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Have you ever put on a pair of polarized sunglasses?
If you take part in any kind of outdoor activity,
you'll definitely appreciate them.
They do a great job blocking glare,
but how do they do that?
Here's a hint.
It has to do with blocking the orientation
of certain electric fields from your eyes.
What do electric fields have to do with sunlight?
And what does the orientation of light
have to do with sunglasses?
Let's find out.
You may remember in another segment,
we told you that light is made up
of oscillating electromagnetic waves.
With any light wave, there's an electric field
and a magnetic field.
The magnetic part of the wave
oscillates in one direction,
and the electric part of the wave
oscillates in the perpendicular direction.
When we talk about polarization,
we're looking at the electric field oscillations.
So, on a sunny day like today,
I am bombarded with lots of sunlight.
The sun's waves are either hitting me directly,
or they're bouncing off things,
like the atmosphere, the water, or the ground.
First, let's talk about the sunlight hitting me directly.
These waves are different than the others,
and here's how.
We've already learned
that light often acts like a water wave.
It has high points and low points,
peaks and troughs that alternate.
As a ray of light moves through space,
its electric field goes up and down,
and up and down in strength.
And if that ray comes directly from the sun,
it has another quality.
Its electric field not only points up and down,
it points left and right and diagonally,
and really any direction
except the direction the ray is moving.
If you're looking at it from the side,
the ray might look like this.
And if that ray of sun is coming right at you,
it would look like this.
The dashed lines show the electric field
along the path the ray is traveling.
And each of those dashed electric field lines
in this diagram is a vector.
The electric oscillations of all light waves,
whether they come directly from the sun or not,
are vectors.
And they're perpendicular
to the ray of light's direction of travel.
Light rays coming straight from the sun
and from sources like a light bulb
are called unpolarized.
When light waves from an unpolarized source
travel without anything interfering with them,
their electric fields are pointing in any direction
perpendicular to the wave's motion.
That's unpolarized.
So, what do you think polarized sunglasses do?
Somehow, they cut down on sun glare
by blocking a bunch of light
that would otherwise reach your eyes.
And how do they do that?
The lens acts like a filter, blocking some light,
and only allowing light
with a specific electric field direction
to pass through the lens.
So the light that reaches your eyes has been polarized
because its electric field
only points in a specific direction.
That direction depends on the filter.
In this case, the filter is pointing up.
So it only allows light with vertical oscillations
to pass through.
That's vertically polarized light.
Okay, so let's see what happens
if we use two filters.
First, let's figure out a way to configure them
so the most light gets through.
Then, let's position them so the least light possible
passes through.
The amount of light that passes through the filters
depends on how the filters are lined up
with one another.
Take a look at this diagram.
And remember, it's unpolarized light
that is passing through a polarizing lens.
When the filter points up,
it only allows vertically polarized light
to pass through.
Those are the light waves with the electric field
that points up and down.
Now, let's put a second filter
after the first one,
and turn it horizontally.
What light do you think would get through?
The answer is... none.
With one filter pointing vertically,
and the next pointing horizontally,
the two filters get rid of both components,
one after the other.
Since a light ray's electric field
is a combination of vectors
perpendicular to the ray of light,
the vertical filter blocks all vectors
except the vertical ones.
And the second filter, which is horizontal,
blocks all vertical vectors
so no electric field remains
and no light is seen.
Thanks to French physicist, Etienne Malus,
we can figure this out mathematically.
In the 1800s, Malus figured out
that the intensity of polarized light, I,
as it approaches a filter,
and the intensity of that light
once it passes through the filter,
are related.
The outgoing light intensity
is equal to the incoming light intensity
times the square of the cosine of theta.
In this relationship, theta is the angle
between the filter's polarization direction
and the ray of light's polarization.
When you look up the cosine of 90 and 270 degrees,
you see that it is zero.
Any two filters lined up perpendicular to each other
will completely extinguish the light.
The bottom line is,
when you put a vertical filter that blocks
everything but vertical light,
then you put a horizontal filter
that gets rid of
everything except horizontal light,
together, they block out all of the light
and all electric fields.
So, here's a question for you.
Given that the two filters are lined up perpendicular
to one another,
what can you do to get sunlight to pass through
that last filter?
How about adding a third filter?
Now, what angle would you position it,
and where?
If you put it between
the vertical and horizontal filters
and angle it 45 degrees to them both,
you would have unpolarized sunlight trying to pass through
a filter pointing 90 degrees,
then one at 45 degrees, then one at zero.
Before we start using Malus's Law,
remember, it only applies to light
that is already polarized.
In our example, we start with an unpolarized ray.
That means its electric field points equally
in all directions.
So, mathematically speaking,
if we took all the vertical components
of the electric field vectors
and added them up,
and all the horizontal parts of the electric field vectors
and added them together,
these two quantities would be the same.
So, when our unpolarized ray
runs into the first filter that points up,
it eliminates all the horizontal
electric field components.
The light that makes it through to the other side
is all vertically polarized,
which is half of all the light we began with.
So, light intensity after filter number 1
equals half the original light intensity.
Now that our ray of light is polarized,
we can use Malus's Law
to figure out how much light passes through
our other two polarizing filters.
Light intensity after filter number 2
equals light intensity after filter number 1,
multiplied by the cosine squared of pi, divided by 4,
since the filter is at a 45 degree angle.
This equals half the light intensity
after filter number 1,
which equals one-fourth the original light intensity.
Filter number 2 cut down the transmitted light
by half. It makes sense.
A 45 degree line
divides a horizontal and vertical line equally.
This 45 degree filter cuts out
half of the vertically polarized light
coming through,
leaving us with half of what we had
after the first filter.
It's important to remember that once a light ray
passes through a filter
with a particular polarization direction,
the rays take on the same polarization direction
as the filter.
So after going through the first two filters,
the ray is at 45 degrees
heading into the final stretch
and into filter number 3.
That filter is horizontal, or 90 degrees.
So the result is not zero.
By sandwiching a filter in between
two perpendicular polarizers,
we saved some light.
What comes out after the third filter
is horizontally polarized light
at one-eighth the original intensity.
Malus's Law explains this mystery,
and it all has to do with the polarization of light.
That's it for this segment of "Physics in Motion".
We'll see you guys next time.
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