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Say you have a piece of glass, which looks specular if propery cut/polished. But if you sand the surface using say sand paper, it will look hazy and glossy. I'm wondering how much surface roughness (10nm, 100nm, 1um?) approximately is needed to make the surface non-specular.

I guess this is material dependent, since reflectance and transmittance also are. But I'm only looking for a rough estimate at this point.

Any useful paper references would also be appreciated.

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The rule of thumb is that optical effects appear when the roughness is comparable to the wavelength of light -- a few hundred nanometers. For roughness far below a few hundred nanometers, it should still look specular. Far above a few hundred nanometers, it should look rough.

Well, like other "rules of thumb" in physics, this may be off by as much as a factor of ten. So maybe someone else will offer a more accurate answer.

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This video describes the process of polishing glass and tells the grit sizes for each step. Grinding and polishing glass with diamond disks.

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I have found a publication here dealing not with glass, but with PP. Nonetheless they mention a rough scale (no pun intended) estimate in the abstract (emphasis added).

The effect of thermal history on the transparency of biaxially-oriented polypropylene (BOPP) films was investigated. Compression molded sheets prepared with different cooling rates were biaxially oriented at several temperatures. Correlations were sought between the light transmission measured at 633 nm and the surface roughness as characterized by atomic force microscopy. It was determined that surface roughness on the 100-$\mu\textrm{m}$ size scale was responsible for a loss in transparency. Surface roughness on the submicron size scale did not affect the transparency. The clearest films were obtained from compression molded sheets with the most homogeneous texture and by orienting at the lowest temperature. POLYM. ENG. SCI., 47:1658–1665, 2007. ª 2007 Society of Plastics Engineers

According to their research, the main thing you want to do when you have a hazy surface is to grind the rough spots down to a sub-micron scale.

It's an interesting read and I think even some of the other results may be applicable to glass, since both glass and PP undergo some thermal processing.

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