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Bill wrote, about an experiment to determine loss of light from use of one
then two combined polarizing filters:

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

Along the way to testing this for myself, one practical problem was
immediately apparent when 3 polarizing filters were laid side by side on a
lightbox (a sheet of well-lit white paper will do):

3 filters from different manufacturers; 3 different densities

(the colour varies too; they certainly can't all be neutral, although this
is another issue).

The other thing that was apparent was that the density of each, while
obviously not identical, looked as though it was in the order of an f/ stop
or two. Laying one half of a filter over another, aligned for maximum light
transmission, lead to a darkening of the combination of about another f/
stop, judged by eye.

The next step was to measure the loss of light passed by one, then two of
them together, using a light meter. While the precise results varied
according to which two were combined (or not) the broad result, or the
result rounded to the nearest f/stop were:
one alone: about 2 f/ stops
two aligned for max. transmission: about 3 f/ stops.

Which is interesting. Similar, while not identical to Bill's results.
What I think is that apart from the polarizing effect there is a muddying
effect due to the (variable) densities of each filter. If there was such a
thing as a polarizing filter without density these effects could perhaps be
measured more accurately.

Then Ken Muldrew wrote:
'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"?'

This is indeed true, and wondrously strange ..
As Professor Julius Sumner Miller used to say:

"Why is it so?"

   

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