I'm in need of the range of percentage of light passing through a
substance defining a substance as translucent and the same for
transparent, so that I can show the difference between translucent and
transparent mathematically.   Or, if there's some other mathematical
way of differentiating the two, like "over "x" index of refraction is
...."

comment by kottekoe-ga is correct in explaining that

 "Translucent materials  prevent the images from being transmitted" 
 
 nevertheless does no give you  mathematical description, which exists
 on several levels, from simple to complex description. So, only question is
 mathematical you want to get.

 On simple level, (lack of) transparency is described by COEFFICIENT OF ABSORPTION,
 usually called alpha:

http://www.its.bldrdoc.gov/fs-1037/dir-001/_0086.htm
http://www.photonics.com/dictionary/lookup/XQ/ASP/url.lookup/entrynum.28/letter.a/pu./QX/lookup.htm
http://www.schorsch.com/kbase/glossary/absorption.html

 For simplicity, people assume (orthogonal incidence) meaning light enters 
head on, and some emerges IN THE SAME direction.  Ration is t - transmittance.


Materials which is translucent is more complex. It scatters light, so that light
emerges in several directions - forming so called Tyndall Cone, which you see 
when you turn on headlights in a fog. Rate of spreading is defined by a 
SCATTERING COEFFICIENT
http://www.universityscience.ie/pages/scientists/sci_johntyndall.php




Of course, in the really light, both effects exist together, and can
be combined with
polarization effects (some materials will rotate plane of
polarization, some will depolarize light..)

 http://www.columbia.edu/~ahh2004/projects/diagnostics/polarization/page1.html

and it can get complex
http://www.marine.maine.edu/~eboss/manuscripts/Boss_and_Pegau2001AO/Bossand
Pegau2001.pdf

but there is a limit. Most complex things which happens when light passes through
materials are described by a 4 by 4 matrix called Mueller Matrix
http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-26-6530

Here is a simple description.
http://www.answers.com/topic/rayleigh-scattering

So, depending on what your application requires, you can stick just
with two numbers,
or go whole hog to 16.

Absorption can be represented by complex (as in complex number) part
of the refraction index,
other depends on anisotropy (n becomes a matrix) or non-local
properties of n (as in fog,
where water and air have different n).


Hedgie

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Clarification of Answer by hedgie-ga on 29 Apr 2005 06:27 PDT

I want to add one more reference - a technical paper
 (which may be unnecessarily complex for your needs)
 but which measures both - absorption and scatering,
present together. 

Fig 2 and Fig 3 show the effect of changes in these two numbers.

Paper may be interesting, since it suggest a practical way how to characterise
such materials - by  transmitting a 'standard image' and than compare 
1) contrast  2) intensity (darkness) of the transmitted image.

Both effects will eventually prevent image from being transmitted, but
differently (either 'smeared', or 'too weak')
Right?

H.

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Request for Answer Clarification by chickencooker-ga on 29 Apr 2005 09:52 PDT

Thank you for having taken the time to answer my question.  You input
is very much appreciated.  One simple difference in transparent &
translucent will do just fine, and I think angle of emergence will do
very well,....so I just want to make sure I understand you.  Would it
be relatively safe to say that a transparent substance has roughly
zero degrees change in the direction of the path of light through
it.... vs. translucent which scatters the light to many degrees of
scattering (including zero degrees change) to a maximum of whatever
degrees wide the Tyndall Cone is?

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Clarification of Answer by hedgie-ga on 29 Apr 2005 17:03 PDT

You are welcome.

" zero degrees change in the direction .."

is correct - but for normal incidence only
http://www.glossary.oilfield.slb.com/Display.cfm?Term=angle%20of%20incidence


In the plain refraction, as described here e.g.

http://www.ps.missouri.edu/rickspage/refract/refraction.html

Light ray which enteres at an angle (not 90 degree = not normal) will change
direction - but only one (or two) rays emerge - so there his no scattering.

In case of scattering, light emerges in many different directions, all  rays
forming a cone.

I am surprized I cannot find a decent image of the effect on the web.

There is an image here 
http://www.galenotech.org/colloidi.htm
but text is in italian

There are some more pictures here:

http://images.google.com/images?hl=en&lr=lang_en&ie=ISO-8859-1&q=Tyndall+effect&btnG=Search

You can find more info under the 
SEARCH TERM: Tyndall effect

e.g.

://www.google.com/search?q=Tyndall+effect&hl=en&lr=lang_en&ie=UTF-8&start=10&sa=N


Hedgie

The difference between translucency and transparency is not determined
by the amount of light that is transmitted. Transparent objects
transmit light in such a way that images of objects are preserved.
Translucent objects diffuse and/or distort the light sufficiently to
prevent the images from being transmitted. There is no precise
mathematical distinction. If you slowly etch the surface of a window,
the image of something behind it will become less and less distinct.