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### Unpolarized Light ... or Is All Light Polarized?

```Date: 04/28/2017 at 23:42:34
From: Fida
Subject: oscillations of light

It is frequently asked whether the oscillations of the electric and
magnetics fields are in the same plane, which includes the direction of

But my question is not exactly discussed in my book: is this only for
polarised light, or for unpolarised light as well?

I picture unpolarised light as this: if you look at it head-on, blue
lines are magnetic planes of oscillation and red lines are electric
fields of oscillation. Since planes have no width, there are an infinite
number of planes.

But polarised light is like this:

|
|
|
-------------------
|
|
|

All planes are realigned to one magnetic and electric field. That's why
when we put another polariser behind it and rotate 90 degrees, light is
blocked: no part of the planes can get realigned to pass through the 2nd
polariser.

Anyway, this was not the question. The direction of motion is included
in any plane of oscillation that you choose. But it is rather the
oscillations themselves which are perpendicular to the direction of
motion -- hence light is a transverse wave.

```

```
Date: 04/29/2017 at 12:06:15
From: Doctor Rick
Subject: Re: oscillations of light

Hi, Fida.

You've got some potentially very interesting questions here. I won't try
to answer every one that I see right now, but just get us started with
some basic ideas.

As Fida wrote to Dr. Math
On 04/28/2017 at 23:42:34 (Eastern Time),
> It is frequently asked whether the oscillations of the electric and
> magnetics fields are in the same plane, which includes the direction of
> motion. The answer is yes.

I am not exactly sure what you are saying. The electric and magnetic
fields in a single electromagnetic wave are not in the same plane as one
another.

Remember how we define the "plane" in which, say, the electric field
lies: we take the direction of the electric field vector (at any time
when it is non-zero), and the direction in which the wave is
propagating, and those two directions define a plane.

The electric field vector and the magnetic field vector are always
orthogonal (perpendicular) to one another. Thus their planes are
orthogonal to one another; the direction of propagation lies along the
intersection of the two planes.

Maybe that's what you were trying to say in that opening passage, but I
want to be sure.

After that passage, I am not sure what you are thinking when you say
"all planes are realigned." What actually happens is a result of the
principle of superposition.

A typical source of EM radiation (let's say light) consists of many tiny
radiators, all producing their own EM waves. For instance, a heated
filament in an incandescent light bulb consists of many atoms, each a
little "antenna" sending out light. A "light ray" is actually the
superposition of all light waves from the source that happen to be
moving in a given direction.

Each of these waves has its own electric and magnetic field directions.
Those are what you show in your drawing. But the superposition principle
tells us that those electric fields are added vectorially to produce a
single resultant electric field vector. The same thing happens with all
the magnetic fields. And the resultant electric and magnetic fields are
orthogonal, as usual.

So what you call "realignment" is really superposition.

> Anyway, this was not the question. The direction of motion is included
> in any plane of oscillation that you choose. But it is rather the
> oscillations themselves which are perpendicular to the direction of
> motion -- hence light is a transverse wave.

What you said here is correct. OK, so what *is* your question?

I'll tell you what *I* would be wondering at this point: If the
resultant EM wave has a single plane of oscillation for the electric
field, and an orthogonal plane of oscillation for the magnetic field,
then isn't it necessarily polarized? What in the world *is*
"unpolarized" light?

But since you haven't asked that, I won't answer it now. :) Let's be
sure we've answered what you're asking; and then if you wish, we can go
on.

- Doctor Rick, The Math Forum at NCTM
http://mathforum.org/dr.math/

```

```
Date: 06/02/2017 at 07:14:25
From: Fida
Subject: oscillations of light

So, yes, what is unpolarised light?!!

The reason why light gets blocked by two polarisers at 90 degrees is
that no component can pass through at 90 degrees. Even at 89 degrees, a
small component is in the plane which the filter allows to pass.

```

```
Date: 06/02/2017 at 12:41:35
From: Doctor Rick
Subject: Re: oscillations of light

Hi, Fida.

Before I address it, let's consider what makes this an interesting (and
challenging) question.

As your diagram before suggested, the usual idea of "unpolarized" light
is that it consists of all planes of polarization mixed together at the
same time.  However, I pointed out that such a combination of
electric-field vectors can be combined by vector addition into a single
vector, which defines light polarized in one plane. Does this mean that
there is no such thing as unpolarized light, because every combination
of planes of polarization is equivalent to a single plane?

There are complexities here that I am not sure of, not having worked
with college-level physics and beyond in some time. However, I believe
that the answer lies in something I said (quite deliberately) last time:

"A typical source of EM radiation (let's say light) consists of many
tiny radiators, all producing their own EM waves. For instance, a
heated filament in an incandescent light bulb consists of many atoms,
each a little 'antenna' sending out light."

To that description, let's add the concept that the many tiny radiators
or antennas don't radiate continuously! Each is only active for a short
time, emitting a burst of EM radiation. And (unless we're talking about
a laser or similar device) these radiators are not synchronized.

What this means is that the mix is constantly changing! At one moment we
have one combination of polarized waves, corresponding to one overall
plane of polarization. A short time later we have a *different* mix, and
the overall plane of polarization is different.

In effect, unpolarized light is really polarized light: its plane of
polarization is constantly, and randomly, changing.

Here is an except from Wikipedia that refers to this concept:

https://en.wikipedia.org/wiki/               Coherence_(physics)#Polarization_and_coherence

Light also has a polarization, which is the direction in which
the electric field oscillates. Unpolarized light is composed of
incoherent light waves with random polarization angles. The
electric field of the unpolarized light wanders in every
direction and changes in phase over the coherence time of the
two light waves. An absorbing polarizer rotated to any angle
will always transmit half the incident intensity when averaged
over time.

Coherence, coherence time, and the related concept of coherence length
come up in relation to lasers. The coherence time is basically the time
after which the phase of a wave is no longer predictable: when
randomness has taken over. Even for a laser, the coherence time isn't
long -- maybe a few milliseconds. (This is a long time, though, viewed
in terms of coherence length, which is the distance the light wave moves
in the coherence time. In 3 milliseconds, light travels nearly a thousand
kilometers!) This means that the polarization plane of a light wave
changes much faster than our eyes could detect.

Now, revisit the last sentence of the quote above. Considering a single
polarizer, at one moment the polarization of the light might be aligned
with the polarizer, so that all the light passes through. At another
moment it may be aligned perpendicular to the polarizer's axis, so that
none of the light passes through. And at other moments the polarization
plane will make some intermediate angle with the transmission axis of
the polarizer, so something less than all the light will pass through.
ON AVERAGE, over time (and not a very long time!), half the light will
be transmitted. This result can be derived from Malus' Law. (You
mentioned a "small component" of the light passing through; Malus' Law
tells you *how much* passes through.)

Let me just mention one more complication. I talked about summing
multiple electric field vectors to get an overall direction of
polarization. However, the electric field is characterized not just by
magnitude and direction (the electric field vector), but by PHASE.
Generally, two oscillating electric fields will differ in when they are
zero. This gives rise to a phenomenon you may not have heard about yet:
CIRCULAR polarization, as opposed to plane polarization.

But I'll leave it at that unless you are *really* interested in pursuing
another topic.

- Doctor Rick, The Math Forum at NCTM
http://mathforum.org/dr.math/

```

```
Date: 06/07/2017 at 09:51:15
From: Fida
Subject: Thank you (oscillations of light)

Thank you so much!
```
hrquot; light is that it consists of all planes of polarization mixed together at the same time. However, I pointed out that such a combination of electric-field vectors can be combined by vector addition into a single vector, which defines light polarized in one plane. Does this mean that there is no such thing as unpolarized light, because every combination of planes of polarization is equivalent to a single plane? There are complexities here that I am not sure of, not having worked with college-level physics and beyond in some time. However, I believe that the answer lies in something I said (quite deliberately) last time:
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