My understanding is that all specular reflection is due to Fresnel reflection at the interface which is a broadband effect.

A classic example might be a white reflection on a polished ball (e.g. pool ball, or apple, etc.). The highlight is almost always white since it is a broadband reflection of the light source, regardless of the colour of the ball. The pigment or colour of the object plays no role in the specular highlight.....

The diffuse reflection of the object can have colour since this is due to absorption of the pigment in the object.

So what about metals? For example, a polished gold sphere. Is the specular highlight white or gold in colour?

  • $\begingroup$ It's goldish. FWIW, 3D rendering programs give you a parameter to control the amount that surface colour affects highlights and reflections. The larger the contribution that the surface colour makes, the more metallic the object looks. $\endgroup$ – PM 2Ring Jun 17 at 3:50
  • $\begingroup$ I think the specular reflection of white light from a red apple is an even more interesting question! $\endgroup$ – uhoh Jun 18 at 0:34

Yes, specular reflection from polished gold is gold colored. Due to the interband transition in gold, green and blue light gets strongly absorbed, biasing the reflected spectrum toward yellow and red. This has nothing to do with diffuse scattering. If you look at a polished gold mirror (of which there are many in my lab), the image you see of objects illuminated by white room light is colored gold.

Highlights that you might see reflected from dielectrics are white because dielectrics are relatively dispersionless (i.e. the refractive index is more-or-less independent of color) throughout the visible range. Gold is decidedly not dispersionless in the visible.

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    $\begingroup$ FWIW, apparently, white light transmitted through gold leaf is greenish, although I've never had the opportunity to observe it myself. $\endgroup$ – PM 2Ring Jun 17 at 5:08
  • $\begingroup$ @PM2Ring It turns out that thin film effects can manifest in unexpected ways for ultrathin absorbers. Check out, e.g. newatlas.com/harvard-metal-film-color/35350 $\endgroup$ – Gilbert Jun 17 at 14:03
  • $\begingroup$ From a physics standpoint, the light is biased towards gold, but physiologically the light is largely the same, as one's brain will compensate to bring the color balance back. $\endgroup$ – Acccumulation Jun 17 at 20:34
  • $\begingroup$ So the Fresnel reflection is still there, but it's magnitude varies substantially due to the spectral variation in refractive index of gold over the visible range. For example, at the extremes gold has refractive index of 1.46 at 380nm, but 0.15 at 780nm meaning the reflected intensity varies between 3.5% and 56% for these wavelengths respectively [link] (refractiveindex.info/?shelf=main&book=Au&page=Johnson) [link] (hyperphysics.phy-astr.gsu.edu/hbase/phyopt/polar.html#c2) So the Fresnel reflection is still there, and is broadband, but biased strongly towards the green and red? $\endgroup$ – Duncan Galbraith Jun 17 at 21:27
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    $\begingroup$ @DuncanGalbraith correct. But don’t disregard the imaginary part of the refractive index for a metal; that’s the dominant component! $\endgroup$ – Gilbert Jun 17 at 21:35

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