Rotated Light by Polarization
Date: Winter 2011-2012
I have a question about polarization having to do with LCD screens and two polarizing discs. LCD screens are polarized, so when I rotate one disc the correct way the LCD looks black through the disc. So far so good. But when I, with the first disc in the same rotation up to my eye, rotate the second disk in front of the screen (halfway between on and off relative to the first in unpolarized light), I can see the screen through the second disc through the first disc or through air to the second and there to the screen but not through the first to the screen of course. My only guess is rotation, though I still do not know exactly what that would do. Also I did not expect these to rotate, just only let one polarization through.
Since the LCD goes fully black with the first polarizer rotated to the right orientation,
from now on you know that that LCD emits only polarized light.
It has a polarizer built into it's outer window.
That's one polarizer in your experimental setup.
The "first disc" is polarizer #2, really.
Your second disc is really polarizer #3.
There is no such thing as a 3-polarizer interaction...
It is always:
1) how much of the polarized light at this point will go through the next polarizer?
2) what will be the polarization of the light that gets through?
1) output_intensity = input_intensity * cosine( input_light_angle - polarizer_angle )
http://en.wikipedia.org/wiki/Polarizer , find "Malus law" equation
2) output_light_angle = polarizer_angle
The figure next to Malus Law equation also illustrates this.
With these two rules you can figure out what should happen in any multiple-polarizer situation
When you put the disc2 between the LCD and disc1,
you are probably choosing to rotate disc2 to 45 degrees,
midway between the LCD light's polarization axis 0 degrees and disc1's polarization axis of 90 degrees.
Then the cosine from Malus law is about 0.71, so 70% of the light gets thru,
and the new light is polarized at 45 degrees instead of, say, vertical like the LCD.
Next the new light tries to go through disc1, which is angled at 90 degrees from the LCD to be black.
So the new light is only 45 degrees from disc1, so again 70% if it gets through.
70% x 70% = 49%.
The light you see going through both discs can be up to 50% of the original intensity
you see with no discs.
Some people find it kind of weird that the polarization of fully polarized light
gets rotated to a different angle by the next polarizer.
But that's how it actually happens.
In order to answer this, you have to consider what polarization is
and what a polarizer does. A simple analogy to understand is a wave
on a rope. Tie one end of a rope and shake the other end up and
down. Undulating waves will be created on the rope and they will
travel down the rope. The wave is like a light wave with an
"up/down" polarization. Shaking the rope from side to side creates a
wave with a "left/right" polarization. The analogy is not perfect,
but it is close enough. Light travels in one direction (propagation)
and has an electric field that oscillates up and down or left and
right (polarization). Polarization can be in any direction in
between as well, just as you can shake a rope diagonally. A
polarizer sets a direction for light, and in our analogy, we can
imagine placing two cylinders on either side of the rope (in the
middle) such that they only allowed an up/down motion to pass
through them. If you shake the rope from side to side, the cylinders
will block the wave from traveling through (in the ideal case. In a
real situation some of the wave may get through). Important here is
to consider the diagonal case where you shake the rope say at a 45
degree angle. The rope travels up and down as well as side to side.
The up/down motion will not be blocked by the cylinders (polarizer)
and the side to side motion will be blocked. The up/down motion that
gets through will not be as large as you originally swung the rope,
though. The wave that travels past the cylinders will only be
up/down or polarized in one direction. Important here is that the
diagonal wave looks to the cylinders as though it has both
polarizations hitting them. It only passes one polarization
(up/down) though. The diagonal wave is a combination of two
polarizations. Shaking from up/down and gradually rotating this
movement to side to side will result in a smaller and smaller wave
getting through the cylinders. This is exactly the effect you see
with the polarized sheet in front of the screen. Rotate it, and the
screen gradually gets black. What gets through the sheet is light
that is now polarized at the angle of the sheet. This light is less
the closer the sheet rotates to 90 degrees and it goes completely
black at 90 degrees.
Consider what has happened. The screen emits light in one
polarization and ends up coming out of the sheet rotated in the
direction of the sheet but dimmer. Now place the second sheet in
front of the first. It will treat the light coming from the first
sheet as rotated in polarization, lined up with first sheet. Rotate
the second sheet and now it goes from light to black based on its
orientation with the first. It seems puzzling, but the same will
happen with the rope analogy if you shake the rope at a diagonal.
The up/down polarization will get through and now two more cylinders
can be placed further down the rope (a second polarizer) and select
for a different polarization by rotating these two cylinders.
Conceivably, you could have the first polarizer at a 45 degree angle
and the second at a 90 degree angle (horizontal) and still see some
of the wave get through both.
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Update: June 2012