a Slinky to model what is happening to the light waves when they are polarized.
Regular light is unpolarized. The filters select light that is polarized in one direction. This can be
demonstrated by making standing waves that vibrate vertically, horizontally, diagonally and circularly.
The filters can be demonstrated by having the Slinky stretched between two people. You can vibrate the
wave in any direction – but only the vertical vibrations will pass through. If you add more people, it
doesn’t change anything. However, if you add people with their arms forming a horizontal barrier – all
vibrations will now be stopped.
Note: The above is a good way to visualize what happens – but the reality is perpendicular to this. This
added detail may be too much for an introduction. Light is an electromagnetic wave with the E and M
fields perpendicular to each other and to the velocity. Vertical electric fields are absorbed - not passed - by
vertical molecules. This can be modelled as follows. Have the students stand in a line. Their bodies
represent the long conductive molecules that are in the filter and their hands are electrons. Which way do
the electrons move if the electric field vector is up, down, horizontal and diagonal? The electrons move up
if the field is down and don’t move if it is sideways. If the electron is made to move, then it has gained
energy which must be taken from the light. The light is absorbed.
You might want to show Polarization from Sixty Symbols https://www.youtube.com/watch?v=KM2TkM0hzW8 from 2 minutes to 4 minutes. It shows how a
visible grid of wires will polarize microwaves and it explains how the absorption takes place.
Looking Through Three Filters:
4) Keep your glasses on and close one eye. Position another filter in front of this eye and rotate it until all
the light is blocked. Now position a third filter in between your glasses and the second filter. Rotate the
middle filter. Describe what you see.
Adding the third filter can let more light through! This effect is strongest when it is at 45o to the other two
filters.
5) Draw arrows on the diagram below, to explain how the third filter lets light get through. Start with a
vertical filter and let a single vertical arrow represent the vertically polarized light that gets through. The
length of the arrow will indicate roughly how bright the light is. Hint: Think about vector components.
Only vertically polarized light passes through a vertical filter. It can be considered as a sum of +45 and 45 polarized light. Only the +45 makes it thought the next filter. This +45 light is a sum of vertical and
horizontal components and only the horizontal components makes it through the final filter.
Light
Source
1
2
3
6) If light is polarized diagonally, what fraction of it will get through a vertical polarizing filter?
A) half
B) cos (45o)
Draw a vector diagram to explain.
o
Math: It looks like it should be the cosine of 45 . Physics: Symmetry suggests that half of the light should
pass. The correct answer is half. The diagrams show the amplitude of the wave, but intensity is
proportional to the amplitude squared which is cos2 (45o) = ½. This is an example of Malus’ Law which
says that for an ideal filter the intensity is proportional to the square of the cosine of the angle between
them or I = Io cos2 ()
7) Unpolarized light heads toward a vertical filter, what fraction of it will get through the filter? Explain.
As we saw above, half of the diagonal will get through. Furthermore, all of the light can be broken into
horizontal and vertical components and all of the vertical components and none of the horizontal will pass
through. By symmetry, that is half of the light.
8) What fraction of unpolarized light will get through three filters at 0o, 45o and 90o?
A) ½
B) ½ x ½
C) ½ x ½ x ½
D) ½ x ½ x ½ x ½
C: Each filter removes half of the original light, so the net effect will be ½ x ½ x ½ = 0.125.
9) What fraction of unpolarized light will get through four filters at 0o, 30o, 60o and 90o?
A) more
B) less
C) same
Explain your answer with math.
Half gets through the first filter. The next filter is at 30o and will be proportional to cos2 (30) = ¾. The
next filter is at 30 o to the light and also passes ¾. The net effect is ½ x ¾ x ¾ x ¾ = 0.21 which is almost
twice the amount for three filters! As you add more filters, it becomes more like gently rotating the
polarization of the light rather than blocking it. The Physics 2000 simulation
http://www.colorado.edu/physics/2000/applets/lens.html shows this really well.
Everyday Polarized Light
13) Polarized light is all around us but we usually do not notice it because our eyes are not sensitive to
polarization. Put on a pair of cardboard polarized glasses and close one eye. Look around you, tilt your
head and switch eyes. What do you notice about:
a) cell phones, computer screens and calculator displays?
Liquid crystal displays use polarizing filters that are controlled electronically. Look at computer screens,
watches, phones and calculators. Many - but not all - will be polarized. At what angle are they polarized?
This will vary. A great on-line explanation of liquid crystal displays can be found at Physics 2000,
(Science Trek > Polarization). http://www.colorado.edu/physics/2000/index.pl.
b) windows, shiny floors and other reflective surfaces?
Reflection will cause light to become polarized parallel to the surface. Polarized sunglasses are great at
reducing the glare off horizontal surfaces like roads, water and snow. The glare off windows is vertical. If
you tilt your head at 45o with the 3-D glasses you will see the glare is reduced in one eye and not the
other.
c) clouds and the sky?
The light in the sky is polarized by the scattering of light off air molecules. Clouds scatter the light so
many times that the light becomes randomly polarized again. If you tilt your head you will see the sky
darken so that the contrast with the clouds is increased. Photographers use polarizing filters to remove
glare and enhance contrast.
Polarization and 3-D Glasses
We are able to see in 3-D because each of our eyes gets slightly different 2-D information. Our brains
combine these two to form a 3-D image. To see the two images, hold a finger in front of your face and
look at it and the background with one eye and then the other eye.
3-D movies work by projecting two images and making sure that each eye receives a different one. The 3D glasses have polarizing filters which will only let in one of the two projected images into each eye.
Your brain combines the two different images into one 3-D image. The filters in the glasses are usually
polarized in one of the three following combinations:
Plus/Minus45o
vertical/horizontal
or clockwise/counter-clockwise.
10) What orientation is used for the glasses with the cardboard frames? How can you tell? What are the
advantages of this arrangement?
They can’t be circularly polarized or else tilting your head would have no effect. Furthermore, they would
not reduce the linearly polarized light from glare off a surface. If they were horizontal/vertical then one
would reduce glare and the other wouldn’t when the head is held normally. However, this glare reduction
occurs at 45o and so they must be diagonally polarized.
The advantage of this arrangement is that if you fold the arms back the wrong way, so that the filters
switch eyes, the polarization of each eye does not change. If the glasses had been H/V, the polarization
would have been switched. The information that was meant for your left eye would go to your right eye.
Your brain would not be able to convert this into 3-D.
11) What orientation is used for the glasses with the plastic frames? How can you tell? What are the
advantages of this arrangement?
These glasses use circular polarization. You can tell because they don’t reduce glare and they don’t vary
much as you tilt your head. The advantage is that you can tilt your head while watching a movie. The
glasses consist of linear polarizers plus a quarter-wave plate made of bi-refringent material.
You can get a set of these glasses by asking your students to save theirs after watching a movie. If you are
interested in a detailed explanation of circular polarization go to
http://www.oapt.ca/newsletter/2009_11_nl.pdf
Note: Measuring Light Intensity – Reality is much Messier than Theory
The quantitative analysis done above assumes that the filters are perfect. Look thorough crossed polarizers
at a light. They do not manage to block all the light 100%. Place several filters in the same orientation and
you will see that it is darker than 1 filter, when ideally it should be the same. The difference between ideal
filters and the reality can be made quantitative with a light meter. The filters vary quite a bit and usually
remove an extra 10 to 20 percent of the light.
Cheap Sources of Polarizing Filters:
a) Rainbow Symphony: http://www.rainbowsymphonystore.com/pol3dglas.html
If you buy 100 glasses it will cost $55.00 plus $31.60 for shipping to Ontario.
b) Arbour: If you buy two sets of 50 films (~2 cm by 3cm. mounted on slide holders) it will cost $70 plus
$13 for shipping to Ontario. http://www.arborsci.com/shop-by-topic/light-optics/polarizationdiffraction/slide-mounted-polarizing-filters