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Sunlight strikes a mirror at a 45 degree angle. The vast majority of light will be reflected about the normal. Some light will be absorbed by the mirror. Some light will be transmitted through the mirror. And some light will be scattered in all directions. For a very smooth mirror, designed to minimize such scattering in the visible spectrum, approximately what percentage of the incoming visible light would be scattered?

Basically I'm wondering if a mirror could be "blacker than black" - if you shine a flashlight on an angled mirror in otherwise total darkness, could you have a mirror that scatters less light back at you than a material like Vantablack does?

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  • $\begingroup$ Mirrors have edges. This is where you always see scattering even if everything else is perfect $\endgroup$
    – fraxinus
    Commented Jun 8 at 13:46
  • $\begingroup$ Even if you could make such a mirror, wouldn't light normally reflected from the mirror scatter off the surface of the flashlight at various angles, and then some of it reflect off the mirror again, so it would look similar to the situation in which the mirror did scatter some light? (In a dark room, this effect would probably be visible). $\endgroup$
    – Obie 2.0
    Commented Jun 10 at 7:07
  • $\begingroup$ @Obie2.0 I don't quite follow. The mirror is at a 45 degree angle so if the mirror is perfect, the light hitting it will make a 90 degree turn and not return to the flashlight. $\endgroup$
    – causative
    Commented Jun 10 at 7:13
  • $\begingroup$ I was thinking of a flashlight beam normally incident on the mirror. $\endgroup$
    – Obie 2.0
    Commented Jun 10 at 14:41

2 Answers 2

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People who make gravitational wave detectors have to care about this.

According to one paper [1]:

Various measurements indicate that the total loss in the initial LIGO arm is around 150ppm per arm or 75ppm per mirror [1,2] with an uncertainty of around 15ppm. Out of these 75ppm loss per mirror, 20-30ppm can be explained by the scattering loss due to mirror surface errors with spatial wavelength > a few millimeters [2]. Other losses, including transmission of ETM (7ppm/2), the absorption loss (4ppm) and diffractive loss (1-2ppm), account for around 9ppm. The loss due to microroughness was originally estimated to be 4.6ppm, based on microroughness data from the substrate polisher (CSIRO). The source of the remaining loss of 30-40ppm is unknown.

The punch line of the paper is that the microroughness loss was originally mismeasured, and is actually 20 ppm, not the originally measured 5 ppm.

Adding together the "microroughness" loss of 20 ppm and the "scattering" loss of 20-30 ppm gives 40-50 ppm of light going the wrong way. This paper is from 2007 and maybe the figures have been brought down by now, or maybe some of the remaining unknown loss is also scattering of some kind. Nevertheless, 50 ppm seems like a reasonable ballpark figure for scattering from the world's best mirrors.

According the manufacturer, Vantablack absorbs up to 99.964% of incident light, depending on wavelength and conditions; presumably the remaining 360 ppm is scattered. [2] So it does seem like a LIGO-quality mirror scatters less light [3] than Vantablack does.

[1] Yamamoto, "LIGO I mirror scattering loss by microroughness," 2007

[2] https://www.surreynanosystems.com/assets/media/vantablack-vb-a4-data-brochure-2016.pdf. This brochure contains contradictory claims; the Key Features section quotes 0.036% total hemispherical reflectance at 700 nm, but the Typical Performance Data table claims a significantly larger value of 0.1% at the same wavelength. I used the better number. Note also that performance is worse at a 45 degree angle of incidence.

[3] Note that LIGO operates in the infrared at 1064 nm range, while Vantablack's claimed performance is best at 700 nm. These are not really that far apart, though.

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A crude model gives the following formula for light scattering losses $L$ as a function of the wavelength $\lambda$ of light and the RMS surface roughness $\sigma$:

$$ L = \left(\frac{4\pi \sigma}{\lambda}\right)^2 $$

J. M. Bennett, Recent developments in surface roughness characterization", Measurement Science and Technology, 3, 1119 (1992)

The best state-of-the-art mirror polishing techniques can give $\sigma \approx 1\:Å$. For visible wavelengths $\lambda \approx 500 \text{ nm}$ this gives $$ L \approx 6.3 \text{ ppm} $$

Note that typical mirrors will have much more surface roughness and correspondingly higher scattering losses.

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