What determines how transparent a material is? Every time light hits a material, both reflection and refraction occurs. How does a material determine how much light gets reflected/ refracted e.g. glass vs silver? So far what I could find is light gets scattered by atoms in the material in all directions, but they all cancel out except in these 2 directions. But that does not explain the different degrees of reflection and refraction.
 A: Classical light is the super position of zillions of photons with the energy of $hν$, mathematically this means their wave functions are added to create light and the images carried by its variations.
Lets take glass:
In order for the material to be transparent, it means that the image information carried by the superposition goes through carrying the same phases and energy photons, so that the colors and shapes pass through unchanged. This means that the photons should scatter elastically with the whole solid state crystal lattice that composes the glass. i.e. individual wave function solutions are photon +lattice elastic scattering.
There are variations on this, from color material, which absorbs some frequency photons and leaves others to scatter thus changing the balance, to opaque which do not carry images through but light goes through in a combination of absorption and reemission scaters. Completely opaque materials absorb all the photons, or reflect them, the energy turning into lattice vibrations and in the end macroscopically heat.
The same goes for reflection, for glass the elastic scattering in the back direction generates reflection. For a silver backed mirror the reflection is elastic scattering of photons at the first atomic level of the silver lattice, but the forward part is absorbed into lattice vibrations.
A: I believe your question has basically two main parts:


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*why does a material let light through, that is translucent, which is more then just transparent. Transparent materials are not only translucent, but they have a single index of refraction throughout the material



Translucency (also called translucence or translucidity) allows light to pass through, but does not necessarily (again, on the macroscopic scale) follow Snell's law; the photons can be scattered at either of the two interfaces, or internally, where there is a change in index of refraction. In other words, a translucent material is made up of components with different indices of refraction. A transparent material is made up of components with a uniform index of refraction.1 Transparent materials appear clear, with the overall appearance of one color, or any combination leading up to a brilliant spectrum of every color. The opposite property of translucency is opacity.

Basically this part of your question is about the material being translucent or opaque. The answer to this question is that the photons as they interact with the material, can either be:


*

*reflected, that is, if a material reflects most of the incident photons, like metals, or shiny materials, 

*refracted, that is certain materials refract most of the photons, like glass, certain plastics, crystals, water etc.

*absorbed (heating up the material)
Now it is very important to understand that all three happen with all materials, and it is all probabilities. Metals reflect most of the photons, and will only refract very little number of photons, and absorb some (that will heat up the material).
Glass does both, refracts most photons, and reflects some, and absorbs some too. If you see a glass window, you can see through, and a reflection too, and some will heat up the glass too.
You are asking how a material decides how much of these photons will be either reflected or refracted or absorbed. The answer is that this is a QM process, and the structure of the material's atoms and molecules decides the interaction, and the ratios.
https://en.wikipedia.org/wiki/Transparency_and_translucency


*and in certain cases, why is this refraction through the material so that it keeps images recognizable (like glass)


This question is answered in the other answer, and that is elastic scattering, throughout the material, as photons refract, if this refraction keeps the relative energy level of the photons, and the relative angle, and phase, then the material will be able to transfer a recognizable image, like certain glasses. 
It is very important to understand that certain materials are translucent, will let light through, or even transparent, having a single index of refraction throughout the material, but they will still not be able to transfer a recognizable image. This is because the structure of the material is so, that the photons' relative energy levels, relative angle, or phase will not be kept. There are certain crystals like that, certain plastics etc.

If you look through certain materials (crystals, plastics), you see they let light through, but the images are not recignizable, because the photons relative energy levels, angle and phase is not kept.
