The wavelength of visible light is between one-half and one micron; it’s convenient to treat it…

The wavelength of visible light is between one-half and one micron; it’s convenient to treat it as about one micron for back-of-the-envelope estimation. To prevent diffraction effects from being significant, microfacets should be at least a couple of wavelengths (say, five) in their minimum dimension. In a surface that’s fairly flat (most microfacets have slope less than 45◦), we can imagine each microfacet is a small disk or square, so its projected length, in any direction, is at least .71 ≈ cos(45◦) times its minimum dimension.

(a) Approximately how many such microfacets can fit into a 1 mm-diameter disk?

(b) If you had that many small mirrorlike facets in such a disk and illuminated them with a laser pointer whose beam covered just that disk, what would the pattern of reflected light look like? Get a laser pointer, a piece of polished metal, and a piece of white paper to “catch” the outgoing light and see whether the reflected light follows the predicted pattern.

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