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George wrote:

"If you look at a scene through a single polaroid, its brightess is reduced,
usually to about half the original, but it depends on how polarised the
light was in the original scene. Now add another similar polaroid. First
find the angle at which the two polarisation planes are crossed, by turning
one until you get blackout. Now turn one through 90 degrees, until they are
aligned, and are transnitting maximal light. Now remove one of the
polaroids. Does the brightness increase significantly when you do that? I
predict that there won't be a noticeable increase. Because the
second polaroid, when its axis is aligned with the first, didn't give rise
to a significant reduction in brightness, compared with what is seen through
a single polaroid, the light already being polarised in the right plane.
Bill may even be able to measure it with a light-meter. Of course, some
reduction, perhaps 10% or so, is expected, simply because any optical
component you put into a light path, even clear glass, loses some light by
surface reflections."

George

Sorry you do not endorse my paraphrase ;-) Googled filters today, and a
maker of fine optics, Schneider, used the same analogy (albeit a better
explanation--a picket fence:

http://www.schneideroptics.com/info/white_papers/true-pol.pdf

"HOW POLARIZERS WORK

Ed.  Rope hung from tree limb

Imagine that you could shake the rope in all directions at any given time,
and you can picture the behavior of unpolarized light. Now, picture that the
rope you are holding passes through a picket fence on its way to the tree.
This picket fence has slots that run in a vertical direction. If you now
shake the rope in all directions (up/down, side-to-side, in between) only
the vibrations that are parallel to the slots will pass through them. The
rope (light) vibrations from the side-to-side motion (horizontally polarized
light waves) will hit the fence slots and not pass through. However, the
vertically polarized light waves will pass through the fence, and are passed
on to the tree.

Light waves move and travel very similarly to the rope. If you have a
polarizing filter with many fence-like slots (called palings) and close
spaces between the palings, you could control (or we could say reject)
almost all light that is not parallel to the palings. If you had a filter
with few palings and large spaces between them, you can have partially
polarized light pass through along with the polarized light. That
would reject only a small amount of glare, and that glare would end up on
the film. The width and quality of the palings determines the quality and
performance of the filter."

As per your request, did a quick series of tests using a tripod mounted
Minolta digital flash meter, pointed at a flat white interior wall
illuminated by an incandescent bulb.

Baseline reading, no filter    f5.6  .9
With Vivitar 77mm filter       f4.0  .4
With Hoya 67mm filter          f4.0  .6
With Nikon 52mm filter         f4.0  .5
77mm and 67mm combined         f4.0  .0

Also tested using an Nikon F3 with 100mm lens.  Same results (but less
precise as I was reading f stops off the barrel.

Nominally 1.5 stops loss per filter, 2 stops with filters combined and
aligned.

Note: these are traditional, linear polarizing filters, not the "circular"
type designed for zoom/auto-focus lenses whose front element may rotated as
the lens is focused/zoomed.

I quickly reversed the order of the filters to see if that appreciably
affected the stacking loss. I did not.

The results are clearly well below my predicted addition of filter factors,
and above your 10% estimate.  Sorry about the fuzzy thinking on the affects
being additive--never had a reason two align filtered light sources and/or
lens filters.  That would sort of the defeat the purpose(s) of using the
filters in the first place. 

Questions that come to mind would include:

What affect will paling difference between manufactures have? (If the
pickets and spacing of the two "fences" are are not identical.)

Is the light coming from the first filter "totally" polarized?

Even if the light from the first filter is "totally" polarized, does it get
diffused kicking around between the facing filter surfaces?

What would be the result from two identical filters, placed surface to
surface, with palings aligned via microscope.

If 2 fences were not identical, or not perfectly aligned, could a rope that
made it through the first gap between the slats whap into a slat on the
second fence?

Beyond your transmission/reflectance observation, will placing slats and
openings by its very nature reduce transmission?  I am out of my depth on
this one, not knowing the scale of light waves vs. openings and spacing of
the openings.  Perhaps one of our physics mavens can address that?

Will try to do some daylight experiments tomorrow to move on the the total
loss by offsetting the filters by 90d.

Bill

   

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