Re: ATM Re:Moon and Polarizing filters (longish)

[Spencer Roedder <roedder@roedder.com>]

Good stuff, your examples are clear and well put; but you invited comments
on nomenclature, so here goes....

At 11:35 AM 98/07/10 -0500, Taras Masnyk wrote:
...
>Polarizing filters do not affect the wavelength of light, but do affect its
>phase- a polarizing filter lets through only light of a certain phase.
>Light 90 degrees out of phase from the filter is blocked completely.

The term "phase" has to do with the relationship of one light wave to
another in time, or equivalently in distance along the path of travel.  Two
light waves 180 degrees out of phase with each other will cancel each other
out.  (The picture I can't draw is of a sine wave and an upside-down sine
wave, adding together to a flat line with no wiggles.)  Most ordinary
light, even polarized light, is of random phase, so we don't see these
phase cancellation effects in ordinary life.  (The exception is
interference effects, like the irridescence of oil films and butterfly
wings, and the color of anti-reflection coatings, which are due to phase
cancellation between a two reflected copies of the same light wave, with
slightly different travel distances.)  However, lasers produce "coherent"
light, meaning it is all of the same wavelength and in phase with itself,
so we can see interference effects in laser light even over longer distances.

To get back to polarization: A light wave is made up of oscillating
electric and magnetic fields.  Both oscillate perpendicularly to the
direction of travel, and their oscillation directions are 90 degrees from
each other.  If the light is coming toward you, the electric field might be
oscillating up and down and the magnetic field left and right.  The
polarization of a light wave is the direction in which the electric field
of the light oscillates.  Ordinary light is a mixture of light waves of
varying polarizations, up-down, left-right, and angles in between.  A
polarizing filter will let through only the light oscillating in a certain
direction.  Light oscillating at 90 degrees to the polarization direction
is cut out completely, and light at other angles is attenuated because only
the component in the polarizing filter's direction is let through.

A common useful analogy is to imagine the light as the waves that travel
down a long rope, one end of which you have tied to a tree, while you shake
the other end back and forth.  You can shake it up and down, or left and
right, or at in-between angles.  A polarizing filter is like a picket fence
between you and the tree - only the up-and-down motion of the rope gets
through it.

(Incidentally, most other forms of wave motion can't be polarized.  For
example, sound is carried by the vibration of the air forward and backward
along the direction of motion, so there is no "perpendicular" vibration to
differentiate.  And ocean waves might be said to all be "polarized" up and
down; clearly water waves moving side-to-side don't exist.  However, some
types of seismic waves, where the vibration of the rock is side-to-side,
can be polarized.)

...
>This feature of polarizing lenses makes them useful as variable density
>filters.  Take TWO polaroid filters, and rotate one with respect to the
>other- the phase orientation of the filters will vary from completely in
>phase to completely out-of-phase, leading to variable transmission from 100%
>of the incident light (or nearly so) when the filters are in phase, to 0% of
>the incident light (or nearly so) when the filters are exactly out of phase.
>In practice, most polarizing filters I have seen also have some degree of a
>neutral density effect to them (I believe this is in addition to the
>polarizing effect, as polarizing itself doesn't cut out alot of light, but I
>may be wrong), so actual transmission at in-phase is less than 100%.

In fact, even a "perfect" polarizing filter will only transmit 50% of the
incident unpolarized light, because it absorbs the portion of the light
which is polarized in the 90-degree direction.  If you then put another
"perfect" polarizer on top of the first, all of the light coming through
the first will get through the second; but as you rotate one of the
filters, transmission will drop to 0% as you reach a 90 degree rotation.

Hope this is a clarification rather than an obfuscation.

--Spencer Roedder   roedder@roedder.com