The question was asked:
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? Why are clouds white? Why is the white screen in a movie theater proverbially called the Silver Screen?
Let’s start with something that isn’t white. A piece of pure crystalline 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.
If, however, the lattice is not quite perfect, an interesting thing happens, called localization. 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. See reference 1 . 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 about pioneer windows:
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 it is nearly impossible to 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.
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.
Physically, an undoped semiconductor is like a vacuum. If you inject some charge into a vacuum, it looks like an excellent conductor. In the absence of injected charge, it looks like an insulator. If you try to measure “the” conductivity of a given semiconductor, the results will vary over many many orders of magnitude, depending on whether there is a source of free charge. With semiconductors (as with so many other things in life) it is better to describe what they are doing, rather than to categorize what they “are”. It is not helpful to say semiconductors “are” conductors or “are” insulators. Instead, it is better to recognize that a given semiconductor might be conducting (at the moment) or might be insulating (at the moment).
In some tightly controlled applications, such as within an integrated circuti chip, it is possible to make conductors out of semiconductors, and to make insulators out of semiconductors (or out of the boundaries between semiconductors). In other applications, such as insulating a household extension cord, semiconductors would be quite unsuitable.
The size of the gap (relative to kT) is relevant if you’re trying to build a minority-carrier device, such as a bipolar junction transistor, but it is quite irrelevant for majority-carrier devices such as field-effect transistors. I’ve built FET circuits that work just fine at cryogenic temperatures. The fact that the gap was huuuge compared to kT did not turn the device into an insulator.
Whether you have an efficient means for injecting charge depends on details. A sharp point is known to be good for injecting charge into a vacuum with very modest driving voltage. This is called field emission. (In air as opposed to vacuum, the same geometry produces corona, with slightly different physics.) Every VLSI chip has multi-millions of ohmic contacts. Making them is a bit of a black art, but I conjecture that the physics is roughly analogous to a field-emission point.
Practical insulators contain traps which immobilize injected charge.