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Question: How smooth must a surface be to produce specular reflection, and do Lunar boot prints meet this standard?

A recent post on Space Exploration asked why footprints on the moon displayed specular reflection. https://space.stackexchange.com/questions/64682/why-do-the-bootprints-on-the-moon-appear-bright-in-some-photographs-or-film

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Surfaces displaying specular reflection are (supposedly) flat to within a fraction of the wavelength being reflected. Visible light has a wavelength of about 0.7 microns, but grains of regolith have a size of roughly 70 microns.

Do boot prints reduce the size of regolith a hundred-fold, or is there more to the specular reflection than the wavelength rule?

Even dry asphalt produces specular relections. Asphalt is obviously not smooth to within 0.7 microns. This effect is prominent enough that computer modeling for PBR imaging takes it into account.

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  • $\begingroup$ Please clarify what “wavelength rule” you’re referring to. $\endgroup$ Nov 8, 2023 at 4:39
  • $\begingroup$ "wavelength rule" = for specular reflection, the surface smoothness must be smaller than the reflected wavelength $\endgroup$
    – Woody
    Nov 8, 2023 at 4:42

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While the surface as a whole might have large-scale roughness, it's possible for small facets to be smooth enough for specular reflections. In rougher materials, these facets point with larger slopes in random directions, so only certain facets will reflect into your eye. But as these facets get bigger and more aligned (e.g. by polishing), you approach a mirror finish.

This approach is called a microfacet model, and there is a lot of literature on it since it is so important for computer graphics rendering. Each model has a way to treat the distribution of the facets and what happens with light as it interacts with the facets.

And not all materials show much specular reflection; compare with the Oren-Nayar model, one basis for realistic diffuse reflections.

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A rough metal surface looks grey. If you polish it, the reflection gets more and more mirror like. It isn't an all or nothing proposition.

The asphalt photo shows a rough mirror image of the sun. But it isn't anything like a reflection from a smooth mirror.

Various online videos show polishing steel with successively finer grits of sandpaper. You can see a mirror like reflection emerge. Here are a couple. How to Sand And Polish Stainless Steel to Mirror Finish, Easy Mirror Polish On Steel! You can see a fairly mirror like image emerge from even 220 grit sandpaper. The scratches are far rougher than a wavelength of light.

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