What is the common characteristic of diamonds, water, glass, plastics,
the iris of the eye and other membranes, that make them transparent?
How can adding amendments to glass or plastic can make them
translucent or opaque?

When light interacts with matter, it can be reflected, absorbed,
scattered, or transmitted. An object is generally described as
"transparent" if a significant fraction of the incident light is
transmitted through the object. An object is considered "opaque" if
very little light is transmitted through it. And object is considered
"translucent" if some light passes through but not in a way that a
coherent image can be seen through it. Typically, this occurs if light
must take a circuitous path through the object, scattering from
embedded particles, defects or grain boundaries.

Thus, the common characteristic of diamonds, water, glass, plastics,
the iris of the eye and other membranes, that make them transparent is
that they (1) do not reflect much incoming light from their surfaces,
(2) do not absorb much of the light, and (3) are uniform enough not to
scatter much light.

In order to make glass or plastic opaque or translucent, you can alter
it in a number of different ways, all of which may be used
commercially for different applications. You can:

-coat it (paint it)
-roughen the surface
-crumble it or grind it (and sinter it back together) or introduce
bubbles
-fill it
-distort it

Whether the result is translucent or opaque depends on the details.
Very thin coatings may be transparent even when made of materials that
are opaque when thicker.

You can roughen a surface to create surface scattering. This is what
you get with "ground glass." Typically the net result is a translucent
object.

Similarly, disturbing the uniformity of a material will introduce
scattering centers throughout the material to make it translucent. You
can do this with glass or plastic by grinding it to a powder and
sintering it back together. You can do it with a liquid by filling it
with bubbles. Some materials are naturally translucent because they
have irregular grain structure or are irregular mixtures of two or
more materials.

A common way to alter the transparency of glass and plastic is to fill
it with a powder. Small amounts may impart color to a transparent
object (sunglasses, for example). Larger amounts of a light-colored
(often white) powder can make an object translucent. Larger amounts of
a colored or black filler can make an object opaque.

Finally, to make an object translucent, it may be sufficient to
introduce strain into the material by stretching or folding it. Many
plastics have significant changes in index of refraction when strained
which may be sufficient to cause significant light scattering.

For further information you can consult many reference sources in
optics, materials science and engineering related to specific
applications. A good starting point for a list of interesting
references from a variety of points of view can be found with the
following Google search:

Optics principles transparent opaque translucent
://www.google.com/search?q=Optics+principles+transparent+opaque+translucent

Dictionary.com
?Capable of transmitting light so that objects or images can be seen
as if there were no intervening material?

The common characteristic of diamonds, water, glass, plastics, the
iris of the eye and other membranes that make them transparent is
directly correlated to their purity of a substance that does not
absorb or reflect much light. With little or no air, debris, cracks,
blemishes, or any other kind of pollutants in diamonds, water, glass,
plastics or the iris of an eye light can pass through them with out
any hindrances. The light we see that passes through needs to pass
straight through the material with out reflecting, getting absorbed,
or being disbursed by anything in its way.

Adding amendments to glass or plastic can make them translucent or
opaque when the additions are robust enough to block out light,
reflect some colors and absorb others or just enough to bend the light
to prevent perception of distinct images.

How does light travel? (Good picture and commentary)
http://van.hep.uiuc.edu/van/qa/section/Light_and_Sound/Properties_of_Light/937167397.htm

Definition of light:
http://www.dictionary.com/search?q=light

Definition of opaque:
http://www.dictionary.com/search?q=opaque

Definition of translucent:
http://www.dictionary.com/search?q=Translucent%20

Definition of transparent:
http://www.dictionary.com/search?q=transparent

luckyluke-ga

Adding to the excellent answers/comments you have received so far,
molecular structure also determines the characteristics of
transparency, translucence, or opacity.  While diamonds are comprised
of carbon atoms, and polyethylene sheeting is comprised of carbon
atoms, the former is a crystalline structure which the latter is
mainly an amorphus structure. A crystalline structure versus an
amorphus one is depicted at:
        http://matse1.mse.uiuc.edu/~tw/ceramics/prin.html

As is often the case, the definitions for crystalline and amorphus are
blurred (sic)....Do the answer and comments help your understanding of
transparency??

The reason that some materials are transparent is maybe because the
photons don't hit the atoms (and/or ions).

Dear elvira6-ga, 

by asking "What is the common characteristic of diamonds, water,
glass, plastics, the iris of the eye and other membranes, that make
them transparent?" you might have meant why are some materials
transparent.

I was thinking aloud on the earlier comment before searching the web,
but here's the answer:

"The clear piece of glass is transparent to visible light because the
available electrons in the material which could absorb the visible
photons have no available energy levels above them in the range of the
quantum energies of visible photons. The glass atoms do have
vibrational energy modes which can absorb infrared photons, so the
glass is not transparent in the infrared."

http://hyperphysics.phy-astr.gsu.edu/hbase/mod4.html

You mentioned transparency in the eye. I read a fascinating article
at:

http://news.independent.co.uk/world/science_medical/story.jsp?story=303839

which reports on some of the first concrete explanations as to why the
eye is transparent.

The cornea of the eye is made up of long collagen protein molecules,
which just about everywhere else appear <i>opaque</i>. Apparently
scientists are only now discovering why the cornea in fact appears
transparent, with the use of X-ray diffraction.

While the proteins in the sclera (or "white") of the eye are arranged
in a rather random fashion, those over the cornea are in fact aligned
in long parallel lines, thus forming a diffraction grating, where the
grating spacing is precisely controlled by other molecules
(proteoglycans) in-between. Light passing through different parts of
the grating (the proteins are about 30nm in width, with 60nm spacing)
interferes. With this spacing, about 96% of visible light passes
through in the straight-ahead direction, making the cornea appear
transparent. This explanation is now helping researchers understand
certain diseases and degenerative conditions with symptoms of haziness
or opacity over the cornea.

Pretty spiffy, I think.

Cheers,
-beckett-ga