Message-Id: <3.0.32.19970329130241.006c1cc4@icefog.polarnet.com>
Date: Sat, 29 Mar 1997 13:05:05 -0900
To: pinhole@exploratorium.edu
From: "J. Lahr" <jlahr@polarnet.com>
Subject: Polarizing filters
Understanding the effect that the addition of polarizing filters between
two that are oriented at right angles has requires a an understanding of
vectors, as Paul D. pointed out. If a polarizer worked by totally blocking
all but the component of incident light that was perfectly aligned with
the filter, then only a negligible amount of unpolarized light would make
it through a single filter and no light would make it through two filters
unless they were perfectly aligned. This is slowly sinking into my brain.
It's interesting to consider placing n filters between two with 90 degree
rotation. For example, for n = 2, each would be rotated 30 degrees from
the previous filter (90 divided by n+1). For "perfect" polarizers it
works out that the larger the value of n the more light exits the final
filter. The equation I derived is:
F = [cos(90/(n+1))] ** (n+1) (The first term raised to the n+1 power)
where F is the fraction of light that makes it through the first filter
that also makes it through the final filter. A few values of F are:
n F
0 0.0
1 .5
2 .65
3 .73
10 .89
I would guess that real polarizing filters reduce the amount of light
with all polarizations by some amount, and that this added reduction
would prevent more and more filters from actually increasing the light
output.
Hope I've got this right. If not, Paul D., please let me know where
I've gone off the track!
JCLahr
***************************************
* John C. and Jan H. Lahr *
* jlahr@polarnet.com *
* P.O. Box 83245, Fairbanks, AK 99708 *
* (907) 474-7997 *
* http://www2.polarnet.com/~lahr *
* http://giseis.alaska.edu/Input/lahr *
***************************************