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Bill quoted an analogy between polarised light rays and a vibrating rope. Such notions are all right
(indeed, can be valuable) in their way, but can not pe expected to predict details which apply only
to a vibrating light beam and not to a vibrating rope.-

He added-
|
| 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

That last observation is  bit of a surprise to me. And what does the second figure represent, that
follows the f-number?  I would have expected the two polaroids combined (and aligned) to let through
a bit less light than a single polaroid does, simply because of surface reflections and
imperfections in the transmission. But I thank Bill for confirming the point that I was trying to
make, in numerical terms. |

|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.

To me, that seems a very reasonable result, though I can't quite see how it follows from the quoted
observations.

Accepting its truth, one could conclude-

Reduction due to applying a perfect polariser to unpolarised light - 1 stop (as it should be
theoretically).
Additional light loss due to passage of polarised light through a perfect aligned polariser - 0
stop.
Additional light loss at each passage through a real polarising filter, due to its imperfections -
0.5 stop.

==========================

| 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. 

The 10% figure, for light absorption that was additional to polarisation loss, was no more than my
order-of-magnitude guess. , and has little bearing on my conclusion, which was this: That inserting
one polaroid reduces brightness to rather less than 50% (if no initial polarisation), and that
adding further aligned polaroids does not significantly reduce brightness much further. I am glad
that Bill now concurs with that notion.

| 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.)

Because they don't work in terms of pickets and fences, the question doesn't really apply. Perhaps a
lower-quality filter may have a worse value for attenuation of the aligned component of the light
(which I had guessed to be about 10%, perhaps wrongly.) But I would not expect to see great
differences between similar products. It's an established technology now. The pickets and fences
that Bill refers to are carefully-aligned crystalline materials embedded in the film (I think)
|
| Is the light coming from the first filter "totally" polarized?

Remarkably well polarised. Few photons remain that are aligned in the "other" direction. They are
the ones that get throgh a second "crossed" polaroid, so that it's not quite completely black, but
is very nearly so.

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

Not significantly. You could shine light through the first polaroid on a sheet of white paper, which
will diffuse the polarisation, and look at the result through the second polaroid, and I predict you
won't then get extinction of that diffused light by twisting it. You would, I think, if you tried
reflecting the light with a mirror, instead..

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

Just the same as a single polaroid filter. Especially if you were to reduce surface reflections,
using Canada balsam or a modern equivalent, between them, to reduce incidental light loss..
|
| 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?
|

Again, Bill is pushing his analogy too hard.

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

Later, Bill added-

"Tried your method on a professional light table, thinking the angle of the
incandescent lighting might have partially polarized the light.  Same
results. 1.5 and 2. "

=============

Ken Muldrew's pushed a nice stick-between-the-spokes, about Bill's homepun analogy, writing-

"If you have 3 polarizers you can easily see how the picket fence analogy
fails. Simply line up 2 filters with a space between them. Rotate one until you
get maximum darkening (here the axes of polarization are at 90? to each
other). Now insert the 3rd polarizer in between the other two. Suddenly light
passes through all three! How could the middle polarizer change the
orientation of the other two "picket fences"?"

I hope that has made everyone think, and reach for old sunglasses.
And indeed, there is much fun to be had between a pair of crossed polaroids.

If you put between them a small square fishtank-like glass or plastic, with a path of a few inches,
and top it up with water, you see no effect. But now stir in a good amount of cane sugar, and now
light passes. You can kill that passing light by rotating one of the polaroids, appropriately.
That's because the sugar (dextrose), rotates the plane of polarisation, in a right-handed way, which
is why it's called dextrose. There's another version of that sugar (laevulose) which is chemically
identical, but shifts polarisation the opposite way, because its molecule is twisted into the
mirror-image opposite of the first.

Or, put a thick slab of perspex between the polaroids, and apply a G-clamp to squeeze between the
edges of the slab, across the diection of the light. Now you see light fringes, corresponding to the
stresses in the perspex. This is a technique that has been used in structural engineering, using
perspex models.

If I've got the above a bit wrong, please go easy on me. It's not "my subject", and I'm dredging
back into memories of 60 years ago.

And it's got nothing at all to do with navigation. Sorry about that.

George.

   

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