Re: how do you make WHITE?

["John S. Denker" <jsd@MONMOUTH.COM>]

At 05:21 PM 3/6/99 -0500, Donald wrote:
> Why can the transmission of light (intensity) be greater through
> oil-soaked paper than through the same paper dry? Pioneer settlers in the
> midwest were said to use oil or lard-soaked paper sheets as windows, they
> shed rain, blocked the wind, but also transmitted light.

That's a good one.  Actually, let's start by addressing the exact opposite
question:

Given a white piece of paper with a translucent oil spot on it, the most
important thing is to understand why the paper is white!  Once you
understand that, the other question is easy.

What is the definition of white?  What is the physics of white?  How do you
make white?

Let's start with something that isn't white.  A piece of quartz is highly
transparent.  It does not absorb light.  It does have an index of
refraction.   A light beam will partially reflect off the air/quartz
interface due to the index mismatch. If you take a zillion identical small
quartz spheres and arrange them in a regular lattice like a crystal, you
might think that all those little reflections would add up to make
something quite non-transparent, but in fact a funny thing happens.  If the
lattice really is perfect, the scattering is coherent.  The coherent
forward scattering reconstructs the incoming wave perfectly, making the
lattice transparent (although it has a refractive index of its own).  You
can visualize this in terms of the Huygens construction if you want.  For
more on this see _The Feynman Lectures on Physics_ volume III chapter 13,
or any solid-state physics text.

Now let's see what happens if the array isn't quite perfect.  If the
locations are exact, but the scattering parameters (e.g. size) is variable
from site to site, then we get Mott localization.  If the sizes are uniform
but the locations are randomized, we get Anderson localization.  We still
have forward scattering, but it is no longer coherent forward scattering.
If you try to do a Huygens construction but randomize the phases of the
contributions, you get nothing.  More quantitatively, the forward wave is
exponentially attenuated with a length scale that depends on the amount of
random scattering.

So what happens to all the light that can't go forward, and can't be
absorbed?  It rattles around for a while and then gets tossed out the front
surface of our lattice of scatterers.  The outgoing light has a wide
distribution of angles.  Our lattice looks white.

It should be emphasized that the individual fibers in a piece of paper are
not white.  They are beautifully transparent.  It is only a moderately
thick collection of randomly-arranged fibers that is white.

Note that you cannot make paper (or paint) that is really thin and really
white.

We are now in a position answer the original questions:

> blocked the wind

Paper is strong.  It holds the oil in place.

> shed rain

Oil is hydrophobic and insoluble.  It protects the paper from the water.

> transmitted light

Oil permeates the pores of the paper and *index matches* to the cellulose.
We no longer have a random array of index-changes.  We a thin sheet of
relatively uniform index, and the light just waltzes through.

You don't get perfect transparency for various reasons:  (1) Typical oil
isn't a perfect match for cellulose.  (2) Typical paper contains not just
cellulose but other junk.  If you match to one, you can't match to the
other. (3) What's worse is that the cellulose fibers are *hollow* and
you'll never get oil into the cores.  Therefore there will always be some
scattering off the cores.  If we could lay hands on some paper made of
randomly-arranged solid fibers (such as rayon, which is solid cellulose), I
predict the oil-spot effect would be really spectacular.

One final remark:  this business about localization can be applied to
electron wavefunctions as well as to light waves.  This is the key to
understanding how/why a real practical insulator is totally different from
the hogwash explanation (large-gap semiconductor) given in almost all
solid-state physics books.  A large-gap semiconductor should be called
merely a semi-non-conductor, since it cannot be used as a practical
insulator.  It will not immobilize any charge injected onto or into it.  To
do that, you need localization of the electron wavefunction.

Cheers --- jsd